Elastic dipoles of point defects from atomistic simulations

NASA Astrophysics Data System (ADS)

Varvenne, Céline; Clouet, Emmanuel

2017-12-01

The interaction of point defects with an external stress field or with other structural defects is usually well described within continuum elasticity by the elastic dipole approximation. Extraction of the elastic dipoles from atomistic simulations is therefore a fundamental step to connect an atomistic description of the defect with continuum models. This can be done either by a fitting of the point-defect displacement field, by a summation of the Kanzaki forces, or by a linking equation to the residual stress. We perform here a detailed comparison of these different available methods to extract elastic dipoles, and show that they all lead to the same values when the supercell of the atomistic simulations is large enough and when the anharmonic region around the point defect is correctly handled. But, for small simulation cells compatible with ab initio calculations, only the definition through the residual stress appears tractable. The approach is illustrated by considering various point defects (vacancy, self-interstitial, and hydrogen solute atom) in zirconium, using both empirical potentials and ab initio calculations.

Finite Element Modeling of the Deformation of a Thin Magnetoelastic Film Compared to a Membrane Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barham, M; White, D; Steigmann, D

2009-04-08

Recently a new class of biocompatible elastic polymers loaded with small ferrous particles (magnetoelastomer) was developed at Lawrence Livermore National Laboratory. This new material was formed as a thin film using spin casting. The deformation of this material using a magnetic field has many possible applications to microfluidics. Two methods will be used to calculate the deformation of a circular magneto-elastomeric film subjected to a magnetic field. The first method is an arbitrary Lagrangian-Eulerian (ALE) finite element method (FEM) and the second is based on nonlinear continuum electromagnetism and continuum elasticity in the membrane limit. The comparison of these twomore » methods is used to test/validate the finite element method.« less

Mass-stiffness substructuring of an elastic metasurface for full transmission beam steering

NASA Astrophysics Data System (ADS)

Lee, Hyuk; Lee, Jun Kyu; Seung, Hong Min; Kim, Yoon Young

2018-03-01

The metasurface concept has a significant potential due to its novel wavefront-shaping functionalities that can be critically useful for ultrasonic and solid wave-based applications. To achieve the desired functionalities, elastic metasurfaces should cover full 2π phase shift and also acquire full transmission within subwavelength scale. However, they have not been explored much with respect to the elastic regime, because the intrinsic proportionality of mass-stiffness within the continuum elastic media causes an inevitable trade-off between abrupt phase shift and sufficient transmission. Our goal is to engineer an elastic metasurface that can realize an inverse relation between (amplified) effective mass and (weakened) stiffness in order to satisfy full 2π phase shift as well as full transmission. To achieve this goal, we propose a continuum elastic metasurface unit cell that is decomposed into two substructures, namely a mass-tuning substructure with a local dipolar resonator and a stiffness-tuning substructure composed of non-resonant multiply-perforated slits. We demonstrate analytically, numerically, and experimentally that this unique substructured unit cell can satisfy the required phase shift with high transmission. The substructuring enables independent tuning of the elastic properties over a wide range of values. We use a mass-spring model of the proposed continuum unit cell to investigate the working mechanism of the proposed metasurface. With the designed metasurface consisting of substructured unit cells embedded in an aluminum plate, we demonstrate that our metasurface can successfully realize anomalous steering and focusing of in-plane longitudinal ultrasonic beams. The proposed substructuring concept is expected to provide a new principle for the design of general elastic metasurfaces that can be used to efficiently engineer arbitrary wave profiles.

Echinocyte shapes: bending, stretching, and shear determine spicule shape and spacing.

PubMed Central

Mukhopadhyay, Ranjan; Lim H W, Gerald; Wortis, Michael

2002-01-01

We study the shapes of human red blood cells using continuum mechanics. In particular, we model the crenated, echinocytic shapes and show how they may arise from a competition between the bending energy of the plasma membrane and the stretching/shear elastic energies of the membrane skeleton. In contrast to earlier work, we calculate spicule shapes exactly by solving the equations of continuum mechanics subject to appropriate boundary conditions. A simple scaling analysis of this competition reveals an elastic length Lambda(el), which sets the length scale for the spicules and is, thus, related to the number of spicules experimentally observed on the fully developed echinocyte. PMID:11916836

Exploring the remarkable limits of continuum elastic theory to understand the nanomechanics of viruses

NASA Astrophysics Data System (ADS)

Roos, Wouter; Gibbons, Melissa; Klug, William; Wuite, Gijs

2009-03-01

We report nanoindentation experiments by atomic force microscopy on capsids of the Hepatitis B Virus (HBV). HBV is investigated because its capsids can form in either a smaller T=3 or a bigger T=4 configuration, making it an ideal system to test the predictive power of continuum elastic theory to describe nanometre-sized objects. It is shown that for small, consecutive indentations the particles behave reversibly linear and no material fatigue occurs. For larger indentations the particles start to deform non-linearly. The experimental force response fits very well with finite element simulations on coarse grained models of HBV capsids. Furthermore, this also fits with thin shell simulations guided by the F"oppl- von K'arm'an (FvK) number (the dimensionless ratio of stretching and bending stiffness of a thin shell). Both the T=3 and T=4 morphology are very well described by the simulations and the capsid material turns out to have the same Young's modulus, as expected. The presented results demonstrate the surprising strength of continuum elastic theory to describe indentation of viral capsids.

Coarse-grained mechanics of viral shells

NASA Astrophysics Data System (ADS)

Klug, William S.; Gibbons, Melissa M.

2008-03-01

We present an approach for creating three-dimensional finite element models of viral capsids from atomic-level structural data (X-ray or cryo-EM). The models capture heterogeneous geometric features and are used in conjunction with three-dimensional nonlinear continuum elasticity to simulate nanoindentation experiments as performed using atomic force microscopy. The method is extremely flexible; able to capture varying levels of detail in the three-dimensional structure. Nanoindentation simulations are presented for several viruses: Hepatitis B, CCMV, HK97, and φ29. In addition to purely continuum elastic models a multiscale technique is developed that combines finite-element kinematics with MD energetics such that large-scale deformations are facilitated by a reduction in degrees of freedom. Simulations of these capsid deformation experiments provide a testing ground for the techniques, as well as insight into the strength-determining mechanisms of capsid deformation. These methods can be extended as a framework for modeling other proteins and macromolecular structures in cell biology.

Microstructure-Based Fatigue Life Prediction Methods for Naval Steel Structures

DTIC Science & Technology

1993-01-30

approach is to work with the lognormal random variable model proposed by Yang et al . [2], which avoids these difficulties. The simplest form of the...I Al - I I 11. and Ti-alloys [ 10- 111 correlate with the elastic modulus only in the continuum growth regime. On the other hand. compilation of...growth. In fact, Eq. (5) implies that microstructure plays no role in the continuum growth regime. Theoretical models of Frost, et al . [35], and

Defects in crystalline packings of twisted filament bundles. I. Continuum theory of disclinations.

PubMed

Grason, Gregory M

2012-03-01

We develop the theory of the coupling between in-plane order and out-of-plane geometry in twisted, two-dimensionally ordered filament bundles based on the nonlinear continuum elasticity theory of columnar materials. We show that twisted textures of filament backbones necessarily introduce stresses into the cross-sectional packing of bundles and that these stresses are formally equivalent to the geometrically induced stresses generated in thin elastic sheets that are forced to adopt spherical curvature. As in the case of crystalline order on curved membranes, geometrically induced stresses couple elastically to the presence of topological defects in the in-plane order. We derive the effective theory of multiple disclination defects in the cross section of bundle with a fixed twist and show that above a critical degree of twist, one or more fivefold disclinations is favored in the elastic energy ground state. We study the structure and energetics of multidisclination packings based on models of equilibrium and nonequilibrium cross-sectional order.

Gating Mechanisms of Mechanosensitive Channels of Large Conductance, I: A Continuum Mechanics-Based Hierarchical Framework

PubMed Central

Chen, Xi; Cui, Qiang; Tang, Yuye; Yoo, Jejoong; Yethiraj, Arun

2008-01-01

A hierarchical simulation framework that integrates information from molecular dynamics (MD) simulations into a continuum model is established to study the mechanical response of mechanosensitive channel of large-conductance (MscL) using the finite element method (FEM). The proposed MD-decorated FEM (MDeFEM) approach is used to explore the detailed gating mechanisms of the MscL in Escherichia coli embedded in a palmitoyloleoylphosphatidylethanolamine lipid bilayer. In Part I of this study, the framework of MDeFEM is established. The transmembrane and cytoplasmic helices are taken to be elastic rods, the loops are modeled as springs, and the lipid bilayer is approximated by a three-layer sheet. The mechanical properties of the continuum components, as well as their interactions, are derived from molecular simulations based on atomic force fields. In addition, analytical closed-form continuum model and elastic network model are established to complement the MDeFEM approach and to capture the most essential features of gating. In Part II of this study, the detailed gating mechanisms of E. coli-MscL under various types of loading are presented and compared with experiments, structural model, and all-atom simulations, as well as the analytical models established in Part I. It is envisioned that such a hierarchical multiscale framework will find great value in the study of a variety of biological processes involving complex mechanical deformations such as muscle contraction and mechanotransduction. PMID:18390626

Elastic scattering of ^4He by ^6Li at E(^4He) = 24, 25, and 26 MeV

NASA Astrophysics Data System (ADS)

Bartosz, E. E.; Cathers, P. D.; Kemper, K. W.; Maréchal, F.; Rusek, K.

1998-11-01

A previous optical model analysis of the elastic scattering of ^4He by ^6Li at E(^4He) = 18.5 MeV (P. V. Green, K. W. Kemper, P. L. Kerr, K. Mohajeri, E. G. Myers, D. Robson, K. Rusek and I. J. Thompson, Phys. Rev. C 53) 2862 (1996)., as well as a cluster-folded continuum- discretized coupled channels analysis (K. Rusek, P. V. Green, P. L. Kerr, and K. W. Kemper, Phys. Rev. C 56) 1895 (1997)., resulted in a good description of the data set, but the optical model analysis yielded a poor description of the 25 MeV elastic scattering data measured at the same time. New elastic and inelastic scattering angular distribution cross sections are reported for ^4He + ^6Li at E(^4He) = 24, 25 and 26 MeV. Three energies were used to rule out anomalous scattering at 25 MeV. The results of a cluster-folded continuum- discretized coupled channels analysis similar to that used with the 18.5 MeV data are presented for the three new data sets at 24, 25, and 26 MeV.

An asymptotic Reissner-Mindlin plate model

NASA Astrophysics Data System (ADS)

Licht, Christian; Weller, Thibaut

2018-06-01

A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner-Mindlin plate model.

Coupling of lipid membrane elasticity and in-plane dynamics

NASA Astrophysics Data System (ADS)

Tsang, Kuan-Yu; Lai, Yei-Chen; Chiang, Yun-Wei; Chen, Yi-Fan

2017-07-01

Biomembranes exhibit liquid and solid features concomitantly with their in-plane fluidity and elasticity tightly regulated by cells. Here, we present experimental evidence supporting the existence of the dynamics-elasticity correlations for lipid membranes and propose a mechanism involving molecular packing densities to explain them. This paper thereby unifies, at the molecular level, the aspects of the continuum mechanics long used to model the two membrane features. This ultimately may elucidate the universal physical principles governing the cellular phenomena involving biomembranes.

Elastic scattering and total reaction cross section of {sup 6}He+{sup 120}Sn

DOE Office of Scientific and Technical Information (OSTI.GOV)

Faria, P. N. de; Lichtenthaeler, R.; Pires, K. C. C.

The elastic scattering of {sup 6}He on {sup 120}Sn has been measured at four energies above the Coulomb barrier using the {sup 6}He beam produced at the RIBRAS (Radioactive Ion Beams in Brasil) facility. The elastic angular distributions have been analyzed with the optical model and three- and four-body continuum-discretized coupled-channels calculations. The total reaction cross sections have been derived and compared with other systems of similar masses.

A penny-shaped crack in a filament reinforced matrix. 1: The filament model

NASA Technical Reports Server (NTRS)

Erdogan, F.; Pacella, A. H.

1973-01-01

The electrostatic problem of a penny-shaped crack in an elastic matrix which reinforced by filaments or fibers perpendicular to the plane of the crack was studied. The elastic filament model was developed for application to evaluation studies of the stress intensity factor along the periphery of the crack, the stresses in the filaments or fibers, and the interface shear between the matrix and the filaments or fibers. The requirements expected of the model are a sufficiently accurate representation of the filament and applicability to the interaction problems involving a cracked elastic continuum with multi-filament reinforcements. The technique for developing the model and numerical examples of it are shown.

Experimental micro mechanics methods for conventional and negative Poisson's ratio cellular solids as Cosserat continua

NASA Technical Reports Server (NTRS)

Lakes, R.

1991-01-01

Continuum representations of micromechanical phenomena in structured materials are described, with emphasis on cellular solids. These phenomena are interpreted in light of Cosserat elasticity, a generalized continuum theory which admits degrees of freedom not present in classical elasticity. These are the rotation of points in the material, and a couple per unit area or couple stress. Experimental work in this area is reviewed, and other interpretation schemes are discussed. The applicability of Cosserat elasticity to cellular solids and fibrous composite materials is considered as is the application of related generalized continuum theories. New experimental results are presented for foam materials with negative Poisson's ratios.

Nonlocal continuum-based modeling of mechanical characteristics of nanoscopic structures

NASA Astrophysics Data System (ADS)

Rafii-Tabar, Hashem; Ghavanloo, Esmaeal; Fazelzadeh, S. Ahmad

2016-06-01

Insight into the mechanical characteristics of nanoscopic structures is of fundamental interest and indeed poses a great challenge to the research communities around the world. These structures are ultra fine in size and consequently performing standard experiments to measure their various properties is an extremely difficult and expensive endeavor. Hence, to predict the mechanical characteristics of the nanoscopic structures, different theoretical models, numerical modeling techniques, and computer-based simulation methods have been developed. Among several proposed approaches, the nonlocal continuum-based modeling is of particular significance because the results obtained from this modeling for different nanoscopic structures are in very good agreement with the data obtained from both experimental and atomistic-based studies. A review of the essentials of this model together with its applications is presented here. Our paper is a self contained presentation of the nonlocal elasticity theory and contains the analysis of the recent works employing this model within the field of nanoscopic structures. In this review, the concepts from both the classical (local) and the nonlocal elasticity theories are presented and their applications to static and dynamic behavior of nanoscopic structures with various morphologies are discussed. We first introduce the various nanoscopic structures, both carbon-based and non carbon-based types, and then after a brief review of the definitions and concepts from classical elasticity theory, and the basic assumptions underlying size-dependent continuum theories, the mathematical details of the nonlocal elasticity theory are presented. A comprehensive discussion on the nonlocal version of the beam, the plate and the shell theories that are employed in modeling of the mechanical properties and behavior of nanoscopic structures is then provided. Next, an overview of the current literature discussing the application of the nonlocal models of nanoscopic carbon allotropes is presented. We then discuss the application of the models to the investigation of the properties of nanoscopic structures from different materials and with different types of morphologies. Furthermore, we also present recent developments in the application of the nonlocal models. Finally, conclusions and discussions regarding the potentiality of these models for future research are provided.

Bipotential continuum models for granular mechanics

NASA Astrophysics Data System (ADS)

Goddard, Joe

2014-03-01

Most currently popular continuum models for granular media are special cases of a generalized Maxwell fluid model, which describes the evolution of stress and internal variables such as granular particle fraction and fabric,in terms of imposed strain rate. It is shown how such models can be obtained from two scalar potentials, a standard elastic free energy and a ``dissipation potential'' given rigorously by the mathematical theory of Edelen. This allows for a relatively easy derivation of properly invariant continuum models for granular media and fluid-particle suspensions within a thermodynamically consistent framework. The resulting continuum models encompass all the prominent regimes of granular flow, ranging from the quasi-static to rapidly sheared, and are readily extended to include higher-gradient or Cosserat effects. Models involving stress diffusion, such as that proposed recently by Kamrin and Koval (PRL 108 178301), provide an alternative approach that is mentioned in passing. This paper provides a brief overview of a forthcoming review articles by the speaker (The Princeton Companion to Applied Mathematics, and Appl. Mech. Rev.,in the press, 2013).

Multi-scale modelling of elastic moduli of trabecular bone

PubMed Central

Hamed, Elham; Jasiuk, Iwona; Yoo, Andrew; Lee, YikHan; Liszka, Tadeusz

2012-01-01

We model trabecular bone as a nanocomposite material with hierarchical structure and predict its elastic properties at different structural scales. The analysis involves a bottom-up multi-scale approach, starting with nanoscale (mineralized collagen fibril) and moving up the scales to sub-microscale (single lamella), microscale (single trabecula) and mesoscale (trabecular bone) levels. Continuum micromechanics methods, composite materials laminate theory and finite-element methods are used in the analysis. Good agreement is found between theoretical and experimental results. PMID:22279160

Modeling of Soft Poroelastic Tissue in Time-Harmonic MR Elastography

PubMed Central

Perriñez, Phillip R.; Kennedy, Francis E.; Van Houten, Elijah E. W.; Weaver, John B.; Paulsen, Keith D.

2010-01-01

Elastography is an emerging imaging technique that focuses on assessing the resistance to deformation of soft biological tissues in vivo. Magnetic resonance elastography (MRE) uses measured displacement fields resulting from low-amplitude, low-frequency (10 Hz–1 kHz) time-harmonic vibration to recover images of the elastic property distribution of tissues including breast, liver, muscle, prostate, and brain. While many soft tissues display complex time-dependent behavior not described by linear elasticity, the models most commonly employed in MRE parameter reconstructions are based on elastic assumptions. Further, elasticity models fail to include the interstitial fluid phase present in vivo. Alternative continuum models, such as consolidation theory, are able to represent tissue and other materials comprising two distinct phases, generally consisting of a porous elastic solid and penetrating fluid. MRE reconstructions of simulated elastic and poroelastic phantoms were performed to investigate the limitations of current-elasticity-based methods in producing accurate elastic parameter estimates in poroelastic media. The results indicate that linearly elastic reconstructions of fluid-saturated porous media at amplitudes and frequencies relevant to steady-state MRE can yield misleading effective property distributions resulting from the complex interaction between their solid and fluid phases. PMID:19272864

Mathematical modeling of spinning elastic bodies for modal analysis.

NASA Technical Reports Server (NTRS)

Likins, P. W.; Barbera, F. J.; Baddeley, V.

1973-01-01

The problem of modal analysis of an elastic appendage on a rotating base is examined to establish the relative advantages of various mathematical models of elastic structures and to extract general inferences concerning the magnitude and character of the influence of spin on the natural frequencies and mode shapes of rotating structures. In realization of the first objective, it is concluded that except for a small class of very special cases the elastic continuum model is devoid of useful results, while for constant nominal spin rate the distributed-mass finite-element model is quite generally tractable, since in the latter case the governing equations are always linear, constant-coefficient, ordinary differential equations. Although with both of these alternatives the details of the formulation generally obscure the essence of the problem and permit very little engineering insight to be gained without extensive computation, this difficulty is not encountered when dealing with simple concentrated mass models.

Elastic interaction of hydrogen atoms on graphene: A multiscale approach from first principles to continuum elasticity

NASA Astrophysics Data System (ADS)

Branicio, Paulo S.; Vastola, Guglielmo; Jhon, Mark H.; Sullivan, Michael B.; Shenoy, Vivek B.; Srolovitz, David J.

2016-10-01

The deformation of graphene due to the chemisorption of hydrogen atoms on its surface and the long-range elastic interaction between hydrogen atoms induced by these deformations are investigated using a multiscale approach based on first principles, empirical interactions, and continuum modeling. Focus is given to the intrinsic low-temperature structure and interactions. Therefore, all calculations are performed at T =0 , neglecting possible temperature or thermal fluctuation effects. Results from different methods agree well and consistently describe the local deformation of graphene on multiple length scales reaching 500 Å . The results indicate that the elastic interaction mediated by this deformation is significant and depends on the deformation of the graphene sheet both in and out of plane. Surprisingly, despite the isotropic elasticity of graphene, within the linear elastic regime, atoms elastically attract or repel each other depending on (i) the specific site they are chemisorbed; (ii) the relative position of the sites; (iii) and if they are on the same or on opposite surface sides. The interaction energy sign and power-law decay calculated from molecular statics agree well with theoretical predictions from linear elasticity theory, considering in-plane or out-of-plane deformations as a superposition or in a coupled nonlinear approach. Deviations on the exact power law between molecular statics and the linear elastic analysis are evidence of the importance of nonlinear effects on the elasticity of monolayer graphene. These results have implications for the understanding of the generation of clusters and regular formations of hydrogen and other chemisorbed atoms on graphene.

Modeling deformation and chaining of flexible shells in a nematic solvent with finite elements on an adaptive moving mesh

NASA Astrophysics Data System (ADS)

DeBenedictis, Andrew; Atherton, Timothy J.; Rodarte, Andrea L.; Hirst, Linda S.

2018-03-01

A micrometer-scale elastic shell immersed in a nematic liquid crystal may be deformed by the host if the cost of deformation is comparable to the cost of elastic deformation of the nematic. Moreover, such inclusions interact and form chains due to quadrupolar distortions induced in the host. A continuum theory model using finite elements is developed for this system, using mesh regularization and dynamic refinement to ensure quality of the numerical representation even for large deformations. From this model, we determine the influence of the shell elasticity, nematic elasticity, and anchoring condition on the shape of the shell and hence extract parameter values from an experimental realization. Extending the model to multibody interactions, we predict the alignment angle of the chain with respect to the host nematic as a function of aspect ratio, which is found to be in excellent agreement with experiments.

Modulating DNA configuration by interfacial traction: an elastic rod model to characterize DNA folding and unfolding.

PubMed

Huang, Zaixing

2011-01-01

As a continuum model of DNA, a thin elastic rod subjected to interfacial interactions is used to investigate the equilibrium configuration of DNA in intracellular solution. The interfacial traction between the rod and the solution environment is derived in detail. Kirchhoff's theory of elastic rods is used to analyze the equilibrium configuration of a DNA segment under the action of the interfacial traction. The influences of the interfacial energy factor and bending stiffness on the toroidal spool formation of the DNA segment are discussed. The results show that the equilibrium configuration of DNA is mainly determined by competition between the interfacial energy and elastic strain energy of the DNA itself, and the interfacial traction is one of the forces that drives DNA folding and unfolding.

Fracture-Based Mesh Size Requirements for Matrix Cracks in Continuum Damage Mechanics Models

NASA Technical Reports Server (NTRS)

Leone, Frank A.; Davila, Carlos G.; Mabson, Gerald E.; Ramnath, Madhavadas; Hyder, Imran

2017-01-01

This paper evaluates the ability of progressive damage analysis (PDA) finite element (FE) models to predict transverse matrix cracks in unidirectional composites. The results of the analyses are compared to closed-form linear elastic fracture mechanics (LEFM) solutions. Matrix cracks in fiber-reinforced composite materials subjected to mode I and mode II loading are studied using continuum damage mechanics and zero-thickness cohesive zone modeling approaches. The FE models used in this study are built parametrically so as to investigate several model input variables and the limits associated with matching the upper-bound LEFM solutions. Specifically, the sensitivity of the PDA FE model results to changes in strength and element size are investigated.

Self-consistent elastic continuum theory of degenerate, equilibrium aperiodic solids.

PubMed

Bevzenko, Dmytro; Lubchenko, Vassiliy

2014-11-07

We show that the vibrational response of a glassy liquid at finite frequencies can be described by continuum mechanics despite the vast degeneracy of the vibrational ground state; standard continuum elasticity assumes a unique ground state. The effective elastic constants are determined by the bare elastic constants of individual free energy minima of the liquid, the magnitude of built-in stress, and temperature, analogously to how the dielectric response of a polar liquid is determined by the dipole moment of the constituent molecules and temperature. In contrast with the dielectric constant--which is enhanced by adding polar molecules to the system--the elastic constants are down-renormalized by the relaxation of the built-in stress. The renormalization flow of the elastic constants has three fixed points, two of which are trivial and correspond to the uniform liquid state and an infinitely compressible solid, respectively. There is also a nontrivial fixed point at the Poisson ratio equal to 1/5, which corresponds to an isospin-like degeneracy between shear and uniform deformation. The present description predicts a discontinuous jump in the (finite frequency) shear modulus at the crossover from collisional to activated transport, consistent with the random first order transition theory.

Effects of Host-rock Fracturing on Elastic-deformation Source Models of Volcano Deflation.

PubMed

Holohan, Eoghan P; Sudhaus, Henriette; Walter, Thomas R; Schöpfer, Martin P J; Walsh, John J

2017-09-08

Volcanoes commonly inflate or deflate during episodes of unrest or eruption. Continuum mechanics models that assume linear elastic deformation of the Earth's crust are routinely used to invert the observed ground motions. The source(s) of deformation in such models are generally interpreted in terms of magma bodies or pathways, and thus form a basis for hazard assessment and mitigation. Using discontinuum mechanics models, we show how host-rock fracturing (i.e. non-elastic deformation) during drainage of a magma body can progressively change the shape and depth of an elastic-deformation source. We argue that this effect explains the marked spatio-temporal changes in source model attributes inferred for the March-April 2007 eruption of Piton de la Fournaise volcano, La Reunion. We find that pronounced deflation-related host-rock fracturing can: (1) yield inclined source model geometries for a horizontal magma body; (2) cause significant upward migration of an elastic-deformation source, leading to underestimation of the true magma body depth and potentially to a misinterpretation of ascending magma; and (3) at least partly explain underestimation by elastic-deformation sources of changes in sub-surface magma volume.

Elastic properties of suspended black phosphorus nanosheets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Jia-Ying; Li, Yang; Zhen, Liang

2016-01-04

The mechanical properties of black phosphorus (BP) nanosheets suspended over circular holes were measured by an atomic force microscope nanoindentation method. The continuum mechanic model was introduced to calculate the elastic modulus and pretension of BP nanosheets with thicknesses ranging from 14.3 to 34 nm. Elastic modulus of BP nanosheets declines with thickness, and the maximum value is 276 ± 32.4 GPa. Besides, the effective strain of BP ranges from 8 to 17% with a breaking strength of 25 GPa. Our results show that BP nanosheets serve as a promising candidate for flexible electronic applications.

The Effect of Chemical Functionalization on Mechanical Properties of Nanotube/Polymer Composites

NASA Technical Reports Server (NTRS)

Odegard, G. M.; Frankland, S. J. V.; Gates, T. S.

2003-01-01

The effects of the chemical functionalization of a carbon nanotube embedded in a nanotube/polyethylene composite on the bulk elastic properties are presented. Constitutive equations are established for both functionalized and non-functionalized nanotube composites systems by using an equivalent-continuum modeling technique. The elastic properties of both composites systems are predicted for various nanotube lengths, volume fractions, and orientations. The results indicate that for the specific composite material considered in this study, most of the elastic stiffness constants of the functionalized composite are either less than or equal to those of the non-functionalized composite.

Rotational strain in Weyl semimetals: A continuum approach

NASA Astrophysics Data System (ADS)

Arjona, Vicente; Vozmediano, María A. H.

2018-05-01

We use a symmetry approach to derive the coupling of lattice deformations to electronic excitations in three-dimensional Dirac and Weyl semimetals in the continuum low-energy model. We focus on the effects of rotational strain and show that it can drive transitions from Dirac to Weyl semimetals, gives rise to elastic gauge fields, tilts the cones, and generates pseudo-Zeeman couplings. It also can generate a deformation potential in volume-preserving deformations. The associated pseudoelectric field contributes to the chiral anomaly.

Toward lattice fractional vector calculus

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-09-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

Angular distribution of elastic scattering induced by 17F on medium-mass target nuclei at energies near the Coulomb barrier

NASA Astrophysics Data System (ADS)

Zhang, G. L.; Zhang, G. X.; Lin, C. J.; Lubian, J.; Rangel, J.; Paes, B.; Ferreira, J. L.; Zhang, H. Q.; Qu, W. W.; Jia, H. M.; Yang, L.; Ma, N. R.; Sun, L. J.; Wang, D. X.; Zheng, L.; Liu, X. X.; Chu, X. T.; Yang, J. C.; Wang, J. S.; Xu, S. W.; Ma, P.; Ma, J. B.; Jin, S. L.; Bai, Z.; Huang, M. R.; Zang, H. L.; Yang, B.; Liu, Y.

2018-04-01

The elastic scattering angular distributions were measured for 50- and 59-MeV 17F radioactive ion beam on a 89Y target. The aim of this work is to study the effect of the breakup of the proton halo projectile on the elastic scattering angular distribution. The experimental data were analyzed by means of the optical model with the double-folding São Paulo potential for both real and imaginary parts. The theoretical calculations reproduced the experimental data reasonably well. It is shown that the method of the data analysis is correct. In order to clarify the difference observed at large angles for the 59-MeV incident energy data, Continuum-Discretized Coupled-Channels (CDCC) calculations were performed to consider the breakup coupling effect. It is found that the experimental data show the Coulomb rainbow peak and that the effect of the coupling to the continuum states is not very significant, producing only a small hindrance of the Coulomb rainbow peak and a very small enhancement of the elastic scattering angular distribution at backward angles, suggesting that the multipole response of the neutron halo projectiles is stronger than that of the proton halo systems.

Microscopic description of elastic and direct inelastic nucleon scattering off spherical nuclei

NASA Astrophysics Data System (ADS)

Dupuis, M.

2017-05-01

The purpose of this study is to improve the modeling of nucleon direct inelastic scattering to the continuum using a microscopic and parameter-free approach. For the first time, direct elastic scattering, inelastic scattering to discrete excitations and to the continuum are described within a microscopic approach without adjustable parameters. Proton scattering off 90Zr and 208Pb are the reactions used as test case examples of the calculations. The model uses the Melbourne g-matrix and the Random Phase Approximation description of nuclear states, implemented with the Gogny D1S interaction. The relevant optical and transition potentials in a finite nucleus are calculated within a local density approximation. As we use the nuclear matter approach we limit our study to incident energies above 40 MeV. We first checked that this model provides an accurate account of measured cross sections for elastic scattering and inelastic scattering to discrete states. It is then applied to the direct inelastic scattering to the continuum considering all one-phonon excitations predicted within the RPA approach. This accounts for a part of the direct pre-equilibrium emission, often labeled as the one-step direct process in quantum-based approaches. Our approach provides a very accurate description of angular distributions where the one-step process dominates. The impact of collective excitations is shown to be non negligible for energy transfer to the target up to 20 MeV, decreasing as the incident energy increases. For incident energies above 80 MeV, our modeling provides a good account of direct proton emission for an energy transfer to the target up to 30 MeV. However, the proton emission we predict underestimates the measured cross sections for incident energies below 80 MeV. We compare our prediction to those of the phenomenological exciton model to help interpret this result. Directions that may improve our modeling are discussed.

Continuum limit of the vibrational properties of amorphous solids.

PubMed

Mizuno, Hideyuki; Shiba, Hayato; Ikeda, Atsushi

2017-11-14

The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomenological explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law.

Continuum limit of the vibrational properties of amorphous solids

PubMed Central

Mizuno, Hideyuki; Ikeda, Atsushi

2017-01-01

The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomenological explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law. PMID:29087941

Distribution function of random strains in an elastically anisotropic continuum and defect strengths of T m3 + impurity ions in crystals with zircon structure

NASA Astrophysics Data System (ADS)

Malkin, B. Z.; Abishev, N. M.; Baibekov, E. I.; Pytalev, D. S.; Boldyrev, K. N.; Popova, M. N.; Bettinelli, M.

2017-07-01

We construct a distribution function of the strain-tensor components induced by point defects in an elastically anisotropic continuum, which can be used to account quantitatively for many effects observed in different branches of condensed matter physics. Parameters of the derived six-dimensional generalized Lorentz distribution are expressed through the integrals computed over the array of strains. The distribution functions for the cubic diamond and elpasolite crystals and tetragonal crystals with the zircon and scheelite structures are presented. Our theoretical approach is supported by a successful modeling of specific line shapes of singlet-doublet transitions of the T m3 + ions doped into AB O4 (A =Y , Lu; B =P , V) crystals with zircon structure, observed in high-resolution optical spectra. The values of the defect strengths of impurity T m3 + ions in the oxygen surroundings, obtained as a result of this modeling, can be used in future studies of random strains in different rare-earth oxides.

Gradient Models in Molecular Biophysics: Progress, Challenges, Opportunities

PubMed Central

Bardhan, Jaydeep P.

2014-01-01

In the interest of developing a bridge between researchers modeling materials and those modeling biological molecules, we survey recent progress in developing nonlocal-dielectric continuum models for studying the behavior of proteins and nucleic acids. As in other areas of science, continuum models are essential tools when atomistic simulations (e.g. molecular dynamics) are too expensive. Because biological molecules are essentially all nanoscale systems, the standard continuum model, involving local dielectric response, has basically always been dubious at best. The advanced continuum theories discussed here aim to remedy these shortcomings by adding features such as nonlocal dielectric response, and nonlinearities resulting from dielectric saturation. We begin by describing the central role of electrostatic interactions in biology at the molecular scale, and motivate the development of computationally tractable continuum models using applications in science and engineering. For context, we highlight some of the most important challenges that remain and survey the diverse theoretical formalisms for their treatment, highlighting the rigorous statistical mechanics that support the use and improvement of continuum models. We then address the development and implementation of nonlocal dielectric models, an approach pioneered by Dogonadze, Kornyshev, and their collaborators almost forty years ago. The simplest of these models is just a scalar form of gradient elasticity, and here we use ideas from gradient-based modeling to extend the electrostatic model to include additional length scales. The paper concludes with a discussion of open questions for model development, highlighting the many opportunities for the materials community to leverage its physical, mathematical, and computational expertise to help solve one of the most challenging questions in molecular biology and biophysics. PMID:25505358

Gradient Models in Molecular Biophysics: Progress, Challenges, Opportunities.

PubMed

Bardhan, Jaydeep P

2013-12-01

In the interest of developing a bridge between researchers modeling materials and those modeling biological molecules, we survey recent progress in developing nonlocal-dielectric continuum models for studying the behavior of proteins and nucleic acids. As in other areas of science, continuum models are essential tools when atomistic simulations (e.g. molecular dynamics) are too expensive. Because biological molecules are essentially all nanoscale systems, the standard continuum model, involving local dielectric response, has basically always been dubious at best. The advanced continuum theories discussed here aim to remedy these shortcomings by adding features such as nonlocal dielectric response, and nonlinearities resulting from dielectric saturation. We begin by describing the central role of electrostatic interactions in biology at the molecular scale, and motivate the development of computationally tractable continuum models using applications in science and engineering. For context, we highlight some of the most important challenges that remain and survey the diverse theoretical formalisms for their treatment, highlighting the rigorous statistical mechanics that support the use and improvement of continuum models. We then address the development and implementation of nonlocal dielectric models, an approach pioneered by Dogonadze, Kornyshev, and their collaborators almost forty years ago. The simplest of these models is just a scalar form of gradient elasticity, and here we use ideas from gradient-based modeling to extend the electrostatic model to include additional length scales. The paper concludes with a discussion of open questions for model development, highlighting the many opportunities for the materials community to leverage its physical, mathematical, and computational expertise to help solve one of the most challenging questions in molecular biology and biophysics.

Gradient models in molecular biophysics: progress, challenges, opportunities

NASA Astrophysics Data System (ADS)

Bardhan, Jaydeep P.

2013-12-01

In the interest of developing a bridge between researchers modeling materials and those modeling biological molecules, we survey recent progress in developing nonlocal-dielectric continuum models for studying the behavior of proteins and nucleic acids. As in other areas of science, continuum models are essential tools when atomistic simulations (e.g., molecular dynamics) are too expensive. Because biological molecules are essentially all nanoscale systems, the standard continuum model, involving local dielectric response, has basically always been dubious at best. The advanced continuum theories discussed here aim to remedy these shortcomings by adding nonlocal dielectric response. We begin by describing the central role of electrostatic interactions in biology at the molecular scale, and motivate the development of computationally tractable continuum models using applications in science and engineering. For context, we highlight some of the most important challenges that remain, and survey the diverse theoretical formalisms for their treatment, highlighting the rigorous statistical mechanics that support the use and improvement of continuum models. We then address the development and implementation of nonlocal dielectric models, an approach pioneered by Dogonadze, Kornyshev, and their collaborators almost 40 years ago. The simplest of these models is just a scalar form of gradient elasticity, and here we use ideas from gradient-based modeling to extend the electrostatic model to include additional length scales. The review concludes with a discussion of open questions for model development, highlighting the many opportunities for the materials community to leverage its physical, mathematical, and computational expertise to help solve one of the most challenging questions in molecular biology and biophysics.

Rate-Dependent Homogenization Based Continuum Plasticity Damage Model for Dendritic Cast Aluminum Alloys

DTIC Science & Technology

2011-01-01

0.25 s−1 to 0.75 s−1 The return mapping algorithm consists of an initial elastic predictor step, where the elastic response is assumed and the stresses...18 different loadings are used. The parameters F, G, H are solved by an iterative algorithm with C = 3. The step is repeated for different values of...a. REPORT unclassified b. ABSTRACT unclassified c . THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 c⃝

A Continuum Method for Determining Membrane Protein Insertion Energies and the Problem of Charged Residues

PubMed Central

Choe, Seungho; Hecht, Karen A.; Grabe, Michael

2008-01-01

Continuum electrostatic approaches have been extremely successful at describing the charged nature of soluble proteins and how they interact with binding partners. However, it is unclear whether continuum methods can be used to quantitatively understand the energetics of membrane protein insertion and stability. Recent translation experiments suggest that the energy required to insert charged peptides into membranes is much smaller than predicted by present continuum theories. Atomistic simulations have pointed to bilayer inhomogeneity and membrane deformation around buried charged groups as two critical features that are neglected in simpler models. Here, we develop a fully continuum method that circumvents both of these shortcomings by using elasticity theory to determine the shape of the deformed membrane and then subsequently uses this shape to carry out continuum electrostatics calculations. Our method does an excellent job of quantitatively matching results from detailed molecular dynamics simulations at a tiny fraction of the computational cost. We expect that this method will be ideal for studying large membrane protein complexes. PMID:18474636

Computation of the effective mechanical response of biological networks accounting for large configuration changes.

PubMed

El Nady, K; Ganghoffer, J F

2016-05-01

The asymptotic homogenization technique is involved to derive the effective elastic response of biological membranes viewed as repetitive beam networks. Thereby, a systematic methodology is established, allowing the prediction of the overall mechanical properties of biological membranes in the nonlinear regime, reflecting the influence of the geometrical and mechanical micro-parameters of the network structure on the overall response of the equivalent continuum. Biomembranes networks are classified based on nodal connectivity, so that we analyze in this work 3, 4 and 6-connectivity networks, which are representative of most biological networks. The individual filaments of the network are described as undulated beams prone to entropic elasticity, with tensile moduli determined from their persistence length. The effective micropolar continuum evaluated as a continuum substitute of the biological network has a kinematics reflecting the discrete network deformation modes, involving a nodal displacement and a microrotation. The statics involves the classical Cauchy stress and internal moments encapsulated into couple stresses, which develop internal work in duality to microcurvatures reflecting local network undulations. The relative ratio of the characteristic bending length of the effective micropolar continuum to the unit cell size determines the relevant choice of the equivalent medium. In most cases, the Cauchy continuum is sufficient to model biomembranes. The peptidoglycan network may exhibit a re-entrant hexagonal configuration due to thermal or pressure fluctuations, for which micropolar effects become important. The homogenized responses are in good agreement with FE simulations performed over the whole network. The predictive nature of the employed homogenization technique allows the identification of a strain energy density of a hyperelastic model, for the purpose of performing structural calculations of the shape evolutions of biomembranes. Copyright © 2015 Elsevier Ltd. All rights reserved.

9Be+120Sn scattering at near-barrier energies within a four-body model

NASA Astrophysics Data System (ADS)

Arazi, A.; Casal, J.; Rodríguez-Gallardo, M.; Arias, J. M.; Lichtenthäler Filho, R.; Abriola, D.; Capurro, O. A.; Cardona, M. A.; Carnelli, P. F. F.; de Barbará, E.; Fernández Niello, J.; Figueira, J. M.; Fimiani, L.; Hojman, D.; Martí, G. V.; Martínez Heimman, D.; Pacheco, A. J.

2018-04-01

Cross sections for elastic and inelastic scattering of the weakly bound 9Be nucleus on a 120Sn target have been measured at seven bombarding energies around and above the Coulomb barrier. The elastic angular distributions are analyzed with a four-body continuum-discretized coupled-channels (CDCC) calculation, which considers 9Be as a three-body projectile (α +α +n ). An optical model analysis using the São Paulo potential is also shown for comparison. The CDCC analysis shows that the coupling to the continuum part of the spectrum is important for the agreement with experimental data even at energies around the Coulomb barrier, suggesting that breakup is an important process at low energies. At the highest incident energies, two inelastic peaks are observed at 1.19(5) and 2.41(5) MeV. Coupled-channels (CC) calculations using a rotational model confirm that the first inelastic peak corresponds to the excitation of the 21+ state in 120Sn, while the second one likely corresponds to the excitation of the 31- state.

Deformation behaviors of three-dimensional graphene honeycombs under out-of-plane compression: Atomistic simulations and predictive modeling

NASA Astrophysics Data System (ADS)

Meng, Fanchao; Chen, Cheng; Hu, Dianyin; Song, Jun

2017-12-01

Combining atomistic simulations and continuum modeling, a comprehensive study of the out-of-plane compressive deformation behaviors of equilateral three-dimensional (3D) graphene honeycombs was performed. It was demonstrated that under out-of-plane compression, the honeycomb exhibits two critical deformation events, i.e., elastic mechanical instability (including elastic buckling and structural transformation) and inelastic structural collapse. The above events were shown to be strongly dependent on the honeycomb cell size and affected by the local atomic bonding at the cell junction. By treating the 3D graphene honeycomb as a continuum cellular solid, and accounting for the structural heterogeneity and constraint at the junction, a set of analytical models were developed to accurately predict the threshold stresses corresponding to the onset of those deformation events. The present study elucidates key structure-property relationships of 3D graphene honeycombs under out-of-plane compression, and provides a comprehensive theoretical framework to predictively analyze their deformation responses, and more generally, offers critical new knowledge for the rational bottom-up design of 3D networks of two-dimensional nanomaterials.

Continuum-Kinetic Models and Numerical Methods for Multiphase Applications

NASA Astrophysics Data System (ADS)

Nault, Isaac Michael

This thesis presents a continuum-kinetic approach for modeling general problems in multiphase solid mechanics. In this context, a continuum model refers to any model, typically on the macro-scale, in which continuous state variables are used to capture the most important physics: conservation of mass, momentum, and energy. A kinetic model refers to any model, typically on the meso-scale, which captures the statistical motion and evolution of microscopic entitites. Multiphase phenomena usually involve non-negligible micro or meso-scopic effects at the interfaces between phases. The approach developed in the thesis attempts to combine the computational performance benefits of a continuum model with the physical accuracy of a kinetic model when applied to a multiphase problem. The approach is applied to modeling a single particle impact in Cold Spray, an engineering process that intimately involves the interaction of crystal grains with high-magnitude elastic waves. Such a situation could be classified a multiphase application due to the discrete nature of grains on the spatial scale of the problem. For this application, a hyper elasto-plastic model is solved by a finite volume method with approximate Riemann solver. The results of this model are compared for two types of plastic closure: a phenomenological macro-scale constitutive law, and a physics-based meso-scale Crystal Plasticity model.

Mesoscale studies of ionic closed membranes with polyhedral geometries

DOE PAGES

Olvera de la Cruz, Monica

2016-06-01

Large crystalline molecular shells buckle spontaneously into icosahedra while multicomponent shells buckle into various polyhedra. Continuum elastic theory explains the buckling of closed shells with one elastic component into icosahedra. A generalized elastic model, on the other hand, describes the spontaneous buckling of inhomogeneous shells into regular and irregular polyhedra. By coassembling water-insoluble anionic (–1) amphiphiles with cationic (3+) amphiphiles, we realized ionic vesicles. Results revealed that surface crystalline domains and the unusual shell shapes observed arise from the competition of ionic correlations with charge-regulation. We explain here the mechanism by which these ionic membranes generate a mechanically heterogeneous vesicle.

The small length scale effect for a non-local cantilever beam: a paradox solved.

PubMed

Challamel, N; Wang, C M

2008-08-27

Non-local continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with microstructures or nanostructures. This paper presents some simplified non-local elastic beam models, for the bending analyses of small scale rods. Integral-type or gradient non-local models abandon the classical assumption of locality, and admit that stress depends not only on the strain value at that point but also on the strain values of all points on the body. There is a paradox still unresolved at this stage: some bending solutions of integral-based non-local elastic beams have been found to be identical to the classical (local) solution, i.e. the small scale effect is not present at all. One example is the Euler-Bernoulli cantilever nanobeam model with a point load which has application in microelectromechanical systems and nanoelectromechanical systems as an actuator. In this paper, it will be shown that this paradox may be overcome with a gradient elastic model as well as an integral non-local elastic model that is based on combining the local and the non-local curvatures in the constitutive elastic relation. The latter model comprises the classical gradient model and Eringen's integral model, and its application produces small length scale terms in the non-local elastic cantilever beam solution.

Seismic waves in a self-gravitating planet

NASA Astrophysics Data System (ADS)

Brazda, Katharina; de Hoop, Maarten V.; Hörmann, Günther

2013-04-01

The elastic-gravitational equations describe the propagation of seismic waves including the effect of self-gravitation. We rigorously derive and analyze this system of partial differential equations and boundary conditions for a general, uniformly rotating, elastic, but aspherical, inhomogeneous, and anisotropic, fluid-solid earth model, under minimal assumptions concerning the smoothness of material parameters and geometry. For this purpose we first establish a consistent mathematical formulation of the low regularity planetary model within the framework of nonlinear continuum mechanics. Using calculus of variations in a Sobolev space setting, we then show how the weak form of the linearized elastic-gravitational equations directly arises from Hamilton's principle of stationary action. Finally we prove existence and uniqueness of weak solutions by the method of energy estimates and discuss additional regularity properties.

Elastic constants of stressed and unstressed materials in the phase-field crystal model

NASA Astrophysics Data System (ADS)

Wang, Zi-Le; Huang, Zhi-Feng; Liu, Zhirong

2018-04-01

A general procedure is developed to investigate the elastic response and calculate the elastic constants of stressed and unstressed materials through continuum field modeling, particularly the phase-field crystal (PFC) models. It is found that for a complete description of system response to elastic deformation, the variations of all the quantities of lattice wave vectors, their density amplitudes (including the corresponding anisotropic variation and degeneracy breaking), the average atomic density, and system volume should be incorporated. The quantitative and qualitative results of elastic constant calculations highly depend on the physical interpretation of the density field used in the model, and also importantly, on the intrinsic pressure that usually pre-exists in the model system. A formulation based on thermodynamics is constructed to account for the effects caused by constant pre-existing stress during the homogeneous elastic deformation, through the introducing of a generalized Gibbs free energy and an effective finite strain tensor used for determining the elastic constants. The elastic properties of both solid and liquid states can be well produced by this unified approach, as demonstrated by an analysis for the liquid state and numerical evaluations for the bcc solid phase. The numerical calculations of bcc elastic constants and Poisson's ratio through this method generate results that are consistent with experimental conditions, and better match the data of bcc Fe given by molecular dynamics simulations as compared to previous work. The general theory developed here is applicable to the study of different types of stressed or unstressed material systems under elastic deformation.

On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models

DOE PAGES

Seleson, Pablo; Du, Qiang; Parks, Michael L.

2016-08-16

The peridynamic theory of solid mechanics is a nonlocal reformulation of the classical continuum mechanics theory. At the continuum level, it has been demonstrated that classical (local) elasticity is a special case of peridynamics. Such a connection between these theories has not been extensively explored at the discrete level. This paper investigates the consistency between nearest-neighbor discretizations of linear elastic peridynamic models and finite difference discretizations of the Navier–Cauchy equation of classical elasticity. While nearest-neighbor discretizations in peridynamics have been numerically observed to present grid-dependent crack paths or spurious microcracks, this paper focuses on a different, analytical aspect of suchmore » discretizations. We demonstrate that, even in the absence of cracks, such discretizations may be problematic unless a proper selection of weights is used. Specifically, we demonstrate that using the standard meshfree approach in peridynamics, nearest-neighbor discretizations do not reduce, in general, to discretizations of corresponding classical models. We study nodal-based quadratures for the discretization of peridynamic models, and we derive quadrature weights that result in consistency between nearest-neighbor discretizations of peridynamic models and discretized classical models. The quadrature weights that lead to such consistency are, however, model-/discretization-dependent. We motivate the choice of those quadrature weights through a quadratic approximation of displacement fields. The stability of nearest-neighbor peridynamic schemes is demonstrated through a Fourier mode analysis. Finally, an approach based on a normalization of peridynamic constitutive constants at the discrete level is explored. This approach results in the desired consistency for one-dimensional models, but does not work in higher dimensions. The results of the work presented in this paper suggest that even though nearest-neighbor discretizations should be avoided in peridynamic simulations involving cracks, such discretizations are viable, for example for verification or validation purposes, in problems characterized by smooth deformations. Furthermore, we demonstrate that better quadrature rules in peridynamics can be obtained based on the functional form of solutions.« less

An Approach to Study Elastic Vibrations of Fractal Cylinders

NASA Astrophysics Data System (ADS)

Steinberg, Lev; Zepeda, Mario

2016-11-01

This paper presents our study of dynamics of fractal solids. Concepts of fractal continuum and time had been used in definitions of a fractal body deformation and motion, formulation of conservation of mass, balance of momentum, and constitutive relationships. A linearized model, which was written in terms of fractal time and spatial derivatives, has been employed to study the elastic vibrations of fractal circular cylinders. Fractal differential equations of torsional, longitudinal and transverse fractal wave equations have been obtained and solution properties such as size and time dependence have been revealed.

Ge growth on vicinal si(001) surfaces: island's shape and pair interaction versus miscut angle.

PubMed

Persichetti, L; Sgarlata, A; Fanfoni, M; Balzarotti, A

2011-10-01

A complete description of Ge growth on vicinal Si(001) surfaces is provided. The distinctive mechanisms of the epitaxial growth process on vicinal surfaces are clarified from the very early stages of Ge deposition to the nucleation of 3D islands. By interpolating high-resolution scanning tunneling microscopy measurements with continuum elasticity modeling, we assess the dependence of island's shape and elastic interaction on the substrate misorientation. Our results confirm that vicinal surfaces offer an additional degree of control over the shape and symmetry of self-assembled nanostructures.

Transient Stress Wave Propagation in One-Dimensional Micropolar Bodies

DTIC Science & Technology

2009-02-01

based on Biot’s theory of poro- elasticity. Two compressional waves were then observed in the resulting one-dimensional model of a poroelastic column...Lisina, S., Potapov, A., Nesterenko, V., 2001. A nonlinear granular medium with particle rotation: a one-dimensional model . Acoustical Physics 47 (5...zones in failed ceramics, may be modeled using continuum theories incorporating additional kinematic degrees of freedom beyond the scope of classical

Spatiotemporal stick-slip phenomena in a coupled continuum-granular system

NASA Astrophysics Data System (ADS)

Ecke, Robert

In sheared granular media, stick-slip behavior is ubiquitous, especially at very small shear rates and weak drive coupling. The resulting slips are characteristic of natural phenomena such as earthquakes and well as being a delicate probe of the collective dynamics of the granular system. In that spirit, we developed a laboratory experiment consisting of sheared elastic plates separated by a narrow gap filled with quasi-two-dimensional granular material (bi-dispersed nylon rods) . We directly determine the spatial and temporal distributions of strain displacements of the elastic continuum over 200 spatial points located adjacent to the gap. Slip events can be divided into large system-spanning events and spatially distributed smaller events. The small events have a probability distribution of event moment consistent with an M - 3 / 2 power law scaling and a Poisson distributed recurrence time distribution. Large events have a broad, log-normal moment distribution and a mean repetition time. As the applied normal force increases, there are fractionally more (less) large (small) events, and the large-event moment distribution broadens. The magnitude of the slip motion of the plates is well correlated with the root-mean-square displacements of the granular matter. Our results are consistent with mean field descriptions of statistical models of earthquakes and avalanches. We further explore the high-speed dynamics of system events and also discuss the effective granular friction of the sheared layer. We find that large events result from stored elastic energy in the plates in this coupled granular-continuum system.

Wave propagation in equivalent continuums representing truss lattice materials

DOE PAGES

Messner, Mark C.; Barham, Matthew I.; Kumar, Mukul; ...

2015-07-29

Stiffness scales linearly with density in stretch-dominated lattice meta-materials offering the possibility of very light yet very stiff structures. Current additive manufacturing techniques can assemble structures from lattice materials, but the design of such structures will require accurate, efficient simulation methods. Equivalent continuum models have several advantages over discrete truss models of stretch dominated lattices, including computational efficiency and ease of model construction. However, the development an equivalent model suitable for representing the dynamic response of a periodic truss in the small deformation regime is complicated by microinertial effects. This study derives a dynamic equivalent continuum model for periodic trussmore » structures suitable for representing long-wavelength wave propagation and verifies it against the full Bloch wave theory and detailed finite element simulations. The model must incorporate microinertial effects to accurately reproduce long wavelength characteristics of the response such as anisotropic elastic soundspeeds. Finally, the formulation presented here also improves upon previous work by preserving equilibrium at truss joints for simple lattices and by improving numerical stability by eliminating vertices in the effective yield surface.« less

A Continuum Description of Nonlinear Elasticity, Slip and Twinning, With Application to Sapphire

DTIC Science & Technology

2009-03-01

Twinning is modelled via the isochoric term FI, and residual volume changes associated with defects are captured by the Jacobian determinant J . The...BF00126994) Farber, Y. A., Yoon, S. Y., Lagerlof, K. P. D. & Heuer, A. H. 1993 Microplasticity during high temperature indentation and the Peierls

Finite elements of nonlinear continua.

NASA Technical Reports Server (NTRS)

Oden, J. T.

1972-01-01

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Du, Qiang

The rational design of materials, the development of accurate and efficient material simulation algorithms, and the determination of the response of materials to environments and loads occurring in practice all require an understanding of mechanics at disparate spatial and temporal scales. The project addresses mathematical and numerical analyses for material problems for which relevant scales range from those usually treated by molecular dynamics all the way up to those most often treated by classical elasticity. The prevalent approach towards developing a multiscale material model couples two or more well known models, e.g., molecular dynamics and classical elasticity, each of whichmore » is useful at a different scale, creating a multiscale multi-model. However, the challenges behind such a coupling are formidable and largely arise because the atomistic and continuum models employ nonlocal and local models of force, respectively. The project focuses on a multiscale analysis of the peridynamics materials model. Peridynamics can be used as a transition between molecular dynamics and classical elasticity so that the difficulties encountered when directly coupling those two models are mitigated. In addition, in some situations, peridynamics can be used all by itself as a material model that accurately and efficiently captures the behavior of materials over a wide range of spatial and temporal scales. Peridynamics is well suited to these purposes because it employs a nonlocal model of force, analogous to that of molecular dynamics; furthermore, at sufficiently large length scales and assuming smooth deformation, peridynamics can be approximated by classical elasticity. The project will extend the emerging mathematical and numerical analysis of peridynamics. One goal is to develop a peridynamics-enabled multiscale multi-model that potentially provides a new and more extensive mathematical basis for coupling classical elasticity and molecular dynamics, thus enabling next generation atomistic-to-continuum multiscale simulations. In addition, a rigorous studyof nite element discretizations of peridynamics will be considered. Using the fact that peridynamics is spatially derivative free, we will also characterize the space of admissible peridynamic solutions and carry out systematic analyses of the models, in particular rigorously showing how peridynamics encompasses fracture and other failure phenomena. Additional aspects of the project include the mathematical and numerical analysis of peridynamics applied to stochastic peridynamics models. In summary, the project will make feasible mathematically consistent multiscale models for the analysis and design of advanced materials.« less

Disorder-induced stiffness degradation of highly disordered porous materials

NASA Astrophysics Data System (ADS)

Laubie, Hadrien; Monfared, Siavash; Radjaï, Farhang; Pellenq, Roland; Ulm, Franz-Josef

2017-09-01

The effective mechanical behavior of multiphase solid materials is generally modeled by means of homogenization techniques that account for phase volume fractions and elastic moduli without considering the spatial distribution of the different phases. By means of extensive numerical simulations of randomly generated porous materials using the lattice element method, the role of local textural properties on the effective elastic properties of disordered porous materials is investigated and compared with different continuum micromechanics-based models. It is found that the pronounced disorder-induced stiffness degradation originates from stress concentrations around pore clusters in highly disordered porous materials. We identify a single disorder parameter, φsa, which combines a measure of the spatial disorder of pores (the clustering index, sa) with the pore volume fraction (the porosity, φ) to scale the disorder-induced stiffness degradation. Thus, we conclude that the classical continuum micromechanics models with one spherical pore phase, due to their underlying homogeneity assumption fall short of addressing the clustering effect, unless additional texture information is introduced, e.g. in form of the shift of the percolation threshold with disorder, or other functional relations between volume fractions and spatial disorder; as illustrated herein for a differential scheme model representative of a two-phase (solid-pore) composite model material.

Microstructure-based hyperelastic models for closed-cell solids

PubMed Central

Wyatt, Hayley

2017-01-01

For cellular bodies involving large elastic deformations, mesoscopic continuum models that take into account the interplay between the geometry and the microstructural responses of the constituents are developed, analysed and compared with finite-element simulations of cellular structures with different architecture. For these models, constitutive restrictions for the physical plausibility of the material responses are established, and global descriptors such as nonlinear elastic and shear moduli and Poisson’s ratio are obtained from the material characteristics of the constituents. Numerical results show that these models capture well the mechanical responses of finite-element simulations for three-dimensional periodic structures of neo-Hookean material with closed cells under large tension. In particular, the mesoscopic models predict the macroscopic stiffening of the structure when the stiffness of the cell-core increases. PMID:28484340

Microstructure-based hyperelastic models for closed-cell solids.

PubMed

Mihai, L Angela; Wyatt, Hayley; Goriely, Alain

2017-04-01

For cellular bodies involving large elastic deformations, mesoscopic continuum models that take into account the interplay between the geometry and the microstructural responses of the constituents are developed, analysed and compared with finite-element simulations of cellular structures with different architecture. For these models, constitutive restrictions for the physical plausibility of the material responses are established, and global descriptors such as nonlinear elastic and shear moduli and Poisson's ratio are obtained from the material characteristics of the constituents. Numerical results show that these models capture well the mechanical responses of finite-element simulations for three-dimensional periodic structures of neo-Hookean material with closed cells under large tension. In particular, the mesoscopic models predict the macroscopic stiffening of the structure when the stiffness of the cell-core increases.

Microstructure-based hyperelastic models for closed-cell solids

NASA Astrophysics Data System (ADS)

Mihai, L. Angela; Wyatt, Hayley; Goriely, Alain

2017-04-01

For cellular bodies involving large elastic deformations, mesoscopic continuum models that take into account the interplay between the geometry and the microstructural responses of the constituents are developed, analysed and compared with finite-element simulations of cellular structures with different architecture. For these models, constitutive restrictions for the physical plausibility of the material responses are established, and global descriptors such as nonlinear elastic and shear moduli and Poisson's ratio are obtained from the material characteristics of the constituents. Numerical results show that these models capture well the mechanical responses of finite-element simulations for three-dimensional periodic structures of neo-Hookean material with closed cells under large tension. In particular, the mesoscopic models predict the macroscopic stiffening of the structure when the stiffness of the cell-core increases.

Cytoskeletal Mechanics

NASA Astrophysics Data System (ADS)

Mofrad, Mohammad R. K.; Kamm, Roger D.

2011-08-01

1. Introduction and the biological basis for cell mechanics Mohammad R. K. Mofrad and Roger Kamm; 2. Experimental measurements of intracellular mechanics Paul Janmey and Christoph Schmidt; 3. The cytoskeleton as a soft glassy material Jeffrey Fredberg and Ben Fabry; 4. Continuum elastic or viscoelastic models for the cell Mohammad R. K. Mofrad, Helene Karcher and Roger Kamm; 5. Multiphasic models of cell mechanics Farshid Guuilak, Mansoor A. Haider, Lori A. Setton, Tod A. Laursen and Frank P. T. Baaijens; 6. Models of cytoskeletal mechanics based on tensegrity Dimitrije Stamenovic; 7. Cells, gels and mechanics Gerald H. Pollack; 8. Polymer-based models of cytoskeletal networks F. C. MacKintosh; 9. Cell dynamics and the actin cytoskeleton James L. McGrath and C. Forbes Dewey, Jr; 10. Active cellular motion: continuum theories and models Marc Herant and Micah Dembo; 11. Summary Mohammad R. K. Mofrad and Roger Kamm.

Dispersive wave propagation in two-dimensional rigid periodic blocky materials with elastic interfaces

NASA Astrophysics Data System (ADS)

Bacigalupo, Andrea; Gambarotta, Luigi

2017-05-01

Dispersive waves in two-dimensional blocky materials with periodic microstructure made up of equal rigid units, having polygonal centro-symmetric shape with mass and gyroscopic inertia, connected with each other through homogeneous linear interfaces, have been analyzed. The acoustic behavior of the resulting discrete Lagrangian model has been obtained through a Floquet-Bloch approach. From the resulting eigenproblem derived by the Euler-Lagrange equations for harmonic wave propagation, two acoustic branches and an optical branch are obtained in the frequency spectrum. A micropolar continuum model to approximate the Lagrangian model has been derived based on a second-order Taylor expansion of the generalized macro-displacement field. The constitutive equations of the equivalent micropolar continuum have been obtained, with the peculiarity that the positive definiteness of the second-order symmetric tensor associated to the curvature vector is not guaranteed and depends both on the ratio between the local tangent and normal stiffness and on the block shape. The same results have been obtained through an extended Hamiltonian derivation of the equations of motion for the equivalent continuum that is related to the Hill-Mandel macro homogeneity condition. Moreover, it is shown that the hermitian matrix governing the eigenproblem of harmonic wave propagation in the micropolar model is exact up to the second order in the norm of the wave vector with respect to the same matrix from the discrete model. To appreciate the acoustic behavior of some relevant blocky materials and to understand the reliability and the validity limits of the micropolar continuum model, some blocky patterns have been analyzed: rhombic and hexagonal assemblages and running bond masonry. From the results obtained in the examples, the obtained micropolar model turns out to be particularly accurate to describe dispersive functions for wavelengths greater than 3-4 times the characteristic dimension of the block. Finally, in consideration that the positive definiteness of the second order elastic tensor of the micropolar model is not guaranteed, the hyperbolicity of the equation of motion has been investigated by considering the Legendre-Hadamard ellipticity conditions requiring real values for the wave velocity.

A Continuum Damage Mechanics Model to Predict Kink-Band Propagation Using Deformation Gradient Tensor Decomposition

NASA Technical Reports Server (NTRS)

Bergan, Andrew C.; Leone, Frank A., Jr.

2016-01-01

A new model is proposed that represents the kinematics of kink-band formation and propagation within the framework of a mesoscale continuum damage mechanics (CDM) model. The model uses the recently proposed deformation gradient decomposition approach to represent a kink band as a displacement jump via a cohesive interface that is embedded in an elastic bulk material. The model is capable of representing the combination of matrix failure in the frame of a misaligned fiber and instability due to shear nonlinearity. In contrast to conventional linear or bilinear strain softening laws used in most mesoscale CDM models for longitudinal compression, the constitutive response of the proposed model includes features predicted by detailed micromechanical models. These features include: 1) the rotational kinematics of the kink band, 2) an instability when the peak load is reached, and 3) a nonzero plateau stress under large strains.

Is Seismically Determined Q an Intrinsic Material Property?

NASA Astrophysics Data System (ADS)

Langston, C. A.

2003-12-01

The seismic quality factor, Q, has a well-defined physical meaning as an intrinsic material property associated with a visco-elastic or a non-linear stress-strain constitutive relation for a material. Measurement of Q from seismic waves, however, involves interpreting seismic wave amplitude and phase as deviations from some ideal elastic wave propagation model. Thus, assumptions in the elastic wave propagation model become the basis for attributing anelastic properties to the earth continuum. Scientifically, the resulting Q model derived from seismic data is no more than a hypothesis that needs to be verified by other independent experiments concerning the continuum constitutive law and through careful examination of the truth of the assumptions in the wave propagation model. A case in point concerns the anelasticity of Mississippi embayment sediments in the central U.S. that has important implications for evaluation of earthquake strong ground motions. Previous body wave analyses using converted Sp phases have suggested that Qs is ~30 in the sediments based on simple ray theory assumptions. However, detailed modeling of 1D heterogeneity in the sediments shows that Qs cannot be resolved by the Sp data. An independent experiment concerning the amplitude decay of surface waves propagating in the sediments shows that Qs must be generally greater than 80 but is also subject to scattering attenuation. Apparent Q effects seen in direct P and S waves can also be produced by wave tunneling mechanisms in relatively simple 1D heterogeneity. Heterogeneity is a general geophysical attribute of the earth as shown by many high-resolution data sets and should be used as the first litmus test on assumptions made in seismic Q studies before a Q model can be interpreted as an intrinsic material property.

Quasi-periodic oscillations in superfluid, relativistic magnetars with nuclear pasta phases

NASA Astrophysics Data System (ADS)

Passamonti, Andrea; Pons, José A.

2016-12-01

We study the torsional magneto-elastic oscillations of relativistic superfluid magnetars and explore the effects of a phase transition in the crust-core interface (nuclear pasta) which results in a weaker elastic response. Exploring various models with different extension of nuclear pasta phases, we find that the differences in the oscillation spectrum present in purely elastic modes (weak magnetic field) are smeared out with increasing strength of the magnetic field. For magnetar conditions, the main characteristic and features of models without nuclear pasta are preserved. We find, in general, two classes of magneto-elastic oscillations which exhibit a different oscillation pattern. For Bp < 4 × 1014 G, the spectrum is characterized by the turning points and edges of the continuum which are mostly confined into the star's core, and have no constant phase. Increasing the magnetic field, we find, in addition, several magneto-elastic oscillations which reach the surface and have an angular structure similar to crustal modes. These global magneto-elastic oscillations show a constant phase and become dominant when Bp > 5 × 1014 G. We do not find any evidence of fundamental pure crustal modes in the low-frequency range (below 200 Hz) for Bp ≥ 1014 G.

A coupled/uncoupled deformation and fatigue damage algorithm utilizing the finite element method

NASA Technical Reports Server (NTRS)

Wilt, Thomas E.; Arnold, Steven M.

1994-01-01

A fatigue damage computational algorithm utilizing a multiaxial, isothermal, continuum based fatigue damage model for unidirectional metal matrix composites has been implemented into the commercial finite element code MARC using MARC user subroutines. Damage is introduced into the finite element solution through the concept of effective stress which fully couples the fatigue damage calculations with the finite element deformation solution. An axisymmetric stress analysis was performed on a circumferentially reinforced ring, wherein both the matrix cladding and the composite core were assumed to behave elastic-perfectly plastic. The composite core behavior was represented using Hill's anisotropic continuum based plasticity model, and similarly, the matrix cladding was represented by an isotropic plasticity model. Results are presented in the form of S-N curves and damage distribution plots.

A continuum-based structural modeling approach for cellulose nanocrystals (CNCs)

NASA Astrophysics Data System (ADS)

Shishehbor, Mehdi; Dri, Fernando L.; Moon, Robert J.; Zavattieri, Pablo D.

2018-02-01

We present a continuum-based structural model to study the mechanical behavior of cellulose nanocrystals (CNCs), and analyze the effect of bonded and non-bonded interactions on the mechanical properties under various loading conditions. In particular, this model assumes the uncoupling between the bonded and non-bonded interactions and their behavior is obtained from atomistic simulations. Our results indicates that the major contribution to the tensile and bending stiffness is mainly due to the cellulose chain stiffness, and the shear behavior is mainly governed by Van der Waals (VdW) forces. In addition, we report a negligible torsional stiffness, which may explain the CNC tendency to easily twist under very small or nonexistent torques. In addition, the sensitivity of geometrical imperfection on the mechanical properties using an analytical model of the CNC structure was investigated. Our results indicate that the presence of imperfections have a small influence on the majority of the elastic properties. Finally, it is shown that a simple homogeneous and orthotropic representation of a CNC under bending underestimates the contribution of non-bonded interaction leading up to 60% error in the calculation of the bending stiffness of CNCs. On the other hand, the proposed model can lead to more accurate predictions of the elastic behavior of CNCs. This is the first step toward the development of a more efficient model that can be used to model the inelastic behavior of single and multiple CNCs.

Packaging double-helical DNA into viral capsids.

PubMed

LaMarque, Jaclyn C; Le, Thuc-Vy L; Harvey, Stephen C

2004-02-15

DNA packaging in bacteriophage P4 has been examined using a molecular mechanics model with a reduced representation containing one pseudoatom per turn of the double helix. The model is a discretized version of an elastic continuum model. The DNA is inserted piecewise into the model capsid, with the structure being reoptimized after each piece is inserted. Various optimization protocols were investigated, and it was found that molecular dynamics at a very low temperature (0.3 K) produces the optimal packaged structure. This structure is a concentric spool, rather than the coaxial spool that has been commonly accepted for so many years. This geometry, which was originally suggested by Hall and Schellman in 1982 (Biopolymers Vol. 21, pp. 2011-2031), produces a lower overall elastic energy than coaxial spooling. Copyright 2003 Wiley Periodicals, Inc.

The notion of a plastic material spin in atomistic simulations

NASA Astrophysics Data System (ADS)

Dickel, D.; Tenev, T. G.; Gullett, P.; Horstemeyer, M. F.

2016-12-01

A kinematic algorithm is proposed to extend existing constructions of strain tensors from atomistic data to decouple elastic and plastic contributions to the strain. Elastic and plastic deformation and ultimately the plastic spin, useful quantities in continuum mechanics and finite element simulations, are computed from the full, discrete deformation gradient and an algorithm for the local elastic deformation gradient. This elastic deformation gradient algorithm identifies a crystal type using bond angle analysis (Ackland and Jones 2006 Phys. Rev. B 73 054104) and further exploits the relationship between bond angles to determine the local deformation from an ideal crystal lattice. Full definitions of plastic deformation follow directly using a multiplicative decomposition of the deformation gradient. The results of molecular dynamics simulations of copper in simple shear and torsion are presented to demonstrate the ability of these new discrete measures to describe plastic material spin in atomistic simulation and to compare them with continuum theory.

A computational continuum model of poroelastic beds

PubMed Central

Zampogna, G. A.

2017-01-01

Despite the ubiquity of fluid flows interacting with porous and elastic materials, we lack a validated non-empirical macroscale method for characterizing the flow over and through a poroelastic medium. We propose a computational tool to describe such configurations by deriving and validating a continuum model for the poroelastic bed and its interface with the above free fluid. We show that, using stress continuity condition and slip velocity condition at the interface, the effective model captures the effects of small changes in the microstructure anisotropy correctly and predicts the overall behaviour in a physically consistent and controllable manner. Moreover, we show that the performance of the effective model is accurate by validating with fully microscopic resolved simulations. The proposed computational tool can be used in investigations in a wide range of fields, including mechanical engineering, bio-engineering and geophysics. PMID:28413355

Carnivora Population Dynamics Are as Slow and as Fast as Those of Other Mammals: Implications for Their Conservation

PubMed Central

van de Kerk, Madelon; de Kroon, Hans; Conde, Dalia A.; Jongejans, Eelke

2013-01-01

Of the 285 species of Carnivora 71 are threatened, while many of these species fulfill important ecological roles in their ecosystems as top or meso-predators. Population transition matrices make it possible to study how age-specific survival and fecundity affect population growth, extinction risks, and responses to management strategies. Here we review 38 matrix models from 35 studies on 27 Carnivora taxa, covering 11% of the threatened Carnivora species. We show that the elasticity patterns (i.e. distribution over fecundity, juvenile survival and adult survival) in Carnivora cover the same range in triangular elasticity plots as those of other mammal species, despite the specific place of Carnivora in the food chain. Furthermore, reproductive loop elasticity analysis shows that the studied species spread out evenly over a slow-fast continuum, but also quantifies the large variation in the duration of important life cycles and their contributions to population growth rate. These general elasticity patterns among species, and their correlation with simple life history characteristics like body mass, age of first reproduction and life span, enables the extrapolation of population dynamical properties to unstudied species. With several examples we discuss how this slow-fast continuum, and related patterns of variation in reproductive loop elasticity, can be used in the formulation of tentative management plans for threatened species that cannot wait for the results of thorough demographic studies. We argue, however, that such management programs should explicitly include a plan for learning about the key demographic rates and how these are affected by environmental drivers and threats. PMID:23950922

On deformation of complex continuum immersed in a plane space

NASA Astrophysics Data System (ADS)

Kovalev, V. A.; Murashkin, E. V.; Radayev, Y. N.

2018-05-01

The present paper is devoted to mathematical modelling of complex continua deformations considered as immersed in an external plane space. The complex continuum is defined as a differential manifold supplied with metrics induced by the external space. A systematic derivation of strain tensors by notion of isometric immersion of the complex continuum into a plane space of a higher dimension is proposed. Problem of establishing complete systems of irreducible objective strain and extrastrain tensors for complex continuum immersed in an external plane space is resolved. The solution to the problem is obtained by methods of the field theory and the theory of rational algebraic invariants. Strain tensors of the complex continuum are derived as irreducible algebraic invariants of contravariant vectors of the external space emerging as functional arguments in the complex continuum action density. Present analysis is restricted to rational algebraic invariants. Completeness of the considered systems of rational algebraic invariants is established for micropolar elastic continua. Rational syzygies for non-quadratic invariants are discussed. Objective strain tensors (indifferent to frame rotations in the external plane space) for micropolar continuum are alternatively obtained by properly combining multipliers of polar decompositions of deformation and extra-deformation gradients. The latter is realized only for continua immersed in a plane space of the equal mathematical dimension.

Patterns of Carbon Nanotubes by Flow-Directed Deposition on Substrates with Architectured Topographies.

PubMed

K Jawed, M; Hadjiconstantinou, N G; Parks, D M; Reis, P M

2018-03-14

We develop and perform continuum mechanics simulations of carbon nanotube (CNT) deployment directed by a combination of surface topography and rarefied gas flow. We employ the discrete elastic rods method to model the deposition of CNT as a slender elastic rod that evolves in time under two external forces, namely, van der Waals (vdW) and aerodynamic drag. Our results confirm that this self-assembly process is analogous to a previously studied macroscopic system, the "elastic sewing machine", where an elastic rod deployed onto a moving substrate forms nonlinear patterns. In the case of CNTs, the complex patterns observed on the substrate, such as coils and serpentines, result from an intricate interplay between van der Waals attraction, rarefied aerodynamics, and elastic bending. We systematically sweep through the multidimensional parameter space to quantify the pattern morphology as a function of the relevant material, flow, and geometric parameters. Our findings are in good agreement with available experimental data. Scaling analysis involving the relevant forces helps rationalize our observations.

A SPH elastic-viscoplastic model for granular flows and bed-load transport

NASA Astrophysics Data System (ADS)

Ghaïtanellis, Alex; Violeau, Damien; Ferrand, Martin; Abderrezzak, Kamal El Kadi; Leroy, Agnès; Joly, Antoine

2018-01-01

An elastic-viscoplastic model (Ulrich, 2013) is combined to a multi-phase SPH formulation (Hu and Adams, 2006; Ghaitanellis et al., 2015) to model granular flows and non-cohesive sediment transport. The soil is treated as a continuum exhibiting a viscoplastic behaviour. Thus, below a critical shear stress (i.e. the yield stress), the soil is assumed to behave as an isotropic linear-elastic solid. When the yield stress is exceeded, the soil flows and behaves as a shear-thinning fluid. A liquid-solid transition threshold based on the granular material properties is proposed, so as to make the model free of numerical parameter. The yield stress is obtained from Drucker-Prager criterion that requires an accurate computation of the effective stress in the soil. A novel method is proposed to compute the effective stress in SPH, solving a Laplace equation. The model is applied to a two-dimensional soil collapse (Bui et al., 2008) and a dam break over mobile beds (Spinewine and Zech, 2007). Results are compared with experimental data and a good agreement is obtained.

Model Reduction in Biomechanics

NASA Astrophysics Data System (ADS)

Feng, Yan

The mechanical characteristic of the cell is primarily performed by the cytoskeleton. Microtubules, actin, and intermediate filaments are the three main cytoskeletal polymers. Of these, microtubules are the stiffest and have multiple functions within a cell that include: providing tracks for intracellular transport, transmitting the mechanical force necessary for cell division during mitosis, and providing sufficient stiffness for propulsion in flagella and cilia. Microtubule mechanics has been studied by a variety of methods: detailed molecular dynamics (MD), coarse-grained models, engineering type models, and elastic continuum models. In principle, atomistic MD simulations should be able to predict all desired mechanical properties of a single molecule, however, in practice the large computational resources are required to carry out a simulation of larger biomolecular system. Due to the limited accessibility using even the most ambitious all-atom models and the demand for the multiscale molecular modeling and simulation, the emergence of the reduced models is critically important to provide the capability for investigating the biomolecular dynamics that are critical to many biological processes. Then the coarse-grained models, such as elastic network models and anisotropic network models, have been shown to bequite accurate in predicting microtubule mechanical response, but still requires significant computational resources. On the other hand, the microtubule is treated as comprising materials with certain continuum material properties. Such continuum models, especially Euler-Bernoulli beam models, are often used to extract mechanical parameters from experimental results. The microtubule is treated as comprising materials with certain continuum material properties. Such continuum models, especially Euler-Bernoulli beam models in which the biomolecular system is assumed as homogeneous isotropic materials with solid cross-sections, are often used to extract mechanical parameters from experimental results. However, in real biological world, these homogeneous and isotropic assumptions are usually invalidate. Thus, instead of using hypothesized model, a specific continuum model at mesoscopic scale can be introduced based upon data reduction of the results from molecular simulations at atomistic level. Once a continuum model is established, it can provide details on the distribution of stresses and strains induced within the biomolecular system which is useful in determining the distribution and transmission of these forces to the cytoskeletal and sub-cellular components, and help us gain a better understanding in cell mechanics. A data-driven model reduction approach to the problem of microtubule mechanics as an application is present, a beam element is constructed for microtubules based upon data reduction of the results from molecular simulation of the carbon backbone chain of alphabeta-tubulin dimers. The data base of mechanical responses to various types of loads from molecular simulation is reduced to dominant modes. The dominant modes are subsequently used to construct the stiffness matrix of a beam element that captures the anisotropic behavior and deformation mode coupling that arises from a microtubule's spiral structure. In contrast to standard Euler-Bernoulli or Timoshenko beam elements, the link between forces and node displacements results not from hypothesized deformation behavior, but directly from the data obtained by molecular scale simulation. Differences between the resulting microtubule data-driven beam model (MTDDBM) and standard beam elements are presented, with a focus on coupling of bending, stretch, shear deformations. The MTDDBM is just as economical to use as a standard beam element, and allows accurate reconstruction of the mechanical behavior of structures within a cell as exemplified in a simple model of a component element of the mitotic spindle.

Cross-Linked Nanotube Materials with Variable Stiffness Tethers

NASA Technical Reports Server (NTRS)

Frankland, Sarah-Jane V.; Odegard, Gregory M.; Herzog, Matthew N.; Gates, Thomas S.; Fay, Catherine C.

2004-01-01

The constitutive properties of a cross-linked single-walled carbon nanotube material are predicted with a multi-scale model. The material is modeled as a transversely isotropic solid using concepts from equivalent-continuum modeling. The elastic constants are determined using molecular dynamics simulation. Some parameters of the molecular force field are determined specifically for the cross-linker from ab initio calculations. A demonstration of how the cross-linked nanotubes may affect the properties of a nanotube/polyimide composite is included using a micromechanical analysis.

He 3 ( α , γ ) Be 7 and H 3 ( α , γ ) Li 7 astrophysical S factors from the no-core shell model with continuum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dohet-Eraly, Jeremy; Navratil, Petr; Quaglioni, Sofia

The 3He(α,γ) 7Be and 3H(α,γ) 7Li astrophysical S factors are calculated within the no-core shell model with continuum using a renormalized chiral nucleon–nucleon interaction. The 3He(α,γ) 7Be astrophysical S factors agree reasonably well with the experimental data while the 3H(α,γ) 7Li ones are overestimated. The seven-nucleon bound and resonance states and the α + 3He/ 3H elastic scattering are also studied and compared with experiment. Here, the low-lying resonance properties are rather well reproduced by our approach. At low energies, the s-wave phase shift, which is non-resonant, is overestimated.

Elastic continuum theory: towards understanding of the twist-bend nematic phases.

PubMed

Barbero, G; Evangelista, L R; Rosseto, M P; Zola, R S; Lelidis, I

2015-09-01

The twist-bend nematic phase, N_{TB}, may be viewed as a heliconical molecular arrangement in which the director n precesses uniformly about an extra director field, t. It corresponds to a nematic ground state exhibiting nanoscale periodic modulation. To demonstrate the stability of this phase from the elastic point of view, a natural extension of the Frank elastic energy density is proposed. The elastic energy density is built in terms of the elements of symmetry of the new phase in which intervene the components of these director fields together with the usual Cartesian tensors. It is shown that the ground state corresponds to a deformed state for which K_{22}>K_{33}. In the framework of the model, the phase transition between the usual and the twist-bend nematic phase is of second order with a finite wave vector. The model does not require a negative K_{33} in agreement with recent experimental data that yield K_{33}>0. A threshold is predicted for the molecular twist power below which no transition to a twist-bend nematic may occur.

A musculo-mechanical model of esophageal transport based on an immersed boundary-finite element approach

NASA Astrophysics Data System (ADS)

Kou, Wenjun; Griffith, Boyce E.; Pandolfino, John E.; Kahrilas, Peter J.; Patankar, Neelesh A.

2015-11-01

This work extends a fiber-based immersed boundary (IB) model of esophageal transport by incorporating a continuum model of the deformable esophageal wall. The continuum-based esophagus model adopts finite element approach that is capable of describing more complex and realistic material properties and geometries. The leakage from mismatch between Lagrangian and Eulerian meshes resulting from large deformations of the esophageal wall is avoided by careful choice of interaction points. The esophagus model, which is described as a multi-layered, fiber-reinforced nonlinear elastic material, is coupled to bolus and muscle-activation models using the IB approach to form the esophageal transport model. Cases of esophageal transport with different esophagus models are studied. Results on the transport characteristics, including pressure field and esophageal wall kinematics and stress, are analyzed and compared. Support from NIH grant R01 DK56033 and R01 DK079902 is gratefully acknowledged. BEG is supported by NSF award ACI 1460334.

Anomalous properties of the acoustic excitations in glasses on the mesoscopic length scale.

PubMed

Monaco, Giulio; Mossa, Stefano

2009-10-06

The low-temperature thermal properties of dielectric crystals are governed by acoustic excitations with large wavelengths that are well described by plane waves. This is the Debye model, which rests on the assumption that the medium is an elastic continuum, holds true for acoustic wavelengths large on the microscopic scale fixed by the interatomic spacing, and gradually breaks down on approaching it. Glasses are characterized as well by universal low-temperature thermal properties that are, however, anomalous with respect to those of the corresponding crystalline phases. Related universal anomalies also appear in the low-frequency vibrational density of states and, despite a longstanding debate, remain poorly understood. By using molecular dynamics simulations of a model monatomic glass of extremely large size, we show that in glasses the structural disorder undermines the Debye model in a subtle way: The elastic continuum approximation for the acoustic excitations breaks down abruptly on the mesoscopic, medium-range-order length scale of approximately 10 interatomic spacings, where it still works well for the corresponding crystalline systems. On this scale, the sound velocity shows a marked reduction with respect to the macroscopic value. This reduction turns out to be closely related to the universal excess over the Debye model prediction found in glasses at frequencies of approximately 1 THz in the vibrational density of states or at temperatures of approximately 10 K in the specific heat.

Nonlinear finite-element analysis of nanoindentation of viral capsids

NASA Astrophysics Data System (ADS)

Gibbons, Melissa M.; Klug, William S.

2007-03-01

Recent atomic force microscope (AFM) nanoindentation experiments measuring mechanical response of the protein shells of viruses have provided a quantitative description of their strength and elasticity. To better understand and interpret these measurements, and to elucidate the underlying mechanisms, this paper adopts a course-grained modeling approach within the framework of three-dimensional nonlinear continuum elasticity. Homogeneous, isotropic, elastic, thick-shell models are proposed for two capsids: the spherical cowpea chlorotic mottle virus (CCMV), and the ellipsocylindrical bacteriophage ϕ29 . As analyzed by the finite-element method, these models enable parametric characterization of the effects of AFM tip geometry, capsid dimensions, and capsid constitutive descriptions. The generally nonlinear force response of capsids to indentation is shown to be insensitive to constitutive particulars, and greatly influenced by geometric and kinematic details. Nonlinear stiffening and softening of the force response is dependent on the AFM tip dimensions and shell thickness. Fits of the models capture the roughly linear behavior observed in experimental measurements and result in estimates of Young’s moduli of ≈280-360MPa for CCMV and ≈4.5GPa for ϕ29 .

Computational mechanics of viral capsids.

PubMed

Gibbons, Melissa M; Perotti, Luigi E; Klug, William S

2015-01-01

Viral capsids undergo significant mechanical deformations during their assembly, maturation, and infective life-span. In order to characterize the mechanics of viral capsids, their response to applied external forces is analyzed in several experimental studies using, for instance, Atomic Force Microscope (AFM) indentation experiments. In recent years, a broader approach to study the mechanics of viral capsids has leveraged the theoretical tools proper of continuum mechanics. Even though the theory of continuum elasticity is most commonly used to study deformable bodies at larger macroscopic length scales, it has been shown that this very rich theoretical field can still offer useful insights into the mechanics of viral structures at the nanometer scale. Here we show the construction of viral capsid continuum mechanics models starting from different forms of experimental data. We will discuss the kinematics assumptions, the issue of the reference configuration, the material constitutive laws, and the numerical discretization necessary to construct a complete Finite Element capsid mechanical model. Some examples in the second part of the chapter will show the predictive capabilities of the constructed models and underline useful practical aspects related to efficiency and accuracy. We conclude each example by collecting several key findings discovered by simulating AFM indentation experiments using the constructed numerical models.

Analytical and experimental investigations of human spine flexure.

NASA Technical Reports Server (NTRS)

Moffatt, C. A.; Advani, S. H.; Lin, C.-J.

1971-01-01

The authors report on experiments to measure the resistance of fresh human spines to flexion in the upper lumbar and lower thoracic regions and evaluate results by using a combination of strength of materials theory and effects of shear and comparing with data reported by other authors. The test results indicate that the thoraco-lumbar spine behaves approximately as a linear elastic beam, without relaxation effects. The authors formulate a simple continuum dynamic model of the spine simulating aircraft ejection and solve the resulting boundary value problem to illustrate the importance of the flexural mode. A constant cross-section, the selected model is a sinusoidally curved elastic beam with an end mass subjected to a Heaviside axial acceleration at the other end. The paper presents transient response results for the spinal model axial and bending displacements and axial force.-

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mandal, A.; Gupta, Y. M.

To understand the elastic-plastic deformation response of shock-compressed molybdenum (Mo) – a body-centered cubic (BCC) metal, single crystal samples were shocked along the [100] crystallographic orientation to an elastic impact stress of 12.5 GPa. Elastic-plastic wave profiles, measured at different propagation distances ranging between ~0.23 to 2.31 mm using laser interferometry, showed a time-dependent material response. Within experimental scatter, the measured elastic wave amplitudes were nearly constant over the propagation distances examined. These data point to a large and rapid elastic wave attenuation near the impact surface, before reaching a threshold value (elastic limit) of ~3.6 GPa. Numerical simulations ofmore » the measured wave profiles, performed using a dislocation-based continuum model, suggested that {110}<111> and/or {112}<111> slip systems are operative under shock loading. In contrast to shocked metal single crystals with close-packed structures, the measured wave profiles in Mo single crystals could not be explained in terms of dislocation multiplication alone. A dislocation generation mechanism, operative for shear stresses larger than that at the elastic limit, was required to model the rapid elastic wave attenuation and to provide a good overall match to the measured wave profiles. However, the physical basis for this mechanism was not established for the high-purity single crystal samples used in this study. As a result, the numerical simulations also suggested that Mo single crystals do not work harden significantly under shock loading in contrast to the behavior observed under quasi-static loading.« less

Continuum Approaches to Understanding Ion and Peptide Interactions with the Membrane

PubMed Central

Latorraca, Naomi R.; Callenberg, Keith M.; Boyle, Jon P.; Grabe, Michael

2014-01-01

Experimental and computational studies have shown that cellular membranes deform to stabilize the inclusion of transmembrane (TM) proteins harboring charge. Recent analysis suggests that membrane bending helps to expose charged and polar residues to the aqueous environment and polar head groups. We previously used elasticity theory to identify membrane distortions that minimize the insertion of charged TM peptides into the membrane. Here, we extend our work by showing that it also provides a novel, computationally efficient method for exploring the energetics of ion and small peptide penetration into membranes. First, we show that the continuum method accurately reproduces energy profiles and membrane shapes generated from molecular simulations of bare ion permeation at a fraction of the computational cost. Next, we demonstrate that the dependence of the ion insertion energy on the membrane thickness arises primarily from the elastic properties of the membrane. Moreover, the continuum model readily provides a free energy decomposition into components not easily determined from molecular dynamics. Finally, we show that the energetics of membrane deformation strongly depend on membrane patch size both for ions and peptides. This dependence is particularly strong for peptides based on simulations of a known amphipathic, membrane binding peptide from the human pathogen Toxoplasma gondii. In total, we address shortcomings and advantages that arise from using a variety of computational methods in distinct biological contexts. PMID:24652510

Additive manufacturing of patient-specific tubular continuum manipulators

NASA Astrophysics Data System (ADS)

Amanov, Ernar; Nguyen, Thien-Dang; Burgner-Kahrs, Jessica

2015-03-01

Tubular continuum robots, which are composed of multiple concentric, precurved, elastic tubes, provide more dexterity than traditional surgical instruments at the same diameter. The tubes can be precurved such that the resulting manipulator fulfills surgical task requirements. Up to now the only material used for the component tubes of those manipulators is NiTi, a super-elastic shape-memory alloy of nickel and titan. NiTi is a cost-intensive material and fabrication processes are complex, requiring (proprietary) technology, e.g. for shape setting. In this paper, we evaluate component tubes made of 3 different thermoplastic materials (PLA, PCL and nylon) using fused filament fabrication technology (3D printing). This enables quick and cost-effective production of custom, patient-specific continuum manipulators, produced on site on demand. Stress-strain and deformation characteristics are evaluated experimentally for 16 fabricated tubes of each thermoplastic with diameters and shapes equivalent to those of NiTi tubes. Tubes made of PCL and nylon exhibit properties comparable to those made of NiTi. We further demonstrate a tubular continuum manipulator composed of 3 nylon tubes in a transnasal, transsphenoidal skull base surgery scenario in vitro.

A constitutive law for degrading bioresorbable polymers.

PubMed

Samami, Hassan; Pan, Jingzhe

2016-06-01

This paper presents a constitutive law that predicts the changes in elastic moduli, Poisson's ratio and ultimate tensile strength of bioresorbable polymers due to biodegradation. During biodegradation, long polymer chains are cleaved by hydrolysis reaction. For semi-crystalline polymers, the chain scissions also lead to crystallisation. Treating each scission as a cavity and each new crystal as a solid inclusion, a degrading semi-crystalline polymer can be modelled as a continuum solid containing randomly distributed cavities and crystal inclusions. The effective elastic properties of a degrading polymer are calculated using existing theories for such solid and the tensile strength of the degrading polymer is predicted using scaling relations that were developed for porous materials. The theoretical model for elastic properties and the scaling law for strength form a complete constitutive relation for the degrading polymers. It is shown that the constitutive law can capture the trend of the experimental data in the literature for a range of biodegradable polymers fairly well. Copyright © 2016 Elsevier Ltd. All rights reserved.

Spatially localized structure-function relations in the elastic properties of sheared articular cartilage

NASA Astrophysics Data System (ADS)

Silverberg, Jesse; Bonassar, Lawrence; Cohen, Itai

2013-03-01

Contemporary developments in therapeutic tissue engineering have been enabled by basic research efforts in the field of biomechanics. Further integration of technology in medicine requires a deeper understanding of the mechanical properties of soft biological materials and the structural origins of their response under extreme stresses and strains. Drawing on the science generated by the ``Extreme Mechanics'' community, we present experimental results on the mechanical properties of articular cartilage, a hierarchically structured soft biomaterial found in the joints of mammalian long bones. Measurements of the spatially localized structure and mechanical properties will be compared with theoretical descriptions based on networks of deformed rods, poro-visco-elasticity, and standard continuum models. Discrepancies between experiment and theory will be highlighted, and suggestions for how models can be improved will be given.

A viscoelastic model for dielectric elastomers based on a continuum mechanical formulation and its finite element implementation

NASA Astrophysics Data System (ADS)

Bueschel, A.; Klinkel, S.; Wagner, W.

2011-04-01

Smart materials are active and multifunctional materials, which play an important part for sensor and actuator applications. These materials have the potential to transform passive structures into adaptive systems. However, a prerequisite for the design and the optimization of these materials is, that reliable models exist, which incorporate the interaction between the different combinations of thermal, electrical, magnetic, optical and mechanical effects. Polymeric electroelastic materials, so-called electroactive polymer (EAP), own the characteristic to deform if an electric field is applied. EAP's possesses the benefit that they share the characteristic of polymers, these are lightweight, inexpensive, fracture tolerant, elastic, and the chemical and physical structure is well understood. However, the description "electroactive polymer" is a generic term for many kinds of different microscopic mechanisms and polymeric materials. Based on the laws of electromagnetism and elasticity, a visco-electroelastic model is developed and implemented into the finite element method (FEM). The presented three-dimensional solid element has eight nodes and trilinear interpolation functions for the displacement and the electric potential. The continuum mechanics model contains finite deformations, the time dependency and the nearly incompressible behavior of the material. To describe the possible, large time dependent deformations, a finite viscoelastic model with a split of the deformation gradient is used. Thereby the time dependent characteristic of polymeric materials is incorporated through the free energy function. The electromechanical interactions are considered by the electrostatic forces and inside the energy function.

High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

NASA Astrophysics Data System (ADS)

Dumbser, Michael; Peshkov, Ilya; Romenski, Evgeniy; Zanotti, Olindo

2016-06-01

This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell-Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic-parabolic Navier-Stokes-Fourier theory is established for the first time via a formal asymptotic analysis in the stiff relaxation limit. From a numerical point of view, the governing partial differential equations are very challenging, since they form a large nonlinear hyperbolic PDE system that includes stiff source terms and non-conservative products. We apply the successful family of one-step ADER-WENO finite volume (FV) and ADER discontinuous Galerkin (DG) finite element schemes to the HPR model in the stiff relaxation limit, and compare the numerical results with exact or numerical reference solutions obtained for the Euler and Navier-Stokes equations. Numerical convergence results are also provided. To show the universality of the HPR model, the paper is rounded-off with an application to wave propagation in elastic solids, for which one only needs to switch off the strain relaxation source term in the governing PDE system. We provide various examples showing that for the purpose of flow visualization, the distortion tensor A seems to be particularly useful.

Elastic-plastic deformation of molybdenum single crystals shocked along [100

DOE PAGES

Mandal, A.; Gupta, Y. M.

2017-01-24

To understand the elastic-plastic deformation response of shock-compressed molybdenum (Mo) – a body-centered cubic (BCC) metal, single crystal samples were shocked along the [100] crystallographic orientation to an elastic impact stress of 12.5 GPa. Elastic-plastic wave profiles, measured at different propagation distances ranging between ~0.23 to 2.31 mm using laser interferometry, showed a time-dependent material response. Within experimental scatter, the measured elastic wave amplitudes were nearly constant over the propagation distances examined. These data point to a large and rapid elastic wave attenuation near the impact surface, before reaching a threshold value (elastic limit) of ~3.6 GPa. Numerical simulations ofmore » the measured wave profiles, performed using a dislocation-based continuum model, suggested that {110}<111> and/or {112}<111> slip systems are operative under shock loading. In contrast to shocked metal single crystals with close-packed structures, the measured wave profiles in Mo single crystals could not be explained in terms of dislocation multiplication alone. A dislocation generation mechanism, operative for shear stresses larger than that at the elastic limit, was required to model the rapid elastic wave attenuation and to provide a good overall match to the measured wave profiles. However, the physical basis for this mechanism was not established for the high-purity single crystal samples used in this study. As a result, the numerical simulations also suggested that Mo single crystals do not work harden significantly under shock loading in contrast to the behavior observed under quasi-static loading.« less

The Constitutive Modeling of Thin Films with Randon Material Wrinkles

NASA Technical Reports Server (NTRS)

Murphey, Thomas W.; Mikulas, Martin M.

2001-01-01

Material wrinkles drastically alter the structural constitutive properties of thin films. Normally linear elastic materials, when wrinkled, become highly nonlinear and initially inelastic. Stiffness' reduced by 99% and negative Poisson's ratios are typically observed. This paper presents an effective continuum constitutive model for the elastic effects of material wrinkles in thin films. The model considers general two-dimensional stress and strain states (simultaneous bi-axial and shear stress/strain) and neglects out of plane bending. The constitutive model is derived from a traditional mechanics analysis of an idealized physical model of random material wrinkles. Model parameters are the directly measurable wrinkle characteristics of amplitude and wavelength. For these reasons, the equations are mechanistic and deterministic. The model is compared with bi-axial tensile test data for wrinkled Kaptong(Registered Trademark) HN and is shown to deterministically predict strain as a function of stress with an average RMS error of 22%. On average, fitting the model to test data yields an RMS error of 1.2%

Martensite Embryology

NASA Astrophysics Data System (ADS)

Reid, Andrew C. E.; Olson, Gregory B.

2000-03-01

Heterogeneous nucleation of martensite is modeled by examining the strain field of a dislocation array in a nonlinear, nonlocal continuum elastic matrix. The dislocations are modeled by including effects from atomic length scales, which control the dislocation Burger's vector, into a mesoscopic continuum model. The dislocation array models the heterogeneous nucleation source of the Olson/Cohen defect dissociation model, and depending on the potency can give rise to embryos of different character. High potency dislocations give rise to fully developed, classical pre-existing embryos, whereas low-potency dislocations result in the formation of highly nonclassical strain embryos. Heterogeneous nucleation theory is related to nucleation kinetics through the critical driving force for nucleation at a defect of a given potency. Recent stereological and calorimetric kinetic studies in thermoelastic TiNi alloys confirm that these materials exhibit the same form of defect potency distribution and resulting sample-size dependent Martensite start temperature, M_s, as nonthermoelastic FeNi systems. These results together point towards a broad theory of heterogeneous nucleation for both thermoelastic and nonthermoelastic martensites.

A trans-phase granular continuum relation and its use in simulation

NASA Astrophysics Data System (ADS)

Kamrin, Ken; Dunatunga, Sachith; Askari, Hesam

The ability to model a large granular system as a continuum would offer tremendous benefits in computation time compared to discrete particle methods. However, two infamous problems arise in the pursuit of this vision: (i) the constitutive relation for granular materials is still unclear and hotly debated, and (ii) a model and corresponding numerical method must wear ``many hats'' as, in general circumstances, it must be able to capture and accurately represent the material as it crosses through its collisional, dense-flowing, and solid-like states. Here we present a minimal trans-phase model, merging an elastic response beneath a fictional yield criterion, a mu(I) rheology for liquid-like flow above the static yield criterion, and a disconnection rule to model separation of the grains into a low-temperature gas. We simulate our model with a meshless method (in high strain/mixing cases) and the finite-element method. It is able to match experimental data in many geometries, including collapsing columns, impact on granular beds, draining silos, and granular drag problems.

Surface elastic properties in silicon nanoparticles

NASA Astrophysics Data System (ADS)

Melis, Claudio; Giordano, Stefano; Colombo, Luciano

2017-09-01

The elastic behavior of the external surface of a solid body plays a key role in nanomechanical phenomena. While bulk elasticity enjoys the benefits of a robust theoretical understanding, many surface elasticity features remain unexplored: some of them are here addressed by blending together continuum elasticity and atomistic simulations. A suitable readdressing of the surface elasticity theory allows to write the balance equations in arbitrary curvilinear coordinates and to investigate the dependence of the surface elastic parameters on the mean and Gaussian curvatures of the surface. In particular, we predict the radial strain induced by surface effects in spherical and cylindrical silicon nanoparticles and provide evidence that the surface parameters are nearly independent of curvatures and, therefore, of the surface conformation.

Computational Materials Research

NASA Technical Reports Server (NTRS)

Hinkley, Jeffrey A. (Editor); Gates, Thomas S. (Editor)

1996-01-01

Computational Materials aims to model and predict thermodynamic, mechanical, and transport properties of polymer matrix composites. This workshop, the second coordinated by NASA Langley, reports progress in measurements and modeling at a number of length scales: atomic, molecular, nano, and continuum. Assembled here are presentations on quantum calculations for force field development, molecular mechanics of interfaces, molecular weight effects on mechanical properties, molecular dynamics applied to poling of polymers for electrets, Monte Carlo simulation of aromatic thermoplastics, thermal pressure coefficients of liquids, ultrasonic elastic constants, group additivity predictions, bulk constitutive models, and viscoplasticity characterization.

Mathematical and computational modelling of skin biophysics: a review

PubMed Central

2017-01-01

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas. PMID:28804267

Mathematical and computational modelling of skin biophysics: a review

NASA Astrophysics Data System (ADS)

Limbert, Georges

2017-07-01

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas.

Multiscale approach including microfibril scale to assess elastic constants of cortical bone based on neural network computation and homogenization method.

PubMed

Barkaoui, Abdelwahed; Chamekh, Abdessalem; Merzouki, Tarek; Hambli, Ridha; Mkaddem, Ali

2014-03-01

The complexity and heterogeneity of bone tissue require a multiscale modeling to understand its mechanical behavior and its remodeling mechanisms. In this paper, a novel multiscale hierarchical approach including microfibril scale based on hybrid neural network (NN) computation and homogenization equations was developed to link nanoscopic and macroscopic scales to estimate the elastic properties of human cortical bone. The multiscale model is divided into three main phases: (i) in step 0, the elastic constants of collagen-water and mineral-water composites are calculated by averaging the upper and lower Hill bounds; (ii) in step 1, the elastic properties of the collagen microfibril are computed using a trained NN simulation. Finite element calculation is performed at nanoscopic levels to provide a database to train an in-house NN program; and (iii) in steps 2-10 from fibril to continuum cortical bone tissue, homogenization equations are used to perform the computation at the higher scales. The NN outputs (elastic properties of the microfibril) are used as inputs for the homogenization computation to determine the properties of mineralized collagen fibril. The mechanical and geometrical properties of bone constituents (mineral, collagen, and cross-links) as well as the porosity were taken in consideration. This paper aims to predict analytically the effective elastic constants of cortical bone by modeling its elastic response at these different scales, ranging from the nanostructural to mesostructural levels. Our findings of the lowest scale's output were well integrated with the other higher levels and serve as inputs for the next higher scale modeling. Good agreement was obtained between our predicted results and literature data. Copyright © 2013 John Wiley & Sons, Ltd.

Interaction Among Inhomogeneities.

DTIC Science & Technology

1980-12-01

imposed to eigenstrain distribu- tions throughout the inclusion and to the anisotropy of elastic media for matrices. -2- When eigenstrains are of a...introduce any stress field. It is called an impotent inclusion. Such an inclusion exists when an eigenstrain is a gradient of a function which vanishes...Appl. Mech. 44, 591-594 (1977). T. Mura, " Eigenstrains in Lattice Theory," Continuum Models in Discrete Systems, Proc. 2nd Int. Conf., Mont Gabriel

Hyper-elastic modeling and mechanical behavior investigation of porous poly-D-L-lactide/nano-hydroxyapatite scaffold material.

PubMed

Han, Quan Feng; Wang, Ze Wu; Tang, Chak Yin; Chen, Ling; Tsui, Chi Pong; Law, Wing Cheung

2017-07-01

Poly-D-L-lactide/nano-hydroxyapatite (PDLLA/nano-HA) can be used as the biological scaffold material in bone tissue engineering as it can be readily made into a porous composite material with excellent performance. However, constitutive modeling for the mechanical response of porous PDLLA/nano-HA under various stress conditions has been very limited so far. In this work, four types of fundamental compressible hyper-elastic constitutive models were introduced for constitutive modeling and investigation of mechanical behaviors of porous PDLLA/nano-HA. Moreover, the unitary expressions of Cauchy stress tensor have been derived for the PDLLA/nano-HA under uniaxial compression (or stretch), biaxial compression (or stretch), pure shear and simple shear load by using the theory of continuum mechanics. The theoretical results determined from the approach based on the Ogden compressible hyper-elastic constitutive model were in good agreement with the experimental data from the uniaxial compression tests. Furthermore, this approach can also be used to predict the mechanical behaviors of the porous PDLLA/nano-HA material under the biaxial compression (or stretch), pure shear and simple shear. Copyright © 2017 Elsevier Ltd. All rights reserved.

Emergence and stability of intermediate open vesicles in disk-to-vesicle transitions.

PubMed

Li, Jianfeng; Zhang, Hongdong; Qiu, Feng; Shi, An-Chang

2013-07-01

The transition between two basic structures, a disk and an enclosed vesicle, of a finite membrane is studied by examining the minimum energy path (MEP) connecting these two states. The MEP is constructed using the string method applied to continuum elastic membrane models. The results reveal that, besides the commonly observed disk and vesicle, open vesicles (bowl-shaped vesicles or vesicles with a pore) can become stable or metastable shapes. The emergence, stability, and probability distribution of these open vesicles are analyzed. It is demonstrated that open vesicles can be stabilized by higher-order elastic energies. The estimated probability distribution of the different structures is in good agreement with available experiments.

An orthotropic viscoelastic model for the passive myocardium: continuum basis and numerical treatment.

PubMed

Gültekin, Osman; Sommer, Gerhard; Holzapfel, Gerhard A

2016-11-01

This study deals with the viscoelastic constitutive modeling and the respective computational analysis of the human passive myocardium. We start by recapitulating the locally orthotropic inner structure of the human myocardial tissue and model the mechanical response through invariants and structure tensors associated with three orthonormal basis vectors. In accordance with recent experimental findings the ventricular myocardial tissue is assumed to be incompressible, thick-walled, orthotropic and viscoelastic. In particular, one spring element coupled with Maxwell elements in parallel endows the model with viscoelastic features such that four dashpots describe the viscous response due to matrix, fiber, sheet and fiber-sheet fragments. In order to alleviate the numerical obstacles, the strictly incompressible model is altered by decomposing the free-energy function into volumetric-isochoric elastic and isochoric-viscoelastic parts along with the multiplicative split of the deformation gradient which enables the three-field mixed finite element method. The crucial aspect of the viscoelastic formulation is linked to the rate equations of the viscous overstresses resulting from a 3-D analogy of a generalized 1-D Maxwell model. We provide algorithmic updates for second Piola-Kirchhoff stress and elasticity tensors. In the sequel, we address some numerical aspects of the constitutive model by applying it to elastic, cyclic and relaxation test data obtained from biaxial extension and triaxial shear tests whereby we assess the fitting capacity of the model. With the tissue parameters identified, we conduct (elastic and viscoelastic) finite element simulations for an ellipsoidal geometry retrieved from a human specimen.

A model for one-dimensional morphoelasticity and its application to fibroblast-populated collagen lattices.

PubMed

Menon, Shakti N; Hall, Cameron L; McCue, Scott W; McElwain, D L Sean

2017-10-01

The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the continual remodelling and associated structural changes in biological tissues. Furthermore, models drawn from plasticity theory are difficult to apply and interpret in this context, where there is no equivalent of a yield stress or flow rule. In this work, we describe a novel one-dimensional mathematical model of tissue remodelling based on the multiplicative decomposition of the deformation gradient. We express the mechanical effects of remodelling as an evolution equation for the effective strain, a measure of the difference between the current state and a hypothetical mechanically relaxed state of the tissue. This morphoelastic model combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. A novel feature of our model is that while most models describe growth as a continuous quantity, here we begin with discrete cells and develop a continuum representation of lattice remodelling based on an appropriate limit of the behaviour of discrete cells. To demonstrate the utility of our approach, we use this framework to capture qualitative aspects of the continual remodelling observed in fibroblast-populated collagen lattices, in particular its contraction and its subsequent sudden re-expansion when remodelling is interrupted.

Computer simulation of morphological evolution and rafting of {gamma}{prime} particles in Ni-based superalloys under applied stresses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, D.Y.; Chen, L.Q.

Mechanical properties of Ni-based superalloys are strongly affected by the morphology, distribution, and size of {gamma}{prime} precipitates in the {gamma} matrix. The main purpose of this paper is to propose a continuum field approach for modeling the morphology and rafting kinetics of coherent precipitates under applied stresses. This approach can be used to simulate the temporal evolution of arbitrary morphologies and microstructures without any a priori assumption. Recently, the authors applied this approach to the selected variant growth in Ni-Ti alloys under applied stresses using an inhomogeneous modulus approximation. For the {gamma}{prime} precipitates in Ni-based superalloys, the eigenstrain is dilatational,more » and hence the {gamma}{prime} morphological evolution can be affected by applied stresses only when the elastic modulus is inhomogeneous. In the present work, the elastic inhomogeneity was taken into account by reformulating a sharp-interface elasticity theory developed recently by Khachaturyan et al. in terms of diffuse interfaces. Although the present work is for a {gamma}{prime} {minus} {gamma} system, this model is general in a sense that it can be applied to other alloy systems containing coherent ordered intermetallic precipitates with elastic inhomogeneity.« less

Quantum gravity model with fundamental spinor fields

NASA Astrophysics Data System (ADS)

Obukhov, Yu. N.; Hehl, F. W.

2014-01-01

We discuss the possibility that gravitational potentials (metric, coframe and connection) may emerge as composite fields from more fundamental spinor constituents. We use the formalism of Poincaré gauge gravity as an appropriate theoretical scheme for the rigorous development of such an approach. We postulate the constitutive relations of an elastic Cosserat type continuum that models spacetime. These generalized Hooke and MacCullagh type laws consistently take into account the translational and Lorentz rotational deformations, respectively. The resulting theory extends the recently proposed Diakonov model. An intriguing feature of our theory is that in the lowest approximation it reproduces Heisenberg's nonlinear spinor model.

Mechanics of composite materials: Recent advances; Proceedings of the Symposium, Virginia Polytechnic Institute and State University, Blacksburg, VA, August 16-19, 1982

NASA Technical Reports Server (NTRS)

Hashin, Z. (Editor); Herakovich, C. T. (Editor)

1983-01-01

The present conference on the mechanics of composites discusses microstructure's influence on particulate and short fiber composites' thermoelastic and transport properties, the elastoplastic deformation of composites, constitutive equations for viscoplastic composites, the plasticity and fatigue of metal matrix composites, laminate damping mechanisms, the micromechanical modeling of Kevlar/epoxy composites' time-dependent failure, the variational characterization of waves in composites, and computational methods for eigenvalue problems in composite design. Also discussed are the elastic response of laminates, elastic coupling nonlinear effects in unsymmetrical laminates, elasticity solutions for laminate problems having stress singularities, the mechanics of bimodular composite structures, the optimization of laminated plates and shells, NDE for laminates, the role of matrix cracking in the continuum constitutive behavior of a damaged composite ply, and the energy release rates of various microcracks in short fiber composites.

Continuum Multiscale Modeling of Finite Deformation Plasticity and Anisotropic Damage in Polycrystals

DTIC Science & Technology

2006-09-01

also been applied to describe degraded composite materials exhibiting a nominally elastic or viscoelastic response [7]. In brittle ceramics, scalar...assumptions regarding the composition of the material (e.g., crystal structure). 2.2. Stresses and balance relations Let s denote the local nominal...nickel (50 wt.%), iron (25 wt.%), and tungsten (25 wt.%). The composite microstructure nominally is comprised of 90% pure W and 10% matrix alloy, and

Frustration and curvature - Glasses and the cholesteric blue phase

NASA Technical Reports Server (NTRS)

Sethna, J. P.

1983-01-01

An analogy is drawn between continuum elastic theories of the blue phase of cholesteric liquid crystals and recent theories of frustration in configurational glasses. Both involve the introduction of a lattice of disclination lines to relieve frustration; the frustration is due to an intrinsic curvature in the natural form of parallel transport. A continuum theory of configurational glasses is proposed.

Parsimonious evaluation of concentric-tube continuum robot equilibrium conformation.

PubMed

Rucker, Daniel Caleb; Webster Iii, Robert J

2009-09-01

Dexterous at small diameters, continuum robots consisting of precurved concentric tubes are well-suited for minimally invasive surgery. These active cannulas are actuated by relative translations and rotations applied at the tube bases, which create bending via elastic tube interaction. An accurate kinematic model of cannula shape is required for applications in surgical and other settings. Previous models are limited to circular tube precurvatures, and neglect torsional deformation in curved sections. Recent generalizations account for arbitrary tube preshaping and bending and torsion throughout the cannula, providing differential equations that define cannula shape. In this paper, we show how to simplify these equations using Frenet-Serret frames. An advantage of this approach is the interpretation of torsional components of the preset tube shapes as "forcing functions" on the cannula's differential equations. We also elucidate a process for numerically solving the differential equations, and use it to produce simulations illustrating the implications of torsional deformation and helical tube shapes.

High order ADER schemes for a unified first order hyperbolic formulation of Newtonian continuum mechanics coupled with electro-dynamics

NASA Astrophysics Data System (ADS)

Dumbser, Michael; Peshkov, Ilya; Romenski, Evgeniy; Zanotti, Olindo

2017-11-01

In this paper, we propose a new unified first order hyperbolic model of Newtonian continuum mechanics coupled with electro-dynamics. The model is able to describe the behavior of moving elasto-plastic dielectric solids as well as viscous and inviscid fluids in the presence of electro-magnetic fields. It is actually a very peculiar feature of the proposed PDE system that viscous fluids are treated just as a special case of elasto-plastic solids. This is achieved by introducing a strain relaxation mechanism in the evolution equations of the distortion matrix A, which in the case of purely elastic solids maps the current configuration to the reference configuration. The model also contains a hyperbolic formulation of heat conduction as well as a dissipative source term in the evolution equations for the electric field given by Ohm's law. Via formal asymptotic analysis we show that in the stiff limit, the governing first order hyperbolic PDE system with relaxation source terms tends asymptotically to the well-known viscous and resistive magnetohydrodynamics (MHD) equations. Furthermore, a rigorous derivation of the model from variational principles is presented, together with the transformation of the Euler-Lagrange differential equations associated with the underlying variational problem from Lagrangian coordinates to Eulerian coordinates in a fixed laboratory frame. The present paper hence extends the unified first order hyperbolic model of Newtonian continuum mechanics recently proposed in [110,42] to the more general case where the continuum is coupled with electro-magnetic fields. The governing PDE system is symmetric hyperbolic and satisfies the first and second principle of thermodynamics, hence it belongs to the so-called class of symmetric hyperbolic thermodynamically compatible systems (SHTC), which have been studied for the first time by Godunov in 1961 [61] and later in a series of papers by Godunov and Romenski [67,69,119]. An important feature of the proposed model is that the propagation speeds of all physical processes, including dissipative processes, are finite. The model is discretized using high order accurate ADER discontinuous Galerkin (DG) finite element schemes with a posteriori subcell finite volume limiter and using high order ADER-WENO finite volume schemes. We show numerical test problems that explore a rather large parameter space of the model ranging from ideal MHD, viscous and resistive MHD over pure electro-dynamics to moving dielectric elastic solids in a magnetic field.

Modeling elastic anisotropy in strained heteroepitaxy

NASA Astrophysics Data System (ADS)

Krishna Dixit, Gopal; Ranganathan, Madhav

2017-09-01

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the Ge0.25 Si0.75 on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to < 1 0 5 > facets on the surface.

Modeling elastic anisotropy in strained heteroepitaxy.

PubMed

Dixit, Gopal Krishna; Ranganathan, Madhav

2017-09-20

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the [Formula: see text] [Formula: see text] on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to [Formula: see text] facets on the surface.

Towards a Model of Reactive-Cracking: the Role of Reactions, Elasticity and Surface Energy Driven Flow in Poro-elastic Media

NASA Astrophysics Data System (ADS)

Evans, O.; Spiegelman, M. W.; Wilson, C. R.; Kelemen, P. B.

2016-12-01

Many critical processes can be described by reactive fluid flow in brittle media, including hydration/alteration of oceanic plates near spreading ridges, chemical weathering, and dehydration/decarbonation of subducting plates. Such hydration reactions can produce volume changes that may induce stresses large enough to drive fracture in the rock, in turn exposing new reactive surface and modifying the permeability. A better understanding of this potentially rich feedback could also be critical in the design of engineered systems for geologic carbon sequestration. To aid understanding of these processes we have developed a macroscopic continuum description of reactive fluid flow in an elastically deformable porous media. We explore the behaviour of this model by considering a simplified hydration reaction (e.g. olivine + H20 -> serpentine + brucite). In a closed system, these hydration reactions will continue to consume available fluids until the permeability reaches zero, leaving behind it a highly stressed residuum. Our model demonstrates this limiting behaviour, and that the elastic stresses generated are large enough to cause failure/fracture of the host rock. Whilst it is understood that `reactive fracture' is an important mechanism for the continued evolution of this process, it is also proposed that imbibition/surface energy driven flow may play a role. Through a simplified set of computational experiments, we investigate the relative roles of elasticity and surface energy in both a non-reactive purely poro-elastic framework, and then in the presence of reaction. We demonstrate that surface energy can drive rapid diffusion of porosity, thus allowing the reaction to propagate over larger areas. As we expect both surface energy and fracture/failure to be of importance in these processes, we plan to integrate the current model into one that allows for fracture once critical stresses are exceeded.

Lattice continuum and diffusional creep.

PubMed

Mesarovic, Sinisa Dj

2016-04-01

Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro-Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro-Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.

Lattice continuum and diffusional creep

NASA Astrophysics Data System (ADS)

Mesarovic, Sinisa Dj.

2016-04-01

Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro-Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro-Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.

Resistance to alveolar shape change limits range of force propagation in lung parenchyma.

PubMed

Ma, Baoshun; Smith, Bradford J; Bates, Jason H T

2015-06-01

We have recently shown that if the lung parenchyma is modeled in 2 dimensions as a network of springs arranged in a pattern of repeating hexagonal cells, the distortional forces around a contracting airway propagate much further from the airway wall than classic continuum theory predicts. In the present study we tested the hypothesis that this occurs because of the negligible shear modulus of a hexagonal spring network. We simulated the narrowing of an airway embedded in a hexagonal network of elastic alveolar walls when the hexagonal cells of the network offered some resistance to a change in shape. We found that as the forces resisting shape change approach about 10% of the forces resisting length change of an individual spring the range of distortional force propagation in the spring network fell of rapidly as in an elastic continuum. We repeated these investigations in a 3-dimensional spring network composed of space-filling polyhedral cells and found similar results. This suggests that force propagation away from a point of local parenchymal distortion also falls off rapidly in real lung tissue. Copyright © 2015 Elsevier B.V. All rights reserved.

Asymmetric wave transmission in a diatomic acoustic/elastic metamaterial

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Bing; Tan, K. T., E-mail: ktan@uakron.edu

2016-08-21

Asymmetric acoustic/elastic wave transmission has recently been realized using nonlinearity, wave diffraction, or bias effects, but always at the cost of frequency distortion, direction shift, large volumes, or external energy. Based on the self-coupling of dual resonators, we propose a linear diatomic metamaterial, consisting of several small-sized unit cells, to realize large asymmetric wave transmission in low frequency domain (below 1 kHz). The asymmetric transmission mechanism is theoretically investigated, and numerically verified by both mass-spring and continuum models. This passive system does not require any frequency conversion or external energy, and the asymmetric transmission band can be theoretically predicted andmore » mathematically controlled, which extends the design concept of unidirectional transmission devices.« less

Application of bi-Helmholtz nonlocal elasticity and molecular simulations to the dynamical response of carbon nanotubes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koutsoumaris, C. Chr.; Tsamasphyros, G. J.; Vogiatzis, G. G.

2015-12-31

The nonlocal theory of elasticity is employed for the study of the free vibrations of carbon nanotubes (CNT). For the first time, a bi-Helmholtz operator has been used instead of the standard Helmholtz operator in a nonlocal beam model. Alongside the continuum formulation and its numerical solution, atomistic Molecular Dynamics (MD) simulations have been conducted in order to directly evaluate the eigenfrequencies of vibrating CNTs with a minimum of adjustable parameters. Our results show that the bi-Helmholtz operator is the most appropriate one to fit MD simulation results. However, the estimation of vibration eigenfrequencies from molecular simulations still remains anmore » open (albeit well-posed) problem.« less

ChainMail based neural dynamics modeling of soft tissue deformation for surgical simulation.

PubMed

Zhang, Jinao; Zhong, Yongmin; Smith, Julian; Gu, Chengfan

2017-07-20

Realistic and real-time modeling and simulation of soft tissue deformation is a fundamental research issue in the field of surgical simulation. In this paper, a novel cellular neural network approach is presented for modeling and simulation of soft tissue deformation by combining neural dynamics of cellular neural network with ChainMail mechanism. The proposed method formulates the problem of elastic deformation into cellular neural network activities to avoid the complex computation of elasticity. The local position adjustments of ChainMail are incorporated into the cellular neural network as the local connectivity of cells, through which the dynamic behaviors of soft tissue deformation are transformed into the neural dynamics of cellular neural network. Experiments demonstrate that the proposed neural network approach is capable of modeling the soft tissues' nonlinear deformation and typical mechanical behaviors. The proposed method not only improves ChainMail's linear deformation with the nonlinear characteristics of neural dynamics but also enables the cellular neural network to follow the principle of continuum mechanics to simulate soft tissue deformation.

Dilation and Hypertrophy: A Cell-Based Continuum Mechanics Approach Towards Ventricular Growth and Remodeling

NASA Astrophysics Data System (ADS)

Ulerich, J.; Göktepe, S.; Kuhl, E.

This manuscript presents a continuum approach towards cardiac growth and remodeling that is capable to predict chronic maladaptation of the heart in response to changes in mechanical loading. It is based on the multiplicative decomposition of the deformation gradient into and elastic and a growth part. Motivated by morphological changes in cardiomyocyte geometry, we introduce an anisotropic growth tensor that can capture both hypertrophic wall thickening and ventricular dilation within one generic concept. In agreement with clinical observations, we propose wall thickening to be a stress-driven phenomenon whereas dilation is introduced as a strain-driven process. The features of the proposed approach are illustrated in terms of the adaptation of thin heart slices and in terms overload-induced dilation in a generic bi-ventricular heart model.

Relativistic viscoelastic fluid mechanics.

PubMed

Fukuma, Masafumi; Sakatani, Yuho

2011-08-01

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

Relativistic viscoelastic fluid mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fukuma, Masafumi; Sakatani, Yuho

2011-08-15

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for themore » propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.« less

The dynamics and control of large flexible space structures. Part B: Development of continuum model and computer simulation

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Kumar, V. K.; James, P. K.

1978-01-01

The equations of motion of an arbitrary flexible body in orbit were derived. The model includes the effects of gravity with all its higher harmonics. As a specific example, the motion of a long, slender, uniform beam in circular orbit was modelled. The example considers both the inplane and three dimensional motion of the beam in orbit. In the case of planar motion with only flexible vibrations, the pitch motion is not influenced by the elastic motion of the beam. For large values of the square of the ratio of the structural modal frequency to the orbital angular rate the elastic motion was decoupled from the pitch motion. However, for small values of the ratio and small amplitude pitch motion, the elastic motion was governed by a Hill's 3 term equation. Numerical simulation of the equation indicates the possibilities of instability for very low values of the square of the ratio of the modal frequency to the orbit angular rate. Also numerical simulations of the first order nonlinear equations of motion for a long flexible beam in orbit were performed. The effect of varying the initial conditions and the number of modes was demonstrated.

Adhesion of single- and multi-walled carbon nanotubes to silicon substrate: atomistic simulations and continuum analysis

NASA Astrophysics Data System (ADS)

Yuan, Xuebo; Wang, Youshan

2017-10-01

The radial deformation of carbon nanotubes (CNTs) adhering to a substrate may prominently affect their mechanical and physical properties. In this study, both classical atomistic simulations and continuum analysis are carried out, to investigate the lateral adhesion of single-walled CNTs (SWCNTs) and multi-walled CNTs (MWCNTs) to a silicon substrate. A linear elastic model for analyzing the adhesion of 2D shells to a rigid semi-infinite substrate is constructed in the framework of continuum mechanics. Good agreement is achieved between the cross-section profiles of adhesive CNTs obtained by the continuum model and by the atomistic simulation approach. It is found that the adhesion of a CNT to the silicon substrate is significantly influenced by its initial diameter and the number of walls. CNTs with radius larger than a certain critical radius are deformed radially on the silicon substrate with flat contact regions. With increasing number of walls, the extent of radial deformation of a MWCNT on the substrate decreases dramatically, and the flat contact area reduces—and eventually vanishes—due to increasing equivalent bending stiffness. It is analytically predicted that large-diameter MWCNTs with a large number of walls are likely to ‘stand’ on the silicon substrate. The present work can be useful for understanding the radial deformation of CNTs adhering to a solid planar substrate.

Wrinkling instability in graphene supported on nanoparticle-patterned SiO2

NASA Astrophysics Data System (ADS)

Cullen, William; Yamamoto, Mahito; Pierre-Louis, Olivier; Einstein, Theodore; Fuhrer, Michael

2012-02-01

Atomically-thin graphene is arguably the thinnest possible mechanical membrane: graphene's effective thickness (the thickness of an isotropic continuum slab which would have the same elastic and bending stiffness) is significantly less than 1 å, indicating that graphene can distort out-of-plane to conform to sub-nanometer features. Here we study the elastic response of graphene supported on a SiO2 substrate covered with SiO2 nanoparticles. At a low density of nanoparticles, graphene is largely pinned to the substrate due to adhesive interaction. However, with increasing nanoparticle density, graphene's elasticity dominates adhesion and strain is relieved by the formation of wrinkles which connect peaks introduced by the supporting nanoparticles. At a critical density, the wrinkles percolate, resulting in a wrinkle network. We develop a simple elastic model allowing for adhesion which accurately predicts the critical spacing between nanoparticles for wrinkle formation. This work has been supported by the University of Maryland NSF-MRSEC under Grant No. DMR 05-20471 with supplemental funding from NRI, and NSF-DMR 08-04976.

Fundamental analysis of the failure of polymer-based fiber reinforced composites

NASA Technical Reports Server (NTRS)

Kanninen, M. F.; Rybicki, E. F.; Griffith, W. I.; Broek, D.

1975-01-01

A mathematical model predicting the strength of unidirectional fiber reinforced composites containing known flaws and with linear elastic-brittle material behavior was developed. The approach was to imbed a local heterogeneous region surrounding the crack tip into an anisotropic elastic continuum. This (1) permits an explicit analysis of the micromechanical processes involved in the fracture, and (2) remains simple enough to be useful in practical computations. Computations for arbitrary flaw size and orientation under arbitrary applied loads were performed. The mechanical properties were those of graphite epoxy. With the rupture properties arbitrarily varied to test the capabilities of the model to reflect real fracture modes, it was shown that fiber breakage, matrix crazing, crack bridging, matrix-fiber debonding, and axial splitting can all occur during a period of (gradually) increasing load prior to catastrophic failure. The calculations also reveal the sequential nature of the stable crack growth process proceding fracture.

The Modeling of Vibration Damping in SMA Wires

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reynolds, D R; Kloucek, P; Seidman, T I

Through a mathematical and computational model of the physical behavior of shape memory alloy wires, this study shows that localized heating and cooling of such materials provides an effective means of damping vibrational energy. The thermally induced pseudo-elastic behavior of a shape memory wire is modeled using a continuum thermodynamic model and solved computationally as described by the authors in [23]. Computational experiments confirm that up to 80% of an initial shock of vibrational energy can be eliminated at the onset of a thermally-induced phase transformation through the use of spatially-distributed transformation regions along the length of a shape memorymore » alloy wire.« less

Consequences of elastic anisotropy in patterned substrate heteroepitaxy.

PubMed

Dixit, Gopal Krishna; Ranganathan, Madhav

2018-06-13

The role of elastic anisotropy on quantum dot formation and evolution on a pre-patterned substrate is evaluated within the framework of a continuum model. We first extend the formulation for surface evolution to take elastic anisotropy into account. Using a small slope approximation, we derive the evolution equation and show how it can be numerically implemented up to linear and second order for stripe and egg-carton patterned substrates using an accurate and efficient procedure. The semi--infinite nature of the substrate is used to solve the elasticity problem subject to other boundary conditions at the free surface and at the film--substrate interface. The positioning of the quantum dots with respect to the peaks and valleys of the pattern is explained by a competition between the length scale of the pattern and the wavelength of the Asaro--Tiller--Grinfeld instability, which is also affected by the elastic anisotropy. The alignment of dots is affected by a competition between the elastic anisotropy of the film and the pattern orientation. A domain of pattern inversion, wherein the quantum dots form exclusively in the valleys of the patterns is identified as a function of the average film thickness and the elastic anisotropy, and the time--scale for this inversion as function of height is analyzed. © 2018 IOP Publishing Ltd.

Inverse tissue mechanics of cell monolayer expansion.

PubMed

Kondo, Yohei; Aoki, Kazuhiro; Ishii, Shin

2018-03-01

Living tissues undergo deformation during morphogenesis. In this process, cells generate mechanical forces that drive the coordinated cell motion and shape changes. Recent advances in experimental and theoretical techniques have enabled in situ measurement of the mechanical forces, but the characterization of mechanical properties that determine how these forces quantitatively affect tissue deformation remains challenging, and this represents a major obstacle for the complete understanding of morphogenesis. Here, we proposed a non-invasive reverse-engineering approach for the estimation of the mechanical properties, by combining tissue mechanics modeling and statistical machine learning. Our strategy is to model the tissue as a continuum mechanical system and to use passive observations of spontaneous tissue deformation and force fields to statistically estimate the model parameters. This method was applied to the analysis of the collective migration of Madin-Darby canine kidney cells, and the tissue flow and force were simultaneously observed by the phase contrast imaging and traction force microscopy. We found that our monolayer elastic model, whose elastic moduli were reverse-engineered, enabled a long-term forecast of the traction force fields when given the tissue flow fields, indicating that the elasticity contributes to the evolution of the tissue stress. Furthermore, we investigated the tissues in which myosin was inhibited by blebbistatin treatment, and observed a several-fold reduction in the elastic moduli. The obtained results validate our framework, which paves the way to the estimation of mechanical properties of living tissues during morphogenesis.

Completed Beltrami-Michell Formulation in Polar Coordinates

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Hopkins, Dale A.

2005-01-01

A set of conditions had not been formulated on the boundary of an elastic continuum since the time of Saint-Venant. This limitation prevented the formulation of a direct stress calculation method in elasticity for a continuum with a displacement boundary condition. The missed condition, referred to as the boundary compatibility condition, is now formulated in polar coordinates. The augmentation of the new condition completes the Beltrami-Michell formulation in polar coordinates. The completed formulation that includes equilibrium equations and a compatibility condition in the field as well as the traction and boundary compatibility condition is derived from the stationary condition of the variational functional of the integrated force method. The new method is illustrated by solving an example of a mixed boundary value problem for mechanical as well as thermal loads.

Electron impact excitation of methane

NASA Technical Reports Server (NTRS)

Vuskovic, L.; Trajmar, S.

1983-01-01

A crossed molecular beam-electron beam apparatus was employed to examine the excitation cross-sections of CH4. Attention was given to 20, 30, and 200 eV impact energies at angles from 8-130 deg. Spectra were obtained in the elastic and inelastic realms as well as in the ionization continuum in the 12.99-15.0 eV energy-loss range. Differential cross-sections were also determined. The results are useful for modeling the behavior of CH4 in planetary atmospheres.

Computational Overlap Coupling Between Micropolar Linear Elastic Continuum Finite Elements and Nonlinear Elastic Spherical Discrete Elements in One Dimension

DTIC Science & Technology

2013-01-01

Cracking in asphalt pavement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Figure 2. 2D...metallic binder, figure 1(b)), particulate energetic materials (explosive crystalline grains with polymeric binder, figure 1(c)), asphalt pavement (stone...explosive HMX grains and at grain-matrix interfaces (2). (d) Cracking in asphalt pavement . 2 (i) it is limited by current computing power (even

An enhanced version of a bone-remodelling model based on the continuum damage mechanics theory.

PubMed

Mengoni, M; Ponthot, J P

2015-01-01

The purpose of this work was to propose an enhancement of Doblaré and García's internal bone remodelling model based on the continuum damage mechanics (CDM) theory. In their paper, they stated that the evolution of the internal variables of the bone microstructure, and its incidence on the modification of the elastic constitutive parameters, may be formulated following the principles of CDM, although no actual damage was considered. The resorption and apposition criteria (similar to the damage criterion) were expressed in terms of a mechanical stimulus. However, the resorption criterion is lacking a dimensional consistency with the remodelling rate. We propose here an enhancement to this resorption criterion, insuring the dimensional consistency while retaining the physical properties of the original remodelling model. We then analyse the change in the resorption criterion hypersurface in the stress space for a two-dimensional (2D) analysis. We finally apply the new formulation to analyse the structural evolution of a 2D femur. This analysis gives results consistent with the original model but with a faster and more stable convergence rate.

Wave dispersion and propagation in state-based peridynamics

NASA Astrophysics Data System (ADS)

Butt, Sahir N.; Timothy, Jithender J.; Meschke, Günther

2017-11-01

Peridynamics is a nonlocal continuum model which offers benefits over classical continuum models in cases, where discontinuities, such as cracks, are present in the deformation field. However, the nonlocal characteristics of peridynamics leads to a dispersive dynamic response of the medium. In this study we focus on the dispersion properties of a state-based linear peridynamic solid model and specifically investigate the role of the peridynamic horizon. We derive the dispersion relation for one, two and three dimensional cases and investigate the effect of horizon size, mesh size (lattice spacing) and the influence function on the dispersion properties. We show how the influence function can be used to minimize wave dispersion at a fixed lattice spacing and demonstrate it qualitatively by wave propagation analysis in one- and two-dimensional models of elastic solids. As a main contribution of this paper, we propose to associate peridynamic non-locality expressed by the horizon with a characteristic length scale related to the material microstructure. To this end, the dispersion curves obtained from peridynamics are compared with experimental data for two kinds of sandstone.

Adaptive Finite Element Methods for Continuum Damage Modeling

NASA Technical Reports Server (NTRS)

Min, J. B.; Tworzydlo, W. W.; Xiques, K. E.

1995-01-01

The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.

A Continuum Model for the Effect of Dynamic Recrystallization on the Stress⁻Strain Response.

PubMed

Kooiker, H; Perdahcıoğlu, E S; van den Boogaard, A H

2018-05-22

Austenitic Stainless Steels and High-Strength Low-Alloy (HSLA) steels show significant dynamic recovery and dynamic recrystallization (DRX) during hot forming. In order to design optimal and safe hot-formed products, a good understanding and constitutive description of the material behavior is vital. A new continuum model is presented and validated on a wide range of deformation conditions including high strain rate deformation. The model is presented in rate form to allow for the prediction of material behavior in transient process conditions. The proposed model is capable of accurately describing the stress⁻strain behavior of AISI 316LN in hot forming conditions, also the high strain rate DRX-induced softening observed during hot torsion of HSLA is accurately predicted. It is shown that the increase in recrystallization rate at high strain rates observed in experiments can be captured by including the elastic energy due to the dynamic stress in the driving pressure for recrystallization. Furthermore, the predicted resulting grain sizes follow the power-law dependence with steady state stress that is often reported in literature and the evolution during hot deformation shows the expected trend.

Quasistatic elastoplasticity via Peridynamics: existence and localization

NASA Astrophysics Data System (ADS)

Kružík, Martin; Mora-Corral, Carlos; Stefanelli, Ulisse

2018-04-01

Peridynamics is a nonlocal continuum mechanical theory based on minimal regularity on the deformations. Its key trait is that of replacing local constitutive relations featuring spacial differential operators with integrals over differences of displacement fields over a suitable positive interaction range. The advantage of such perspective is that of directly including nonregular situations, in which discontinuities in the displacement field may occur. In the linearized elastic setting, the mechanical foundation of the theory and its mathematical amenability have been thoroughly analyzed in the last years. We present here the extension of Peridynamics to linearized elastoplasticity. This calls for considering the time evolution of elastic and plastic variables, as the effect of a combination of elastic energy storage and plastic energy dissipation mechanisms. The quasistatic evolution problem is variationally reformulated and solved by time discretization. In addition, by a rigorous evolutive Γ -convergence argument we prove that the nonlocal peridynamic model converges to classic local elastoplasticity as the interaction range goes to zero.

Dirac bubble potential for He-He and inadequacies in the continuum: Comparing an analytic model with elastic collision experiments

NASA Astrophysics Data System (ADS)

Chrysos, Michael

2017-01-01

We focus on the long-pending issue of the inadequacy of the Dirac bubble potential model in the description of He-He interactions in the continuum [L. L. Lohr and S. M. Blinder, Int. J. Quantum Chem. 53, 413 (1995)]. We attribute this failure to the lack of a potential wall to mimic the onset of the repulsive interaction at close range separations. This observation offers the explanation to why this excessively simple model proves incapable of quantitatively reproducing previous experimental findings of glory scattering in He-He, although being notorious for its capability of reproducing several distinctive features of the atomic and isotopic helium dimers and trimers [L. L. Lohr and S. M. Blinder, Int. J. Quantum Chem. 90, 419 (2002)]. Here, we show that an infinitely high, energy-dependent potential wall of properly calculated thickness rc(E) taken as a supplement to the Dirac bubble potential suffices for agreement with variable-energy elastic collision cross section experiments for 4He-4He, 3He-4He, and 3He-3He [R. Feltgen et al., J. Chem. Phys. 76, 2360 (1982)]. In the very low energy regime, consistency is found between the Dirac bubble potential (to which our extended model is shown to reduce) and cold collision experiments [J. C. Mester et al., Phys. Rev. Lett. 71, 1343 (1993)]; this consistency, which in this regime lends credence to the Dirac bubble potential, was never noticed by its authors. The revised model being still analytic is of high didactical value while expected to increase in predictive power relative to other appraisals.

Continuum mathematical modelling of pathological growth of blood vessels

NASA Astrophysics Data System (ADS)

Stadnik, N. E.; Dats, E. P.

2018-04-01

The present study is devoted to the mathematical modelling of a human blood vessel pathological growth. The vessels are simulated as the thin-walled circular tube. The boundary value problem of the surface growth of an elastic thin-walled cylinder is solved. The analytical solution is obtained in terms of velocities of stress strain state parameters. The condition of thinness allows us to study finite displacements of cylinder surfaces by means of infinitesimal deformations. The stress-strain state characteristics, which depend on the mechanical parameters of the biological processes, are numerically computed and graphically analysed.

Modeling of plasticity and fracture of metals at shock loading

NASA Astrophysics Data System (ADS)

Mayer, A. E.; Khishchenko, K. V.; Levashov, P. R.; Mayer, P. N.

2013-05-01

In this paper, we present a model of dislocation plasticity and fracture of metals, which in combination with the wide-range equation of state and the continuum mechanics equations is a necessary component for simulation of the shock-wave loading. We take into account immobilization of dislocations and nucleation of micro-voids in weakened zones of substance; this is distinguished feature of the present version of the model. Accounting of the dislocations immobilization provides a better description of the unloading wave structure, while the detailed consideration of processes in the weakened zones expands the domain of applicability of fracture model to higher strain rates. We compare our results with the experimental data for the shock loading of aluminum, copper, and nickel samples; the comparison indicates satisfactory description of the elastic precursor, unloading wave, and spall pulse. Using the model, we investigate intently the early stage of the shock formation in solids; it is found out that the elastic precursor is formed even for a strong shock wave, and initially the precursor has very large amplitude and propagation velocity.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dumbser, Michael, E-mail: michael.dumbser@unitn.it; Peshkov, Ilya, E-mail: peshkov@math.nsc.ru; Romenski, Evgeniy, E-mail: evrom@math.nsc.ru

Highlights: • High order schemes for a unified first order hyperbolic formulation of continuum mechanics. • The mathematical model applies simultaneously to fluid mechanics and solid mechanics. • Viscous fluids are treated in the frame of hyper-elasticity as generalized visco-plastic solids. • Formal asymptotic analysis reveals the connection with the Navier–Stokes equations. • The distortion tensor A in the model appears to be well-suited for flow visualization. - Abstract: This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. Inmore » that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell–Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic–parabolic Navier–Stokes–Fourier theory is established for the first time via a formal asymptotic analysis in the stiff relaxation limit. From a numerical point of view, the governing partial differential equations are very challenging, since they form a large nonlinear hyperbolic PDE system that includes stiff source terms and non-conservative products. We apply the successful family of one-step ADER–WENO finite volume (FV) and ADER discontinuous Galerkin (DG) finite element schemes to the HPR model in the stiff relaxation limit, and compare the numerical results with exact or numerical reference solutions obtained for the Euler and Navier–Stokes equations. Numerical convergence results are also provided. To show the universality of the HPR model, the paper is rounded-off with an application to wave propagation in elastic solids, for which one only needs to switch off the strain relaxation source term in the governing PDE system. We provide various examples showing that for the purpose of flow visualization, the distortion tensor A seems to be particularly useful.« less

Lattice continuum and diffusional creep

PubMed Central

2016-01-01

Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro–Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro–Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate. PMID:27274696

Frontiers of Theoretical Research on Shape Memory Alloys: A General Overview

NASA Astrophysics Data System (ADS)

Chowdhury, Piyas

2018-03-01

In this concise review, general aspects of modeling shape memory alloys (SMAs) are recounted. Different approaches are discussed under four general categories, namely, (a) macro-phenomenological, (b) micromechanical, (c) molecular dynamics, and (d) first principles models. Macro-phenomenological theories, stemming from empirical formulations depicting continuum elastic, plastic, and phase transformation, are primarily of engineering interest, whereby the performance of SMA-made components is investigated. Micromechanical endeavors are generally geared towards understanding microstructural phenomena within continuum mechanics such as the accommodation of straining due to phase change as well as role of precipitates. By contrast, molecular dynamics, being a more recently emerging computational technique, concerns attributes of discrete lattice structures, and thus captures SMA deformation mechanism by means of empirically reconstructing interatomic bonding forces. Finally, ab initio theories utilize quantum mechanical framework to peek into atomistic foundation of deformation, and can pave the way for studying the role of solid-sate effects. With specific examples, this paper provides concise descriptions of each category along with their relative merits and emphases.

Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM

NASA Astrophysics Data System (ADS)

Asemi, S. R.; Farajpour, A.; Asemi, H. R.; Mohammadi, M.

2014-09-01

In this paper, a nonlocal continuum plate model is developed for the transverse vibration of double-piezoelectric-nanoplate systems (DPNPSs) with initial stress under an external electric voltage. The Pasternak foundation model is employed to take into account the effect of shearing between the two piezoelectric nanoplates in combination with normal behavior of coupling elastic medium. Size effects are taken into consideration using nonlocal continuum mechanics. Hamilton's principle is used to derive the differential equations of motion. The governing equations are solved for various boundary conditions by using the differential quadrature method (DQM). In addition, exact solutions are presented for the natural frequencies and critical electric voltages of DPNPS under biaxial prestressed conditions in in-phase and out-of-phase vibrational modes. It is shown that the natural frequencies of the DPNPS are quite sensitive to both nonlocal parameter and initial stress. The effects of in-plane preload and small scale are very important in the resonance mode of smart nanostructures using piezoelectric nanoplates.

Structure, Nanomechanics and Dynamics of Dispersed Surfactant-Free Clay Nanocomposite Films

NASA Astrophysics Data System (ADS)

Zhang, Xiao; Zhao, Jing; Snyder, Chad; Karim, Alamgir; National Institute of Standards; Technology Collaboration

Natural Montmorillonite particles were dispersed as tactoids in thin films of polycaprolactone (PCL) through a flow coating technique assisted by ultra-sonication. Wide angle X-ray scattering (WAXS), Grazing-incidence wide angle X-ray scattering (GI-WAXS), and transmission electron microscopy (TEM) were used to confirm the level of dispersion. These characterization techniques are in conjunction with its nanomechanical properties via strain-induced buckling instability for modulus measurements (SIEBIMM), a high throughput technique to characterize thin film mechanical properties. The linear strengthening trend of the elastic modulus enhancements was fitted with Halpin-Tsai (HT) model, correlating the nanoparticle geometric effects and mechanical behaviors based on continuum theories. The overall aspect ratio of dispersed tactoids obtained through HT model fitting is in reasonable agreement with digital electron microscope image analysis. Moreover, glass transition behaviors of the composites were characterized using broadband dielectric relaxation spectroscopy. The segmental relaxation behaviors indicate that the associated mechanical property changes are due to the continuum filler effect rather than the interfacial confinement effect.

9Be scattering with microscopic wave functions and the continuum-discretized coupled-channel method

NASA Astrophysics Data System (ADS)

Descouvemont, P.; Itagaki, N.

2018-01-01

We use microscopic 9Be wave functions defined in a α +α +n multicluster model to compute 9Be+target scattering cross sections. The parameter sets describing 9Be are generated in the spirit of the stochastic variational method, and the optimal solution is obtained by superposing Slater determinants and by diagonalizing the Hamiltonian. The 9Be three-body continuum is approximated by square-integral wave functions. The 9Be microscopic wave functions are then used in a continuum-discretized coupled-channel (CDCC) calculation of 9Be+208Pb and of 9Be+27Al elastic scattering. Without any parameter fitting, we obtain a fair agreement with experiment. For a heavy target, the influence of 9Be breakup is important, while it is weaker for light targets. This result confirms previous nonmicroscopic CDCC calculations. One of the main advantages of the microscopic CDCC is that it is based on nucleon-target interactions only; there is no adjustable parameter. The present work represents a first step towards more ambitious calculations involving heavier Be isotopes.

Scale transition using dislocation dynamics and the nudged elastic band method

DOE PAGES

Sobie, Cameron; Capolungo, Laurent; McDowell, David L.; ...

2017-08-01

Microstructural features such as precipitates or irradiation-induced defects impede dislocation motion and directly influence macroscopic mechanical properties such as yield point and ductility. In dislocation-defect interactions both atomic scale and long range elastic interactions are involved. Thermally assisted dislocation bypass of obstacles occurs when thermal fluctuations and driving stresses contribute sufficient energy to overcome the energy barrier. The Nudged Elastic Band (NEB) method is typically used in the context of atomistic simulations to quantify the activation barriers for a given reaction. In this work, the NEB method is generalized to coarse-grain continuum representations of evolving microstructure states beyond the discretemore » particle descriptions of first principles and atomistics. The method we employed enables the calculation of activation energies for a View the MathML source glide dislocation bypassing a [001] self-interstitial atom loop of size in the range of 4-10 nm with a spacing larger than 150nm in α-iron for a range of applied stresses and interaction geometries. This study is complemented by a comparison between atomistic and continuum based prediction of barriers.« less

Multiscale multiphysics and multidomain models—Flexibility and rigidity

PubMed Central

Xia, Kelin; Opron, Kristopher; Wei, Guo-Wei

2013-01-01

The emerging complexity of large macromolecules has led to challenges in their full scale theoretical description and computer simulation. Multiscale multiphysics and multidomain models have been introduced to reduce the number of degrees of freedom while maintaining modeling accuracy and achieving computational efficiency. A total energy functional is constructed to put energies for polar and nonpolar solvation, chemical potential, fluid flow, molecular mechanics, and elastic dynamics on an equal footing. The variational principle is utilized to derive coupled governing equations for the above mentioned multiphysical descriptions. Among these governing equations is the Poisson-Boltzmann equation which describes continuum electrostatics with atomic charges. The present work introduces the theory of continuum elasticity with atomic rigidity (CEWAR). The essence of CEWAR is to formulate the shear modulus as a continuous function of atomic rigidity. As a result, the dynamics complexity of a macromolecular system is separated from its static complexity so that the more time-consuming dynamics is handled with continuum elasticity theory, while the less time-consuming static analysis is pursued with atomic approaches. We propose a simple method, flexibility-rigidity index (FRI), to analyze macromolecular flexibility and rigidity in atomic detail. The construction of FRI relies on the fundamental assumption that protein functions, such as flexibility, rigidity, and energy, are entirely determined by the structure of the protein and its environment, although the structure is in turn determined by all the interactions. As such, the FRI measures the topological connectivity of protein atoms or residues and characterizes the geometric compactness of the protein structure. As a consequence, the FRI does not resort to the interaction Hamiltonian and bypasses matrix diagonalization, which underpins most other flexibility analysis methods. FRI's computational complexity is of \\documentclass[12pt]{minimal}\\begin{document}${\\cal O}(N^2)$\\end{document}O(N2) at most, where N is the number of atoms or residues, in contrast to \\documentclass[12pt]{minimal}\\begin{document}${\\cal O}(N^3)$\\end{document}O(N3) for Hamiltonian based methods. We demonstrate that the proposed FRI gives rise to accurate prediction of protein B-Factor for a set of 263 proteins. We show that a parameter free FRI is able to achieve about 95% accuracy of the parameter optimized FRI. An interpolation algorithm is developed to construct continuous atomic flexibility functions for visualization and use with CEWAR. PMID:24320318

Multiscale multiphysics and multidomain models—Flexibility and rigidity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xia, Kelin; Opron, Kristopher; Wei, Guo-Wei, E-mail: wei@math.msu.edu

The emerging complexity of large macromolecules has led to challenges in their full scale theoretical description and computer simulation. Multiscale multiphysics and multidomain models have been introduced to reduce the number of degrees of freedom while maintaining modeling accuracy and achieving computational efficiency. A total energy functional is constructed to put energies for polar and nonpolar solvation, chemical potential, fluid flow, molecular mechanics, and elastic dynamics on an equal footing. The variational principle is utilized to derive coupled governing equations for the above mentioned multiphysical descriptions. Among these governing equations is the Poisson-Boltzmann equation which describes continuum electrostatics with atomicmore » charges. The present work introduces the theory of continuum elasticity with atomic rigidity (CEWAR). The essence of CEWAR is to formulate the shear modulus as a continuous function of atomic rigidity. As a result, the dynamics complexity of a macromolecular system is separated from its static complexity so that the more time-consuming dynamics is handled with continuum elasticity theory, while the less time-consuming static analysis is pursued with atomic approaches. We propose a simple method, flexibility-rigidity index (FRI), to analyze macromolecular flexibility and rigidity in atomic detail. The construction of FRI relies on the fundamental assumption that protein functions, such as flexibility, rigidity, and energy, are entirely determined by the structure of the protein and its environment, although the structure is in turn determined by all the interactions. As such, the FRI measures the topological connectivity of protein atoms or residues and characterizes the geometric compactness of the protein structure. As a consequence, the FRI does not resort to the interaction Hamiltonian and bypasses matrix diagonalization, which underpins most other flexibility analysis methods. FRI's computational complexity is of O(N{sup 2}) at most, where N is the number of atoms or residues, in contrast to O(N{sup 3}) for Hamiltonian based methods. We demonstrate that the proposed FRI gives rise to accurate prediction of protein B-Factor for a set of 263 proteins. We show that a parameter free FRI is able to achieve about 95% accuracy of the parameter optimized FRI. An interpolation algorithm is developed to construct continuous atomic flexibility functions for visualization and use with CEWAR.« less

Elastic anisotropy effects on the electrical responses of a thin sample of nematic liquid crystal.

PubMed

Gomes, O A; Yednak, C A R; Ribeiro de Almeida, R R; Teixeira-Souza, R T; Evangelista, L R

2017-03-01

The electrical responses of a nematic liquid crystal cell are investigated by means of the elastic continuum theory. The nematic medium is considered as a parallel circuit of a resistance and a capacitance and the electric current profile across the sample is determined as a function of the elastic constants. In the reorientation process of the nematic director, the resistance and capacitance of the sample are determined by taking into account the elastic anisotropy. A nonmonotonic profile for the current is observed in which a minimum value of the current may be used to estimate the elastic constants values. This scenario suggests a theoretical method to determine the values of the bulk elastic constants in a single planar aligned cell just by changing the direction of applied electrical field and measuring the resulting electrical current.

A nonlinear generalized continuum approach for electro-elasticity including scale effects

NASA Astrophysics Data System (ADS)

Skatulla, S.; Arockiarajan, A.; Sansour, C.

2009-01-01

Materials characterized by an electro-mechanically coupled behaviour fall into the category of so-called smart materials. In particular, electro-active polymers (EAP) recently attracted much interest, because, upon electrical loading, EAP exhibit a large amount of deformation while sustaining large forces. This property can be utilized for actuators in electro-mechanical systems, artificial muscles and so forth. When it comes to smaller structures, it is a well-known fact that the mechanical response deviates from the prediction of classical mechanics theory. These scale effects are due to the fact that the size of the microscopic material constituents of such structures cannot be considered to be negligible small anymore compared to the structure's overall dimensions. In this context so-called generalized continuum formulations have been proven to account for the micro-structural influence to the macroscopic material response. Here, we want to adopt a strain gradient approach based on a generalized continuum framework [Sansour, C., 1998. A unified concept of elastic-viscoplastic Cosserat and micromorphic continua. J. Phys. IV Proc. 8, 341-348; Sansour, C., Skatulla, S., 2007. A higher gradient formulation and meshfree-based computation for elastic rock. Geomech. Geoeng. 2, 3-15] and extend it to also encompass the electro-mechanically coupled behaviour of EAP. The approach introduces new strain and stress measures which lead to the formulation of a corresponding generalized variational principle. The theory is completed by Dirichlet boundary conditions for the displacement field and its derivatives normal to the boundary as well as the electric potential. The basic idea behind this generalized continuum theory is the consideration of a micro- and a macro-space which together span the generalized space. As all quantities are defined in this generalized space, also the constitutive law, which is in this work conventional electro-mechanically coupled nonlinear hyperelasticity, is embedded in the generalized continuum. In this way material information of the micro-space, which are here only the geometrical specifications of the micro-continuum, can naturally enter the constitutive law. Several applications with moving least square-based approximations (MLS) demonstrate the potential of the proposed method. This particular meshfree method is chosen, as it has been proven to be highly flexible with regard to continuity and consistency required by this generalized approach.

Gaussian curvature elasticity determined from global shape transformations and local stress distributions: a comparative study using the MARTINI model.

PubMed

Hu, Mingyang; de Jong, Djurre H; Marrink, Siewert J; Deserno, Markus

2013-01-01

We calculate the Gaussian curvature modulus kappa of a systematically coarse-grained (CG) one-component lipid membrane by applying the method recently proposed by Hu et al. [Biophys. J., 2012, 102, 1403] to the MARTINI representation of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). We find the value kappa/kappa = -1.04 +/- 0.03 for the elastic ratio between the Gaussian and the mean curvature modulus and deduce kappa(m)/kappa(m) = -0.98 +/- 0.09 for the monolayer elastic ratio, where the latter is based on plausible assumptions for the distance z0 of the monolayer neutral surface from the bilayer midplane and the spontaneous lipid curvature K(0m). By also analyzing the lateral stress profile sigma0(z) of our system, two other lipid types and pertinent data from the literature, we show that determining K(0m) and kappa through the first and second moment of sigma0(z) gives rise to physically implausible values for these observables. This discrepancy, which we previously observed for a much simpler CG model, suggests that the moment conditions derived from simple continuum assumptions miss the effect of physically important correlations in the lipid bilayer.

Dynamic load mitigation using dissipative elastic metamaterials with multiple Maxwell-type oscillators

NASA Astrophysics Data System (ADS)

Alamri, Sagr; Li, Bing; Tan, K. T.

2018-03-01

Dissipative elastic metamaterials have attracted increased attention in recent times. This paper presents the development of a dissipative elastic metamaterial with multiple Maxwell-type resonators for stress wave attenuation. The mechanism of the dissipation effect on the vibration characteristics is systematically investigated by mass-spring-damper models with single and dual resonators. Based on the parameter optimization, it is revealed that a broadband wave attenuation region (stopping band) can be obtained by properly utilizing interactions from resonant motions and viscoelastic effects of the Maxwell-type oscillators. The relevant numerical verifications are conducted for various cases, and excellent agreement between the numerical and theoretical frequency response functions is shown. The design of this dissipative metamaterial system is further applied for dynamic load mitigation and blast wave attenuation. Moreover, the transient response in the continuum model is designed and analyzed for more robust design. By virtue of the bandgap merging effect induced by the Maxwell-type damper, the transient blast wave can be almost completely suppressed in the low frequency range. A significantly improved performance of the proposed dissipative metamaterials for stress wave mitigation is verified in both time and frequency domains.

Studies on Effective Elastic Properties of CNT/Nano-Clay Reinforced Polymer Hybrid Composite

NASA Astrophysics Data System (ADS)

Thakur, Arvind Kumar; Kumar, Puneet; Srinivas, J.

2016-02-01

This paper presents a computational approach to predict elastic propertiesof hybrid nanocomposite material prepared by adding nano-clayplatelets to conventional CNT-reinforced epoxy system. In comparison to polymers alone/single-fiber reinforced polymers, if an additional fiber is added to the composite structure, it was found a drastic improvement in resultant properties. In this regard, effective elastic moduli of a hybrid nano composite are determined by using finite element (FE) model with square representative volume element (RVE). Continuum mechanics based homogenization of the nano-filler reinforced composite is considered for evaluating the volumetric average of the stresses and the strains under different periodic boundary conditions.A three phase Halpin-Tsai approach is selected to obtain the analytical result based on micromechanical modeling. The effect of the volume fractions of CNTs and nano-clay platelets on the mechanical behavior is studied. Two different RVEs of nano-clay platelets were used to investigate the influence of nano-filler geometry on composite properties. The combination of high aspect ratio of CNTs and larger surface area of clay platelets contribute to the stiffening effect of the hybrid samples. Results of analysis are validated with Halpin-Tsai empirical formulae.

Matched Interface and Boundary Method for Elasticity Interface Problems

PubMed Central

Wang, Bao; Xia, Kelin; Wei, Guo-Wei

2015-01-01

Elasticity theory is an important component of continuum mechanics and has had widely spread applications in science and engineering. Material interfaces are ubiquity in nature and man-made devices, and often give rise to discontinuous coefficients in the governing elasticity equations. In this work, the matched interface and boundary (MIB) method is developed to address elasticity interface problems. Linear elasticity theory for both isotropic homogeneous and inhomogeneous media is employed. In our approach, Lamé’s parameters can have jumps across the interface and are allowed to be position dependent in modeling isotropic inhomogeneous material. Both strong discontinuity, i.e., discontinuous solution, and weak discontinuity, namely, discontinuous derivatives of the solution, are considered in the present study. In the proposed method, fictitious values are utilized so that the standard central finite different schemes can be employed regardless of the interface. Interface jump conditions are enforced on the interface, which in turn, accurately determines fictitious values. We design new MIB schemes to account for complex interface geometries. In particular, the cross derivatives in the elasticity equations are difficult to handle for complex interface geometries. We propose secondary fictitious values and construct geometry based interpolation schemes to overcome this difficulty. Numerous analytical examples are used to validate the accuracy, convergence and robustness of the present MIB method for elasticity interface problems with both small and large curvatures, strong and weak discontinuities, and constant and variable coefficients. Numerical tests indicate second order accuracy in both L∞ and L2 norms. PMID:25914439

The interplay between mechanics and stability of viral cages

NASA Astrophysics Data System (ADS)

Hernando-Pérez, Mercedes; Pascual, Elena; Aznar, María; Ionel, Alina; Castón, José R.; Luque, Antoni; Carrascosa, José L.; Reguera, David; de Pablo, Pedro J.

2014-02-01

The stability and strength of viral nanoparticles are crucial to fulfill the functions required through the viral cycle as well as using capsids for biomedical and nanotechnological applications. The mechanical properties of viral shells obtained through Atomic Force Microscopy (AFM) and continuum elasticity theory, such as stiffness or Young's modulus, have been interpreted very often in terms of stability. However, viruses are normally subjected to chemical rather than to mechanical aggression. Thus, a correct interpretation of mechanics in terms of stability requires an adequate linkage between the ability of viral cages to support chemical and mechanical stresses. Here we study the mechanical fragility and chemical stability of bacteriophage T7 in two different maturation states: the early proheads and the final mature capsids. Using chemical stress experiments we show that proheads are less stable than final mature capsids. Still, both particles present similar anisotropic stiffness, indicating that a continuum elasticity description in terms of Young's modulus is not an adequate measure of viral stability. In combination with a computational coarse-grained model we demonstrate that mechanical anisotropy of T7 emerges out of the discrete nature of the proheads and empty capsids. Even though they present the same stiffness, proheads break earlier and have fractures ten times larger than mature capsids, in agreement with chemical stability, thus demonstrating that fragility rather than stiffness is a better indicator of viral cages' stability.The stability and strength of viral nanoparticles are crucial to fulfill the functions required through the viral cycle as well as using capsids for biomedical and nanotechnological applications. The mechanical properties of viral shells obtained through Atomic Force Microscopy (AFM) and continuum elasticity theory, such as stiffness or Young's modulus, have been interpreted very often in terms of stability. However, viruses are normally subjected to chemical rather than to mechanical aggression. Thus, a correct interpretation of mechanics in terms of stability requires an adequate linkage between the ability of viral cages to support chemical and mechanical stresses. Here we study the mechanical fragility and chemical stability of bacteriophage T7 in two different maturation states: the early proheads and the final mature capsids. Using chemical stress experiments we show that proheads are less stable than final mature capsids. Still, both particles present similar anisotropic stiffness, indicating that a continuum elasticity description in terms of Young's modulus is not an adequate measure of viral stability. In combination with a computational coarse-grained model we demonstrate that mechanical anisotropy of T7 emerges out of the discrete nature of the proheads and empty capsids. Even though they present the same stiffness, proheads break earlier and have fractures ten times larger than mature capsids, in agreement with chemical stability, thus demonstrating that fragility rather than stiffness is a better indicator of viral cages' stability. Electronic supplementary information (ESI) available: Purification of T7 proheads and capsids, coarse-grained simulations of the indentation of T7 empty capsids, Finite Element (FE) simulations, and justification of the anisotropic stiffness based on structural information. See DOI: 10.1039/c3nr05763a

Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method

NASA Astrophysics Data System (ADS)

Zhou, Zhenhuan; Li, Yuejie; Fan, Junhai; Rong, Dalun; Sui, Guohao; Xu, Chenghui

2018-05-01

A new Hamiltonian-based approach is presented for finding exact solutions for transverse vibrations of double-nanobeam-systems embedded in an elastic medium. The continuum model is established within the frameworks of the symplectic methodology and the nonlocal Euler-Bernoulli and Timoshenko beam beams. The symplectic eigenfunctions are obtained after expressing the governing equations in a Hamiltonian form. Exact frequency equations, vibration modes and displacement amplitudes are obtained by using symplectic eigenfunctions and end conditions. Comparisons with previously published work are presented to illustrate the accuracy and reliability of the proposed method. The comprehensive results for arbitrary boundary conditions could serve as benchmark results for verifying numerically obtained solutions. In addition, a study on the difference between the nonlocal beam and the nonlocal plate is also included.

Radial breathing mode of carbon nanotubes subjected to axial pressure

PubMed Central

2011-01-01

In this paper, a theoretical analysis of the radial breathing mode (RBM) of carbon nanotubes (CNTs) subjected to axial pressure is presented based on an elastic continuum model. Single-walled carbon nanotubes (SWCNTs) are described as an individual elastic shell and double-walled carbon nanotubes (DWCNTs) are considered to be two shells coupled through the van der Waals force. The effects of axial pressure, wave numbers and nanotube diameter on the RBM frequency are investigated in detail. The validity of these theoretical results is confirmed through the comparison of the experiment, calculation and simulation. Our results show that the RBM frequency is linearly dependent on the axial pressure and is affected by the wave numbers. We concluded that RBM frequency can be used to characterize the axial pressure acting on both ends of a CNT. PMID:21834961

The application of continuum damage mechanics to solve problems in geodynamics

NASA Astrophysics Data System (ADS)

Manaker, David Martin

Deformation within the Earth's lithosphere is largely controlled by the rheology of the rock. Ductile behavior in rocks is often associated with plasticity due to dislocation motion or diffusion under high pressures and temperatures. However, ductile behavior can also occur in brittle materials. An example would be cataclastic flow associated with folding at shallow crustal levels, steep subduction zones, and large-scale deformation at plate boundaries. Engineers utilize damage mechanics to model the continuum deformation of brittle materials. We utilize a modified form of damage mechanics where damage represents a reduction in frictional strength and includes a yield stress. We use this empirical approach to simulate the bending of the lithosphere. We use numerical simulations to obtain elastostatic solutions for plate bending and where the stress exceeds a yield stress, we apply damage to reduce the elastic moduli. Damage is calculated at each time step by a power-law relationship of the ratio of the yield stress to stress and the yield strain to the strain. To test our method, we apply our damage rheology to a plate deforming under applied shear, a constant bending moment, and a constant load. We simulate a wide range of behaviors from slow relaxation to instantaneous failure, over timescales that span six orders of magnitude. Stress relaxation produces elastic-perfectly plastic behavior in cases where failure does not occur. For cases of failure, we observe a rapid increase in damage leading to failure. The changes in the rate of damage accumulation in failure cases are similar to the changes in b-values of acoustic emissions observed in triaxial compression tests of fractured rock and b-value changes prior to some large earthquakes. Thus continuum damage mechanics can simulate ductile behavior due to brittle mechanisms as well as observations of laboratory experiments and seismicity.

An Elastic Model of Blebbing in Nuclear Lamin Meshworks

NASA Astrophysics Data System (ADS)

Funkhouser, Chloe; Sknepnek, Rastko; Shimi, Takeshi; Goldman, Anne; Goldman, Robert; Olvera de La Cruz, Monica

2013-03-01

A two-component continuum elastic model is introduced to analyze a nuclear lamin meshwork, a structural element of the lamina of the nuclear envelope. The main component of the lamina is a meshwork of lamin protein filaments providing mechanical support to the nucleus and also playing a role in gene expression. Abnormalities in nuclear shape are associated with a variety of pathologies, including some forms of cancer and Hutchinson-Gilford progeria syndrome, and are often characterized by protruding structures termed nuclear blebs. Nuclear blebs are rich in A-type lamins and may be related to pathological gene expression. We apply the two-dimensional elastic shell model to determine which characteristics of the meshwork could be responsible for blebbing, including heterogeneities in the meshwork thickness and mesh size. We find that if one component of the lamin meshwork, rich in A-type lamins, has a tendency to form a larger mesh size than that rich in B-type lamins, this is sufficient to cause segregation of the lamin components and also to form blebs rich in A-type lamins. The model produces structures with comparable morphologies and mesh size distributions as the lamin meshworks of real, pathological nuclei. Funded by US DoE Award DEFG02-08ER46539 and by the DDR&E and AFOSR under Award FA9550-10-1-0167; simulations performed on NU Quest cluster

Two-dimensional membrane as elastic shell with proof on the folds revealed by three-dimensional atomic mapping

NASA Astrophysics Data System (ADS)

Zhao, Jiong; Deng, Qingming; Ly, Thuc Hue; Han, Gang Hee; Sandeep, Gorantla; Rümmeli, Mark H.

2015-11-01

The great application potential for two-dimensional (2D) membranes (MoS2, WSe2, graphene and so on) aroused much effort to understand their fundamental mechanical properties. The out-of-plane bending rigidity is the key factor that controls the membrane morphology under external fields. Herein we provide an easy method to reconstruct the 3D structures of the folded edges of these 2D membranes on the atomic scale, using high-resolution (S)TEM images. After quantitative comparison with continuum mechanics shell model, it is verified that the bending behaviour of the studied 2D materials can be well explained by the linear elastic shell model. And the bending rigidities can thus be derived by fitting with our experimental results. Recall almost only theoretical approaches can access the bending properties of these 2D membranes before, now a new experimental method to measure the bending rigidity of such flexible and atomic thick 2D membranes is proposed.

Phase-field modelling of ductile fracture: a variational gradient-extended plasticity-damage theory and its micromorphic regularization.

PubMed

Miehe, C; Teichtmeister, S; Aldakheel, F

2016-04-28

This work outlines a novel variational-based theory for the phase-field modelling of ductile fracture in elastic-plastic solids undergoing large strains. The phase-field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage modelling. It is linked to a formulation of gradient plasticity at finite strains. The framework includes two independent length scales which regularize both the plastic response as well as the crack discontinuities. This ensures that the damage zones of ductile fracture are inside of plastic zones, and guarantees on the computational side a mesh objectivity in post-critical ranges. © 2016 The Author(s).

Final Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Issen, Kathleen

2017-06-05

This project employed a continuum approach to formulate an elastic constitutive model for Castlegate sandstone. The resulting constitutive framework for high porosity sandstone is thermodynamically sound, (i.e., does not violate the 1st and 2nd law of thermodynamics), represents known material constitutive response, and is able to be calibrated using available mechanical response data. To authenticate the accuracy of this model, a series of validation criteria were employed, using an existing mechanical response data set for Castlegate sandstone. The resulting constitutive framework is applicable to high porosity sandstones in general, and is tractable for scientists and researchers endeavoring to solve problemsmore » of practical interest.« less

Continuum modeling of three-dimensional truss-like space structures

NASA Technical Reports Server (NTRS)

Nayfeh, A. H.; Hefzy, M. S.

1978-01-01

A mathematical and computational analysis capability has been developed for calculating the effective mechanical properties of three-dimensional periodic truss-like structures. Two models are studied in detail. The first, called the octetruss model, is a three-dimensional extension of a two-dimensional model, and the second is a cubic model. Symmetry considerations are employed as a first step to show that the specific octetruss model has four independent constants and that the cubic model has two. The actual values of these constants are determined by averaging the contributions of each rod element to the overall structure stiffness. The individual rod member contribution to the overall stiffness is obtained by a three-dimensional coordinate transformation. The analysis shows that the effective three-dimensional elastic properties of both models are relatively close to each other.

Finite-strain large-deflection elastic-viscoplastic finite-element transient response analysis of structures

NASA Technical Reports Server (NTRS)

Rodal, J. J. A.; Witmer, E. A.

1979-01-01

A method of analysis for thin structures that incorporates finite strain, elastic-plastic, strain hardening, time dependent material behavior implemented with respect to a fixed configuration and is consistently valid for finite strains and finite rotations is developed. The theory is formulated systematically in a body fixed system of convected coordinates with materially embedded vectors that deform in common with continuum. Tensors are considered as linear vector functions and use is made of the dyadic representation. The kinematics of a deformable continuum is treated in detail, carefully defining precisely all quantities necessary for the analysis. The finite strain theory developed gives much better predictions and agreement with experiment than does the traditional small strain theory, and at practically no additional cost. This represents a very significant advance in the capability for the reliable prediction of nonlinear transient structural responses, including the reliable prediction of strains large enough to produce ductile metal rupture.

Soft particles at a fluid interface

NASA Astrophysics Data System (ADS)

Mehrabian, Hadi; Harting, Jens; Snoeijer, Jacco H.

2015-11-01

Particles added to a fluid interface can be used as a surface stabilizer in the food, oil and cosmetic industries. As an alternative to rigid particles, it is promising to consider highly deformable particles that can adapt their conformation at the interface. In this study, we compute the shapes of soft elastic particles using molecular dynamics simulations of a cross-linked polymer gel, complemented by continuum calculations based on the linear elasticity. It is shown that the particle shape is not only affected by the Young's modulus of the particle, but also strongly depends on whether the gel is partially or completely wetting the fluid interface. We find that the molecular simulations for the partially wetting case are very accurately described by the continuum theory. By contrast, when the gel is completely wetting the fluid interface the linear theory breaks down and we reveal that molecular details have a strong influence on the equilibrium shape.

A Continuum Model for the Effect of Dynamic Recrystallization on the Stress–Strain Response

PubMed Central

Perdahcıoğlu, E. S.; van den Boogaard, A. H.

2018-01-01

Austenitic Stainless Steels and High-Strength Low-Alloy (HSLA) steels show significant dynamic recovery and dynamic recrystallization (DRX) during hot forming. In order to design optimal and safe hot-formed products, a good understanding and constitutive description of the material behavior is vital. A new continuum model is presented and validated on a wide range of deformation conditions including high strain rate deformation. The model is presented in rate form to allow for the prediction of material behavior in transient process conditions. The proposed model is capable of accurately describing the stress–strain behavior of AISI 316LN in hot forming conditions, also the high strain rate DRX-induced softening observed during hot torsion of HSLA is accurately predicted. It is shown that the increase in recrystallization rate at high strain rates observed in experiments can be captured by including the elastic energy due to the dynamic stress in the driving pressure for recrystallization. Furthermore, the predicted resulting grain sizes follow the power-law dependence with steady state stress that is often reported in literature and the evolution during hot deformation shows the expected trend. PMID:29789492

Fundamental analysis of the failure of polymer-based fiber reinforced composites

NASA Technical Reports Server (NTRS)

Kanninen, M. F.; Rybicki, E. F.; Griffith, W. I.; Broek, D.

1976-01-01

A mathematical model is described which will permit predictions of the strength of fiber reinforced composites containing known flaws to be made from the basic properties of their constituents. The approach was to embed a local heterogeneous region (LHR) surrounding the crack tip into an anisotropic elastic continuum. The model should (1) permit an explicit analysis of the micromechanical processes involved in the fracture process, and (2) remain simple enough to be useful in practical computations. Computations for arbitrary flaw size and orientation under arbitrary applied load combinations were performed from unidirectional composites with linear elastic-brittle constituent behavior. The mechanical properties were nominally those of graphite epoxy. With the rupture properties arbitrarily varied to test the capability of the model to reflect real fracture modes in fiber composites, it was shown that fiber breakage, matrix crazing, crack bridging, matrix-fiber debonding, and axial splitting can all occur during a period of (gradually) increasing load prior to catastrophic fracture. The computations reveal qualitatively the sequential nature of the stable crack process that precedes fracture.

A Finite Element Framework for Studying the Mechanical Response of Macromolecules: Application to the Gating of the Mechanosensitive Channel MscL

PubMed Central

Tang, Yuye; Cao, Guoxin; Chen, Xi; Yoo, Jejoong; Yethiraj, Arun; Cui, Qiang

2006-01-01

The gating pathways of mechanosensitive channels of large conductance (MscL) in two bacteria (Mycobacterium tuberculosis and Escherichia coli) are studied using the finite element method. The phenomenological model treats transmembrane helices as elastic rods and the lipid membrane as an elastic sheet of finite thickness; the model is inspired by the crystal structure of MscL. The interactions between various continuum components are derived from molecular-mechanics energy calculations using the CHARMM all-atom force field. Both bacterial MscLs open fully upon in-plane tension in the membrane and the variation of pore diameter with membrane tension is found to be essentially linear. The estimated gating tension is close to the experimental value. The structural variations along the gating pathway are consistent with previous analyses based on structural models with experimental constraints and biased atomistic molecular-dynamics simulations. Upon membrane bending, neither MscL opens substantially, although there is notable and nonmonotonic variation in the pore radius. This emphasizes that the gating behavior of MscL depends critically on the form of the mechanical perturbation and reinforces the idea that the crucial gating parameter is lateral tension in the membrane rather than the curvature of the membrane. Compared to popular all-atom-based techniques such as targeted or steered molecular-dynamics simulations, the finite element method-based continuum-mechanics framework offers a unique alternative to bridge detailed intermolecular interactions and biological processes occurring at large spatial scales and long timescales. It is envisioned that such a hierarchical multiscale framework will find great value in the study of a variety of biological processes involving complex mechanical deformations such as muscle contraction and mechanotransduction. PMID:16731564

Determination of baryon-baryon elastic scattering phase shift from finite volume spectra in elongated boxes

NASA Astrophysics Data System (ADS)

Li, Ning; Wu, Ya-Jie; Liu, Zhan-Wei

2018-01-01

The relations between the baryon-baryon elastic scattering phase shifts and the two-particle energy spectrum in the elongated box are established. We studied the cases with both the periodic boundary condition and twisted boundary condition in the center of mass frame. The framework is also extended to the system of nonzero total momentum with periodic boundary condition in the moving frame. Moreover, we discussed the sensitivity functions σ (q ) that represent the sensitivity of higher scattering phases. Our analytical results will be helpful to extract the baryon-baryon elastic scattering phase shifts in the continuum from lattice QCD data by using elongated boxes.

Toward the Design of Personalized Continuum Surgical Robots.

PubMed

Morimoto, Tania K; Greer, Joseph D; Hawkes, Elliot W; Hsieh, Michael H; Okamura, Allison M

2018-05-31

Robot-assisted minimally invasive surgical systems enable procedures with reduced pain, recovery time, and scarring compared to traditional surgery. While these improvements benefit a large number of patients, safe access to diseased sites is not always possible for specialized patient groups, including pediatric patients, due to their anatomical differences. We propose a patient-specific design paradigm that leverages the surgeon's expertise to design and fabricate robots based on preoperative medical images. The components of the patient-specific robot design process are a virtual reality design interface enabling the surgeon to design patient-specific tools, 3-D printing of these tools with a biodegradable polyester, and an actuation and control system for deployment. The designed robot is a concentric tube robot, a type of continuum robot constructed from precurved, elastic, nesting tubes. We demonstrate the overall patient-specific design workflow, from preoperative images to physical implementation, for an example clinical scenario: nonlinear renal access to a pediatric kidney. We also measure the system's behavior as it is deployed through real and artificial tissue. System integration and successful benchtop experiments in ex vivo liver and in a phantom patient model demonstrate the feasibility of using a patient-specific design workflow to plan, fabricate, and deploy personalized, flexible continuum robots.

Dual number algebra method for Green's function derivatives in 3D magneto-electro-elasticity

NASA Astrophysics Data System (ADS)

Dziatkiewicz, Grzegorz

2018-01-01

The Green functions are the basic elements of the boundary element method. To obtain the boundary integral formulation the Green function and its derivative should be known for the considered differential operator. Today the interesting group of materials are electronic composites. The special case of the electronic composite is the magnetoelectroelastic continuum. The mentioned continuum is a model of the piezoelectric-piezomagnetic composites. The anisotropy of their physical properties makes the problem of Green's function determination very difficult. For that reason Green's functions for the magnetoelectroelastic continuum are not known in the closed form and numerical methods should be applied to determine such Green's functions. These means that the problem of the accurate and simply determination of Green's function derivatives is even harder. Therefore in the present work the dual number algebra method is applied to calculate numerically the derivatives of 3D Green's functions for the magnetoelectroelastic materials. The introduced method is independent on the step size and it can be treated as a special case of the automatic differentiation method. Therefore, the dual number algebra method can be applied as a tool for checking the accuracy of the well-known finite difference schemes.

Normal mode analysis and applications in biological physics.

PubMed

Dykeman, Eric C; Sankey, Otto F

2010-10-27

Normal mode analysis has become a popular and often used theoretical tool in the study of functional motions in enzymes, viruses, and large protein assemblies. The use of normal modes in the study of these motions is often extremely fruitful since many of the functional motions of large proteins can be described using just a few normal modes which are intimately related to the overall structure of the protein. In this review, we present a broad overview of several popular methods used in the study of normal modes in biological physics including continuum elastic theory, the elastic network model, and a new all-atom method, recently developed, which is capable of computing a subset of the low frequency vibrational modes exactly. After a review of the various methods, we present several examples of applications of normal modes in the study of functional motions, with an emphasis on viral capsids.

CCC calculated integrated cross sections of electron-H2 scattering

NASA Astrophysics Data System (ADS)

Zammit, Mark; Fursa, Dmitry; Savage, Jeremy; Bray, Igor

2016-09-01

Recently we applied the molecular convergent close-coupling (CCC) method to electron scattering from molecular hydrogen H2. Convergence of the major integrated cross sections has been explicitly demonstrated in the fixed-nuclei approximation by increasing the number of H2 target states in the close-coupling expansion from 9 to 491. The calculations have been performed using a projectile partial wave expansion with maximum orbital angular momentum Lmax = 8 and total orbital angular momentum projections | M | <= 8 . Coupling to the ionization continuum is modeled via a large pseudo state expansion, which we found is required to obtain reliable elastic and excitation cross sections. Here we present benchmark elastic, single-ionization, electronic excitation and total integrated cross sections over a broad energy range (0.1 to 300 eV) and compare with available experiment and previous calculations. Los Alamos National Laboratory and Curtin University.

A nonlinear fracture mechanics approach to the growth of small cracks

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.

1983-01-01

An analytical model of crack closure is used to study the crack growth and closure behavior of small cracks in plates and at notches. The calculated crack opening stresses for small and large cracks, together with elastic and elastic plastic fracture mechanics analyses, are used to correlate crack growth rate data. At equivalent elastic stress intensity factor levels, calculations predict that small cracks in plates and at notches should grow faster than large cracks because the applied stress needed to open a small crack is less than that needed to open a large crack. These predictions agree with observed trends in test data. The calculations from the model also imply that many of the stress intensity factor thresholds that are developed in tests with large cracks and with load reduction schemes do not apply to the growth of small cracks. The current calculations are based upon continuum mechanics principles and, thus, some crack size and grain structure exist where the underlying fracture mechanics assumptions become invalid because of material inhomogeneity (grains, inclusions, etc.). Admittedly, much more effort is needed to develop the mechanics of a noncontinuum. Nevertheless, these results indicate the importance of crack closure in predicting the growth of small cracks from large crack data.

Using Non-linear Homogenization to Improve the Performance of Macroscopic Damage Models of Trabecular Bone.

PubMed

Levrero-Florencio, Francesc; Pankaj, Pankaj

2018-01-01

Realistic macro-level finite element simulations of the mechanical behavior of trabecular bone, a cellular anisotropic material, require a suitable constitutive model; a model that incorporates the mechanical response of bone for complex loading scenarios and includes post-elastic phenomena, such as plasticity (permanent deformations) and damage (permanent stiffness reduction), which bone is likely to experience. Some such models have been developed by conducting homogenization-based multiscale finite element simulations on bone micro-structure. While homogenization has been fairly successful in the elastic regime and, to some extent, in modeling the macroscopic plastic response, it has remained a challenge with respect to modeling damage. This study uses a homogenization scheme to upscale the damage behavior from the tissue level (microscale) to the organ level (macroscale) and assesses the suitability of different damage constitutive laws. Ten cubic specimens were each subjected to 21 strain-controlled load cases for a small range of macroscopic post-elastic strains. Isotropic and anisotropic criteria were considered, density and fabric relationships were used in the formulation of the damage law, and a combined isotropic/anisotropic law with tension/compression asymmetry was formulated, based on the homogenized results, as a possible alternative to the currently used single scalar damage criterion. This computational study enhances the current knowledge on the macroscopic damage behavior of trabecular bone. By developing relationships of damage progression with bone's micro-architectural indices (density and fabric) the study also provides an aid for the creation of more precise macroscale continuum models, which are likely to improve clinical predictions.

A discrete mesoscopic particle model of the mechanics of a multi-constituent arterial wall.

PubMed

Witthoft, Alexandra; Yazdani, Alireza; Peng, Zhangli; Bellini, Chiara; Humphrey, Jay D; Karniadakis, George Em

2016-01-01

Blood vessels have unique properties that allow them to function together within a complex, self-regulating network. The contractile capacity of the wall combined with complex mechanical properties of the extracellular matrix enables vessels to adapt to changes in haemodynamic loading. Homogenized phenomenological and multi-constituent, structurally motivated continuum models have successfully captured these mechanical properties, but truly describing intricate microstructural details of the arterial wall may require a discrete framework. Such an approach would facilitate modelling interactions between or the separation of layers of the wall and would offer the advantage of seamless integration with discrete models of complex blood flow. We present a discrete particle model of a multi-constituent, nonlinearly elastic, anisotropic arterial wall, which we develop using the dissipative particle dynamics method. Mimicking basic features of the microstructure of the arterial wall, the model comprises an elastin matrix having isotropic nonlinear elastic properties plus anisotropic fibre reinforcement that represents the stiffer collagen fibres of the wall. These collagen fibres are distributed evenly and are oriented in four directions, symmetric to the vessel axis. Experimental results from biaxial mechanical tests of an artery are used for model validation, and a delamination test is simulated to demonstrate the new capabilities of the model. © 2016 The Author(s).

Dynamic Effective Mass of Granular Media

NASA Astrophysics Data System (ADS)

Hsu, Chaur-Jian; Johnson, David L.; Ingale, Rohit A.; Valenza, John J.; Gland, Nicolas; Makse, Hernán A.

2009-02-01

We develop the concept of frequency dependent effective mass, Mtilde (ω), of jammed granular materials which occupy a rigid cavity to a filling fraction of 48%, the remaining volume being air of normal room condition or controlled humidity. The dominant features of Mtilde (ω) provide signatures of the dissipation of acoustic modes, elasticity, and aging effects in the granular medium. We perform humidity controlled experiments and interpret the data in terms of a continuum model and a “trap” model of thermally activated capillary bridges at the contact points. The results suggest that attenuation of acoustic waves in granular materials can be influenced significantly by the kinetics of capillary condensation between the asperities at the contacts.

Nonlocal continuum analysis of a nonlinear uniaxial elastic lattice system under non-uniform axial load

NASA Astrophysics Data System (ADS)

Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud

2016-09-01

The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.

Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model

NASA Astrophysics Data System (ADS)

Farajpour, A.; Mohammadi, M.; Shahidi, A. R.; Mahzoon, M.

2011-08-01

In this article, the buckling behavior of nanoscale circular plates under uniform radial compression is studied. Small-scale effect is taken into consideration. Using nonlocal elasticity theory the governing equations are derived for the circular single-layered graphene sheets (SLGS). Explicit expressions for the buckling loads are obtained for clamped and simply supported boundary conditions. It is shown that nonlocal effects play an important role in the buckling of circular nanoplates. The effects of the small scale on the buckling loads considering various parameters such as the radius of the plate and mode numbers are investigated.

PAFAC- PLASTIC AND FAILURE ANALYSIS OF COMPOSITES

NASA Technical Reports Server (NTRS)

Bigelow, C. A.

1994-01-01

The increasing number of applications of fiber-reinforced composites in industry demands a detailed understanding of their material properties and behavior. A three-dimensional finite-element computer program called PAFAC (Plastic and Failure Analysis of Composites) has been developed for the elastic-plastic analysis of fiber-reinforced composite materials and structures. The evaluation of stresses and deformations at edges, cut-outs, and joints is essential in understanding the strength and failure for metal-matrix composites since the onset of plastic yielding starts very early in the loading process as compared to the composite's ultimate strength. Such comprehensive analysis can only be achieved by a finite-element program like PAFAC. PAFAC is particularly suited for the analysis of laminated metal-matrix composites. It can model the elastic-plastic behavior of the matrix phase while the fibers remain elastic. Since the PAFAC program uses a three-dimensional element, the program can also model the individual layers of the laminate to account for thickness effects. In PAFAC, the composite is modeled as a continuum reinforced by cylindrical fibers of vanishingly small diameter which occupy a finite volume fraction of the composite. In this way, the essential axial constraint of the phases is retained. Furthermore, the local stress and strain fields are uniform. The PAFAC finite-element solution is obtained using the displacement method. Solution of the nonlinear equilibrium equations is obtained with a Newton-Raphson iteration technique. The elastic-plastic behavior of composites consisting of aligned, continuous elastic filaments and an elastic-plastic matrix is described in terms of the constituent properties, their volume fractions, and mutual constraints between phases indicated by the geometry of the microstructure. The program uses an iterative procedure to determine the overall response of the laminate, then from the overall response determines the stress state in each phase of the composite material. Failure of the fibers or matrix within an element can also be modeled by PAFAC. PAFAC is written in FORTRAN IV for batch execution and has been implemented on a CDC CYBER 170 series computer with a segmented memory requirement of approximately 66K (octal) of 60 bit words. PAFAC was developed in 1982.

King post truss as a motif for internal structure of (meta)material with controlled elastic properties

NASA Astrophysics Data System (ADS)

Turco, Emilio; Giorgio, Ivan; Misra, Anil; dell'Isola, Francesco

2017-10-01

One of the most interesting challenges in the modern theory of materials consists in the determination of those microstructures which produce, at the macro-level, a class of metamaterials whose elastic range is many orders of magnitude wider than the one exhibited by `standard' materials. In dell'Isola et al. (2015 Zeitschrift für angewandte Mathematik und Physik 66, 3473-3498. (doi:10.1007/s00033-015-0556-4)), it was proved that, with a pantographic microstructure constituted by `long' micro-beams it is possible to obtain metamaterials whose elastic range spans up to an elongation exceeding 30%. In this paper, we demonstrate that the same behaviour can be obtained by means of an internal microstructure based on a king post motif. This solution shows many advantages: it involves only microbeams; all constituting beams are undergoing only extension or compression; all internal constraints are terminal pivots. While the elastic deformation energy can be determined as easily as in the case of long-beam microstructure, the proposed design seems to have obvious remarkable advantages: it seems to be more damage resistant and therefore to be able to have a wider elastic range; it can be realized with the same three-dimensional printing technology; it seems to be less subject to compression buckling. The analysis which we present here includes: (i) the determination of Hencky-type discrete models for king post trusses, (ii) the application of an effective integration scheme to a class of relevant deformation tests for the proposed metamaterial and (iii) the numerical determination of an equivalent second gradient continuum model. The numerical tools which we have developed and which are presented here can be readily used to develop an extensive measurement campaign for the proposed metamaterial.

Constitutive Modeling of Crosslinked Nanotube Materials

NASA Technical Reports Server (NTRS)

Odegard, G. M.; Frankland, S. J. V.; Herzog, M. N.; Gates, T. S.; Fay, C. C.

2004-01-01

A non-linear, continuum-based constitutive model is developed for carbon nanotube materials in which bundles of aligned carbon nanotubes have varying amounts of crosslinks between the nanotubes. The model accounts for the non-linear elastic constitutive behavior of the material in terms of strain, and is developed using a thermodynamic energy approach. The model is used to examine the effect of the crosslinking on the overall mechanical properties of variations of the crosslinked carbon nanotube material with varying degrees of crosslinking. It is shown that the presence of the crosslinks has significant effects on the mechanical properties of the carbon nanotube materials. An increase in the transverse shear properties is observed when the nanotubes are crosslinked. However, this increase is accompanied by a decrease in axial mechanical properties of the nanotube material upon crosslinking.

Simulation of Anisotropic Rock Damage for Geologic Fracturing

NASA Astrophysics Data System (ADS)

Busetti, S.; Xu, H.; Arson, C. F.

2014-12-01

A continuum damage model for differential stress-induced anisotropic crack formation and stiffness degradation is used to study geologic fracturing in rocks. The finite element-based model solves for deformation in the quasi-linear elastic domain and determines the six component damage tensor at each deformation increment. The model permits an isotropic or anisotropic intact or pre-damaged reference state, and the elasticity tensor evolves depending on the stress path. The damage variable, similar to Oda's fabric tensor, grows when the surface energy dissipated by three-dimensional opened cracks exceeds a threshold defined at the appropriate scale of the representative elementary volume (REV). At the laboratory or wellbore scale (<1m) brittle continuum damage reflects microcracking, grain boundary separation, grain crushing, or fine delamination, such as in shale. At outcrop (1m-100m), seismic (10m-1000m), and tectonic (>1000m) scales the damaged REV reflects early natural fracturing (background or tectonic fracturing) or shear strain localization (fault process zone, fault-tip damage, etc.). The numerical model was recently benchmarked against triaxial stress-strain data from laboratory rock mechanics tests. However, the utility of the model to predict geologic fabric such as natural fracturing in hydrocarbon reservoirs was not fully explored. To test the ability of the model to predict geological fracturing, finite element simulations (Abaqus) of common geologic scenarios with known fracture patterns (borehole pressurization, folding, faulting) are simulated and the modeled damage tensor is compared against physical fracture observations. Simulated damage anisotropy is similar to that derived using fractured rock-mass upscaling techniques for pre-determined fracture patterns. This suggests that if model parameters are constrained with local data (e.g., lab, wellbore, or reservoir domain), forward modeling could be used to predict mechanical fabric at the relevant REV scale. This reference fabric also can be used as the starting material property to pre-condition subsequent deformation or fluid flow. Continuing efforts are to expand the present damage model to couple damage evolution with plasticity and with permeability for more geologically realistic simulation.

Rotational elasticity

NASA Astrophysics Data System (ADS)

Vassiliev, Dmitri

2017-04-01

We consider an infinite three-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis that gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory, we choose the coframe and a density. We write down the general dynamic variational functional for our rotational theory of elasticity, assuming our material to be physically linear but the kinematic model geometrically nonlinear. Allowing geometric nonlinearity is natural when dealing with rotations because rotations in dimension three are inherently nonlinear (rotations about different axes do not commute) and because there is no reason to exclude from our study large rotations such as full turns. The main result of the talk is an explicit construction of a class of time-dependent solutions that we call plane wave solutions; these are travelling waves of rotations. The existence of such explicit closed-form solutions is a non-trivial fact given that our system of Euler-Lagrange equations is highly nonlinear. We also consider a special case of our rotational theory of elasticity which in the stationary setting (harmonic time dependence and arbitrary dependence on spatial coordinates) turns out to be equivalent to a pair of massless Dirac equations. The talk is based on the paper [1]. [1] C.G.Boehmer, R.J.Downes and D.Vassiliev, Rotational elasticity, Quarterly Journal of Mechanics and Applied Mathematics, 2011, vol. 64, p. 415-439. The paper is a heavily revised version of preprint https://arxiv.org/abs/1008.3833

Analysis of tablet compaction. I. Characterization of mechanical behavior of powder and powder/tooling friction.

PubMed

Cunningham, J C; Sinka, I C; Zavaliangos, A

2004-08-01

In this first of two articles on the modeling of tablet compaction, the experimental inputs related to the constitutive model of the powder and the powder/tooling friction are determined. The continuum-based analysis of tableting makes use of an elasto-plastic model, which incorporates the elements of yield, plastic flow potential, and hardening, to describe the mechanical behavior of microcrystalline cellulose over the range of densities experienced during tableting. Specifically, a modified Drucker-Prager/cap plasticity model, which includes material parameters such as cohesion, internal friction, and hydrostatic yield pressure that evolve with the internal state variable relative density, was applied. Linear elasticity is assumed with the elastic parameters, Young's modulus, and Poisson's ratio dependent on the relative density. The calibration techniques were developed based on a series of simple mechanical tests including diametrical compression, simple compression, and die compaction using an instrumented die. The friction behavior is measured using an instrumented die and the experimental data are analyzed using the method of differential slices. The constitutive model and frictional properties are essential experimental inputs to the finite element-based model described in the companion article. Copyright 2004 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 93:2022-2039, 2004

From coherent to incoherent mismatched interfaces: A generalized continuum formulation of surface stresses

NASA Astrophysics Data System (ADS)

Dingreville, Rémi; Hallil, Abdelmalek; Berbenni, Stéphane

2014-12-01

The equilibrium of coherent and incoherent mismatched interfaces is reformulated in the context of continuum mechanics based on the Gibbs dividing surface concept. Two surface stresses are introduced: a coherent surface stress and an incoherent surface stress, as well as a transverse excess strain. The coherent surface stress and the transverse excess strain represent the thermodynamic driving forces of stretching the interface while the incoherent surface stress represents the driving force of stretching one crystal while holding the other fixed and thereby altering the structure of the interface. These three quantities fully characterize the elastic behavior of coherent and incoherent interfaces as a function of the in-plane strain, the transverse stress and the mismatch strain. The isotropic case is developed in detail and particular attention is paid to the case of interfacial thermo-elasticity. This exercise provides an insight on the physical significance of the interfacial elastic constants introduced in the formulation and illustrates the obvious coupling between the interface structure and its associated thermodynamics quantities. Finally, an example based on atomistic simulations of Cu/Cu2O interfaces is given to demonstrate the relevance of the generalized interfacial formulation and to emphasize the dependence of the interfacial thermodynamic quantities on the incoherency strain with an actual material system.

From coherent to incoherent mismatched interfaces. A generalized continuum formulation of surface stresses

DOE PAGES

Dingreville, Rémi; Hallil, Abdelmalek; Berbenni, Stéphane

2014-08-19

The equilibrium of coherent and incoherent mismatched interfaces is reformulated in the context of continuum mechanics based on the Gibbs dividing surface concept. Two surface stresses are introduced: a coherent surface stress and an incoherent surface stress, as well as a transverse excess strain. Additionally, the coherent surface stress and the transverse excess strain represent the thermodynamic driving forces of stretching the interface while the incoherent surface stress represents the driving force of stretching one crystal while holding the other fixed and thereby altering the structure of the interface. These three quantities fully characterize the elastic behavior of coherent andmore » incoherent interfaces as a function of the in-plane strain, the transverse stress and the mismatch strain. The isotropic case is developed in detail and particular attention is paid to the case of interfacial thermo-elasticity. This exercise provides an insight on the physical significance of the interfacial elastic constants introduced in the formulation and illustrates the obvious coupling between the interface structure and its associated thermodynamics quantities. Finally, an example based on atomistic simulations of Cu/Cu 2O interfaces is given to demonstrate the relevance of the generalized interfacial formulation and to emphasize the dependence of the interfacial thermodynamic quantities on the incoherency strain with an actual material system.« less

Understanding the effects of strain on morphological instabilities of a nanoscale island during heteroepitaxial growth

DOE Office of Scientific and Technical Information (OSTI.GOV)

Feng, Lu; Wang, Jing; Wang, Shibin

A comprehensive morphological stability analysis of a nanoscale circular island during heteroepitaxial growth is presented based on continuum elasticity theory. The interplay between kinetic and thermodynamic mechanisms is revealed by including strain-related kinetic processes. In the kinetic regime, the Burton-Cabrera-Frank model is adopted to describe the growth front of the island. Together with kinetic boundary conditions, various kinetic processes including deposition flow, adatom diffusion, attachment-detachment kinetics, and the Ehrlich-Schwoebel barrier can be taken into account at the same time. In the thermodynamic regime, line tension, surface energy, and elastic energy are considered. As the strain relief in the early stagesmore » of heteroepitaxy is more complicated than commonly suggested by simple consideration of lattice mismatch, we also investigate the effects of external applied strain and elastic response due to perturbations on the island shape evolution. The analytical expressions for elastic fields induced by mismatch strain, external applied strain, and relaxation strain are presented. A systematic approach is developed to solve the system via a perturbation analysis which yields the conditions of film morphological instabilities. Consistent with previous experimental and theoretical work, parametric studies show the kinetic evolution of elastic relaxation, island morphology, and film composition under various conditions. Our present work offers an effective theoretical approach to get a comprehensive understanding of the interplay between different growth mechanisms and how to tailor the growth mode by controlling the nature of the crucial factors.« less

Influence of intra-molecular flexibility on the elastic property of double-stranded DNA film on a substrate

NASA Astrophysics Data System (ADS)

Wu, Jun-Zheng; Meng, Wei-Lie; Tang, Heng-Song; Zhang, Neng-Hui

2017-05-01

DNA film self-assembled or nanografted on a substrate, as a kind of soft matter, consists of fixed DNA chains endowed with negative charges and an aqueous solution full of cations, anions and water molecules. Their thermal/electrical/mechanical properties are closely related to the complex biodetection signals in nano-/micro-scale biosensors and other new genome technologies. This makes it important to properly characterize these properties. In this paper, the effect of flexible micro-scale configurations on the elastic moduli of DNA films is investigated. First, illuminated by Qiu’s sphere model, an alternative bead-chain model in terms of the Yukawa potential is presented for flexible intra-DNA configurations to describe interactions between DNA fragments. The effective charges of coarse-grained DNA beads could be derived, in which the empirical parameters are identified by curve fitting with Qiu’s experimental data. Second, the updated mesoscopic bead-chain model and the thought experiment of a continuum compression bar are used to compare the elastic moduli of double-stranded DNA (dsDNA) films prepared by self-assembling and nanografting techniques. Configurational sampling is achieved via Monte Carlo simulation. Our predictions quantitatively or qualitatively agree well with the relevant experiments on the effective charge of dsDNA from low to moderate monovalent counterion concentration, immobilization deflection of single-stranded DNA (ssDNA) or dsDNA microcantilever with the variation of salt concentration, and elastic modulus of ssDNA film in the air. The results reveal that different solution environment stimulates the diverse mechanical properties of dsDNA film on a substrate, and the end effect (i.e. terminal group effect) makes self-assembling dsDNA film stiffer in the sense of the same average packing density.

Energy approach to brittle fracture in strain-gradient modelling.

PubMed

Placidi, Luca; Barchiesi, Emilio

2018-02-01

In this paper, we exploit some results in the theory of irreversible phenomena to address the study of quasi-static brittle fracture propagation in a two-dimensional isotropic continuum. The elastic strain energy density of the body has been assumed to be geometrically nonlinear and to depend on the strain gradient. Such generalized continua often arise in the description of microstructured media. These materials possess an intrinsic length scale, which determines the size of internal boundary layers. In particular, the non-locality conferred by this internal length scale avoids the concentration of deformations, which is usually observed when dealing with local models and which leads to mesh dependency. A scalar Lagrangian damage field, ranging from zero to one, is introduced to describe the internal state of structural degradation of the material. Standard Lamé and second-gradient elastic coefficients are all assumed to decrease as damage increases and to be locally zero if the value attained by damage is one. This last situation is associated with crack formation and/or propagation. Numerical solutions of the model are provided in the case of an obliquely notched rectangular specimen subjected to monotonous tensile and shear loading tests, and brittle fracture propagation is discussed.

Competing effects of particle and medium inertia on particle diffusion in viscoelastic materials, and their ramifications for passive microrheology.

PubMed

Indei, Tsutomu; Schieber, Jay D; Córdoba, Andrés

2012-04-01

We analyze the appropriate form for the generalized Stokes-Einstein relation (GSER) for viscoelastic solids and fluids when bead inertia and medium inertia are taken into account, which we call the inertial GSER. It was previously shown for Maxwell fluids that the Basset (or Boussinesq) force arising from medium inertia can act purely dissipatively at high frequencies, where elasticity of the medium is dominant. In order to elucidate the cause of this counterintuitive result, we consider Brownian motion in a purely elastic solid where ordinary Stokes-type dissipation is not possible. The fluctuation-dissipation theorem requires the presence of a dissipative mechanism for the particle to experience fluctuating Brownian forces in a purely elastic solid. We show that the mechanism for such dissipation arises from the radiation of elastic waves toward the system boundaries. The frictional force associated with this mechanism is the Basset force, and it exists only when medium inertia is taken into consideration in the analysis of such a system. We consider first a one-dimensional harmonic lattice where all terms in the generalized Langevin equation--i.e., the elastic term, the memory kernel, and Brownian forces-can be found analytically from projection-operator methods. We show that the dissipation is purely from radiation of elastic waves. A similar analysis is made on a particle in a continuum, three-dimensional purely elastic solid, where the memory kernel is determined from continuum mechanics. Again, dissipation arises only from radiation of elastic shear waves toward infinite boundaries when medium inertia is taken into account. If the medium is a viscoelastic solid, Stokes-type dissipation is possible in addition to radiational dissipation so that the wave decays at the penetration depth. Inertial motion of the bead couples with the elasticity of the viscoelastic material, resulting in a possible resonant oscillation of the mean-square displacement (MSD) of the bead. On the other hand, medium inertia (the Basset force) tends to attenuate the oscillations by the dissipation mechanism described above. Thus competition between bead inertia and medium inertia determines whether or not the MSD oscillates. We find that, if the medium density is larger than 4/7 of the bead density, the Basset damping will suppress oscillations in the MSD; this criterion is sufficient but not necessary to present oscillations.

Elastic Response and Failure Studies of Multi-Wall Carbon Nanotube Twisted Yarns

NASA Technical Reports Server (NTRS)

Gates, Thomas S.; Jefferson, Gail D.; Frankland, Sarah-Jane V.

2007-01-01

Experimental data on the stress-strain behavior of a polymer multiwall carbon nanotube (MWCNT) yarn composite are used to motivate an initial study in multi-scale modeling of strength and stiffness. Atomistic and continuum length scale modeling methods are outlined to illustrate the range of parameters required to accurately model behavior. The carbon nanotubes yarns are four-ply, twisted, and combined with an elastomer to form a single-layer, unidirectional composite. Due to this textile structure, the yarn is a complicated system of unique geometric relationships subjected to combined loads. Experimental data illustrate the local failure modes induced by static, tensile tests. Key structure-property relationships are highlighted at each length scale indicating opportunities for parametric studies to assist the selection of advantageous material development and manufacturing methods.

Experiments on elastic cloaking in thin plates.

PubMed

Stenger, Nicolas; Wilhelm, Manfred; Wegener, Martin

2012-01-06

Following a theoretical proposal [M. Farhat et al., Phys. Rev. Lett. 103, 024301 (2009)], we design, fabricate, and characterize a cloaking structure for elastic waves in 1 mm thin structured polymer plates. The cloak consists of 20 concentric rings of 16 different metamaterials, each being a tailored composite of polyvinyl chloride and polydimethylsiloxane. By using stroboscopic imaging with a camera from the direction normal to the plate, we record movies of the elastic waves for monochromatic plane-wave excitation. We observe good cloaking behavior for carrier frequencies in the range from 200 to 400 Hz (one octave), in good agreement with a complete continuum-mechanics numerical treatment. This system is thus ideally suited for demonstration experiments conveying the ideas of transformation optics.

Highly porous layers of silica nanospheres sintered by drying: scaling up of the elastic properties of the beads to the macroscopic mechanical properties.

PubMed

Lesaine, Arnaud; Bonamy, Daniel; Gauthier, Georges; Rountree, Cindy L; Lazarus, Véronique

2018-05-16

Layers obtained by drying a colloidal dispersion of silica spheres are found to be a good benchmark to test the elastic behaviour of porous media, in the challenging case of high porosities and nano-sized microstructures. Classically used for these systems, Kendall's approach explicitly considers the effect of surface adhesive forces onto the contact area between the particles. This approach provides the Young's modulus using a single adjustable parameter (the adhesion energy) but provides no further information on the tensorial nature and possible anisotropy of elasticity. On the other hand, homogenization approaches (e.g. rule of mixtures, and Eshelby, Mori-Tanaka and self-consistent schemes), based on continuum mechanics and asymptotic analysis, provide the stiffness tensor from the knowledge of the porosity and the elastic constants of the beads. Herein, the self-consistent scheme accurately predicts both bulk and shear moduli, with no adjustable parameter, provided the porosity is less than 35%, for layers composed of particles as small as 15 nm in diameter. Conversely, Kendall's approach is found to predict the Young's modulus over the full porosity range. Moreover, the adhesion energy in Kendall's model has to be adjusted to a value of the order of the fracture energy of the particle material. This suggests that sintering during drying leads to the formation of covalent siloxane bonds between the particles.

Modeling of Tool-Tissue Interactions for Computer-Based Surgical Simulation: A Literature Review

PubMed Central

Misra, Sarthak; Ramesh, K. T.; Okamura, Allison M.

2009-01-01

Surgical simulators present a safe and potentially effective method for surgical training, and can also be used in robot-assisted surgery for pre- and intra-operative planning. Accurate modeling of the interaction between surgical instruments and organs has been recognized as a key requirement in the development of high-fidelity surgical simulators. Researchers have attempted to model tool-tissue interactions in a wide variety of ways, which can be broadly classified as (1) linear elasticity-based, (2) nonlinear (hyperelastic) elasticity-based finite element (FE) methods, and (3) other techniques that not based on FE methods or continuum mechanics. Realistic modeling of organ deformation requires populating the model with real tissue data (which are difficult to acquire in vivo) and simulating organ response in real time (which is computationally expensive). Further, it is challenging to account for connective tissue supporting the organ, friction, and topological changes resulting from tool-tissue interactions during invasive surgical procedures. Overcoming such obstacles will not only help us to model tool-tissue interactions in real time, but also enable realistic force feedback to the user during surgical simulation. This review paper classifies the existing research on tool-tissue interactions for surgical simulators specifically based on the modeling techniques employed and the kind of surgical operation being simulated, in order to inform and motivate future research on improved tool-tissue interaction models. PMID:20119508

Coupled modeling and simulation of electro-elastic materials at large strains

NASA Astrophysics Data System (ADS)

Possart, Gunnar; Steinmann, Paul; Vu, Duc-Khoi

2006-03-01

In the recent years various novel materials have been developed that respond to the application of electrical loading by large strains. An example is the class of so-called electro-active polymers (EAP). Certainly these materials are technologically very interesting, e.g. for the design of actuators in mechatronics or in the area of artificial tissues. This work focuses on the phenomenological modeling of such materials within the setting of continuum-electro-dynamics specialized to the case of electro-hyperelastostatics and the corresponding computational setting. Thereby a highly nonlinear coupled problem for the deformation and the electric potential has to be considered. The finite element method is applied to solve the underlying equations numerically and some exemplary applications are presented.

PNNL Technical Support to The Implementation of EMTA and EMTA-NLA Models in Autodesk® Moldflow® Packages

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nguyen, Ba Nghiep; Wang, Jin

2012-12-01

Under the Predictive Engineering effort, PNNL developed linear and nonlinear property prediction models for long-fiber thermoplastics (LFTs). These models were implemented in PNNL’s EMTA and EMTA-NLA codes. While EMTA is a standalone software for the computation of the composites thermoelastic properties, EMTA-NLA presents a series of nonlinear models implemented in ABAQUS® via user subroutines for structural analyses. In all these models, it is assumed that the fibers are linear elastic while the matrix material can exhibit a linear or typical nonlinear behavior depending on the loading prescribed to the composite. The key idea is to model the constitutive behavior ofmore » the matrix material and then to use an Eshelby-Mori-Tanaka approach (EMTA) combined with numerical techniques for fiber length and orientation distributions to determine the behavior of the as-formed composite. The basic property prediction models of EMTA and EMTA-NLA have been subject for implementation in the Autodesk® Moldflow® software packages. These models are the elastic stiffness model accounting for fiber length and orientation distributions, the fiber/matrix interface debonding model, and the elastic-plastic models. The PNNL elastic-plastic models for LFTs describes the composite nonlinear stress-strain response up to failure by an elastic-plastic formulation associated with either a micromechanical criterion to predict failure or a continuum damage mechanics formulation coupling damage to plasticity. All the models account for fiber length and orientation distributions as well as fiber/matrix debonding that can occur at any stage of loading. In an effort to transfer the technologies developed under the Predictive Engineering project to the American automotive and plastics industries, PNNL has obtained the approval of the DOE Office of Vehicle Technologies to provide Autodesk, Inc. with the technical support for the implementation of the basic property prediction models of EMTA and EMTA-NLA in the Autodesk® Moldflow® packages. This report summarizes the recent results from Autodesk Simulation Moldlow Insight (ASMI) analyses using the EMTA models and EMTA-NLA/ABAQUS® analyses for further assessment of the EMTA-NLA models to support their implementation in Autodesk Moldflow Structural Alliance (AMSA). PNNL’s technical support to Autodesk, Inc. included (i) providing the theoretical property prediction models as described in published journal articles and reports, (ii) providing explanations of these models and computational procedure, (iii) providing the necessary LFT data for process simulations and property predictions, and (iv) performing ABAQUS/EMTA-NLA analyses to further assess and illustrate the models for selected LFT materials.« less

Trampoline Effect: Observations and Modeling

NASA Astrophysics Data System (ADS)

Guyer, R.; Larmat, C. S.; Ulrich, T. J.

2009-12-01

The Iwate-Miyagi earthquake at site IWTH25 (14 June 2008) had large, asymmetric at surface vertical accelerations prompting the sobriquet trampoline effect (Aoi et. al. 2008). In addition the surface acceleration record showed long-short waiting time correlations and vertical-horizontal acceleration correlations. A lumped element model, deduced from the equations of continuum elasticity, is employed to describe the behavior at this site in terms of a surface layer and substrate. Important ingredients in the model are the nonlinear vertical coupling between the surface layer and the substrate and the nonlinear horizontal frictional coupling between the surface layer and the substrate. The model produces results in qualitative accord with observations: acceleration asymmetry, Fourier spectrum, waiting time correlations and vertical acceleration-horizontal acceleration correlations. [We gratefully acknowledge the support of the U. S. Department of Energy through the LANL/LDRD Program for this work].

Unusual expression of tension of a massless cable with application to the oscillations of a mass suspended to a cable with a variable length

NASA Astrophysics Data System (ADS)

Babaz, Mathieu; Jezequel, Louis; Lamarque, Claude-Henri; Perrard, Patrick

2016-02-01

A new approach of cables' dynamics is presented in this paper. It is based on the exact expression of tension coming from continuum mechanics, while the previous elastic models of cables in open literature consider an approximation of small strain which reduces the cable to a linear spring. The equations of a mass suspended to a massless cable are derived on the basis of this new formulation. The problem is studied and numerically calculated for one and two degrees of freedom. A comparison with the classical approach and a nonlinear analysis are presented.

Equilibrium Conformations of Concentric-tube Continuum Robots

PubMed Central

Rucker, D. Caleb; Webster, Robert J.; Chirikjian, Gregory S.; Cowan, Noah J.

2013-01-01

Robots consisting of several concentric, preshaped, elastic tubes can work dexterously in narrow, constrained, and/or winding spaces, as are commonly found in minimally invasive surgery. Previous models of these “active cannulas” assume piecewise constant precurvature of component tubes and neglect torsion in curved sections of the device. In this paper we develop a new coordinate-free energy formulation that accounts for general preshaping of an arbitrary number of component tubes, and which explicitly includes both bending and torsion throughout the device. We show that previously reported models are special cases of our formulation, and then explore in detail the implications of torsional flexibility for the special case of two tubes. Experiments demonstrate that this framework is more descriptive of physical prototype behavior than previous models; it reduces model prediction error by 82% over the calibrated bending-only model, and 17% over the calibrated transmissional torsion model in a set of experiments. PMID:25125773

Effects of thermal noise on the transitional dynamics of an inextensible elastic filament in stagnation flow.

PubMed

Deng, Mingge; Grinberg, Leopold; Caswell, Bruce; Karniadakis, George Em

2015-06-28

We investigate the dynamics of a single inextensible elastic filament subject to anisotropic friction in a viscous stagnation-point flow, by employing both a continuum model represented by Langevin type stochastic partial differential equations (SPDEs) and a dissipative particle dynamics (DPD) method. Unlike previous works, the filament is free to rotate and the tension along the filament is determined by the local inextensible constraint. The kinematics of the filament is recorded and studied with normal modes analysis. The results show that the filament displays an instability induced by negative tension, which is analogous to Euler buckling of a beam. Symmetry breaking of normal modes dynamics and stretch-coil transitions are observed above the threshold of the buckling instability point. Furthermore, both temporal and spatial noise are amplified resulting from the interaction of thermal fluctuations and nonlinear filament dynamics. Specifically, the spatial noise is amplified with even normal modes being excited due to symmetry breaking, while the temporal noise is amplified with increasing time correlation length and variance.

Micromechanics of Ultrafine Particle Adhesion—Contact Models

NASA Astrophysics Data System (ADS)

Tomas, Jürgen

2009-06-01

Ultrafine, dry, cohesive and compressible powders (particle diameter d<10 μm) show a wide variety of flow problems that cause insufficient apparatus and system reliability of processing plants. Thus, the understanding of the micromechanics of particle adhesion is essential to assess the product quality and to improve the process performance in particle technology. Comprehensive models are shown that describe the elastic-plastic force-displacement and frictional moment-angle behavior of adhesive contacts of isotropic smooth spheres. By the model stiff particles with soft contacts, a sphere-sphere interaction of van der Waals forces without any contact deformation describes the stiff attractive term. But, the soft micro-contact response generates a flattened contact, i.e. plate-plate interaction, and increasing adhesion. These increasing adhesion forces between particles directly depend on this frozen irreversible deformation. Thus, the adhesion force is found to be load dependent. It contributes to the tangential forces in an elastic-plastic frictional contact with partially sticking and micro-slip within the contact plane. The load dependent rolling resistance and torque of mobilized frictional contact rotation (spin around its principal axis) are also shown. This reasonable combination of particle contact micromechanics and powder continuum mechanics is used to model analytically the macroscopic friction limits of incipient powder consolidation, yield and cohesive steady-state shear flow on physical basis.

Wave-packet continuum-discretization approach to ion-atom collisions including rearrangement: Application to differential ionization in proton-hydrogen scattering

NASA Astrophysics Data System (ADS)

Abdurakhmanov, I. B.; Bailey, J. J.; Kadyrov, A. S.; Bray, I.

2018-03-01

In this work, we develop a wave-packet continuum-discretization approach to ion-atom collisions that includes rearrangement processes. The total scattering wave function is expanded using a two-center basis built from wave-packet pseudostates. The exact three-body Schrödinger equation is converted into coupled-channel differential equations for time-dependent expansion coefficients. In the asymptotic region these time-dependent coefficients represent transition amplitudes for all processes including elastic scattering, excitation, ionization, and electron capture. The wave-packet continuum-discretization approach is ideal for differential ionization studies as it allows one to generate pseudostates with arbitrary energies and distribution. The approach is used to calculate the double differential cross section for ionization in proton collisions with atomic hydrogen. Overall good agreement with experiment is obtained for all considered cases.

Continuum Excitation and Pseudospin Wave in Quantum Spin-Liquid and Quadrupole Ordered States of Tb2+xTi2-xO7+y

NASA Astrophysics Data System (ADS)

Kadowaki, Hiroaki; Wakita, Mika; Fåk, Björn; Ollivier, Jacques; Ohira-Kawamura, Seiko; Nakajima, Kenji; Takatsu, Hiroshi; Tamai, Mototake

2018-06-01

The ground states of the frustrated pyrochlore oxide Tb2+xTi2-xO7+y have been studied by inelastic neutron scattering experiments. Three single-crystal samples are investigated; one shows no phase transition (x = -0.007 < xc ˜ -0.0025), being a putative quantum spin-liquid (QSL), and the other two (x = 0.000,0.003) show electric quadrupole ordering (QO) below Tc ˜ 0.5 K. The QSL sample shows continuum excitation spectra with an energy scale 0.1 meV as well as energy-resolution-limited (nominally) elastic scattering. As x is increased, pseudospin wave of the QO state emerges from this continuum excitation, which agrees with that of powder samples and consequently verifies good x control for the present single crystal samples.

Differential Geometry Based Multiscale Models

PubMed Central

Wei, Guo-Wei

2010-01-01

Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that are coupled to generalized Navier–Stokes equations for fluid dynamics, Newton's equation for molecular dynamics, and potential and surface driving geometric flows for the micro-macro interface. For excessively large aqueous macromolecular complexes in chemistry and biology, we further develop differential geometry based multiscale fluid-electro-elastic models to replace the expensive molecular dynamics description with an alternative elasticity formulation. PMID:20169418

Geometrical influence of a deposited particle on the performance of bridged carbon nanotube-based mass detectors

NASA Astrophysics Data System (ADS)

Ali-Akbari, H. R.; Ceballes, S.; Abdelkefi, A.

2017-10-01

A nonlocal continuum-based model is derived to simulate the dynamic behavior of bridged carbon nanotube-based nano-scale mass detectors. The carbon nanotube (CNT) is modeled as an elastic Euler-Bernoulli beam considering von-Kármán type geometric nonlinearity. In order to achieve better accuracy in characterization of the CNTs, the geometrical properties of an attached nano-scale particle are introduced into the model by its moment of inertia with respect to the central axis of the beam. The inter-atomic long-range interactions within the structure of the CNT are incorporated into the model using Eringen's nonlocal elastic field theory. In this model, the mass can be deposited along an arbitrary length of the CNT. After deriving the full nonlinear equations of motion, the natural frequencies and corresponding mode shapes are extracted based on a linear eigenvalue problem analysis. The results show that the geometry of the attached particle has a significant impact on the dynamic behavior of the CNT-based mechanical resonator, especially, for those with small aspect ratios. The developed model and analysis are beneficial for nano-scale mass identification when a CNT-based mechanical resonator is utilized as a small-scale bio-mass sensor and the deposited particles are those, such as proteins, enzymes, cancer cells, DNA and other nano-scale biological objects with different and complex shapes.

Elastic Face, An Anatomy-Based Biometrics Beyond Visible Cue

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsap, L V; Zhang, Y; Kundu, S J

2004-03-29

This paper describes a face recognition method that is designed based on the consideration of anatomical and biomechanical characteristics of facial tissues. Elastic strain pattern inferred from face expression can reveal an individual's biometric signature associated with the underlying anatomical structure, and thus has the potential for face recognition. A method based on the continuum mechanics in finite element formulation is employed to compute the strain pattern. Experiments show very promising results. The proposed method is quite different from other face recognition methods and both its advantages and limitations, as well as future research for improvement are discussed.

Elastic alpha-particle resonances as evidence of clustering at high excitation in 40Ca

NASA Astrophysics Data System (ADS)

Norrby, M.; Lönnroth, T.; Goldberg, V. Z.; Rogachev, G. V.; Golovkov, M. S.; Källman, K.-M.; Lattuada, M.; Perov, S. V.; Romano, S.; Skorodumov, B. B.; Tiourin, G. P.; Trzaska, W. H.; Tumino, A.; Vorontsov, A. N.

2011-08-01

The elastic-scattering reaction 36Ar + α was studied using the Thick Target Inverse Kinematics technique. Data were taken at a beam energy of 150 MeV in a reaction chamber filled with 4He gas, corresponding to the excitation region of 12-20 MeV in 40Ca. Using a simplified R -matrix method of analysis energies, widths and spin assignments were obtained for 137 resonances. The structure is discussed within the concept of α-cluster structure in the quasi-continuum of 40Ca and is compared to other nuclei in the same mass region.

Effect of ripples on the finite temperature elastic properties of hexagonal boron nitride using strain-fluctuation method

NASA Astrophysics Data System (ADS)

Thomas, Siby; Ajith, K. M.; Valsakumar, M. C.

2017-11-01

This work intents to put forth the results of a classical molecular dynamics study to investigate the temperature dependent elastic constants of monolayer hexagonal boron nitride (h-BN) between 100 and 1000 K for the first time using strain fluctuation method. The temperature dependence of out-of-plane fluctuations (ripples) is quantified and is explained using continuum theory of membranes. At low temperatures, negative in-plane thermal expansion is observed and at high temperatures, a transition to positive thermal expansion has been observed due to the presence of thermally excited ripples. The decrease of Young's modulus, bulk modulus, shear modulus and Poisson's ratio with increase in temperature has been analyzed. The thermal rippling in h-BN leads to strong anharmonic behaviour that causes large deviation from the isotropic elasticity. A detailed study shows that the strong thermal rippling in large systems is also responsible for the softening of elastic constants in h-BN. From the determined values of elastic constants and elastic moduli, it has been elucidated that 2D h-BN sheets meet the Born's mechanical stability criterion in the investigated temperature range. The variation of longitudinal and shear velocities with temperature is also calculated from the computed values of elastic constants and elastic moduli.

Continuum Theory of Retroviral Capsids

NASA Astrophysics Data System (ADS)

Nguyen, T. T.; Bruinsma, R. F.; Gelbart, W. M.

2006-02-01

We present a self-assembly phase diagram for the shape of retroviral capsids, based on continuum elasticity theory. The spontaneous curvature of the capsid proteins drives a weakly first-order transition from spherical to spherocylindrical shapes. The conical capsid shape which characterizes the HIV-1 retrovirus is never stable under unconstrained energy minimization. Only under conditions of fixed volume and/or fixed spanning length can the conical shape be a minimum energy structure. Our results indicate that, unlike the capsids of small viruses, retrovirus capsids are not uniquely determined by the molecular structure of the constituent proteins but depend in an essential way on physical constraints present during assembly.

Crash energy management on the base of Movable cellular automata method

NASA Astrophysics Data System (ADS)

Psakhie, Serguei; Dmitriev, Andrei; Shilko, Evgueni; Tatarintsev, Evgueni; Korostelev, Serguei

2001-06-01

One of the main problems of materials science is increasing of structure's viability under dynamic loading. In general, a solution is the management of transformation of the energy of loading to the energy of destroying of the least important parts and details of the structure. It has to be noted that similar problem also exists in materials science, since a majority of modern materials are heterogeneous and have a complex internal structure. To optimize this structure for working under dynamic loading it is necessary to take into account the redistribution of elastic energy including phase transformation, generation and accumulation of micro-damages, etc. As far as real experiments on destroying the complex objects are sufficiently expensive and getting of detailed information is often associates with essential difficulties, the methods of computer modeling are used in solving the similar problems. As a rule, these are the methods of continuum mechanics. Although essential achievements have been obtained on the basis of these methods the continuum approach has several limitations, connected first of all with the possibility of description of generation of damages, formation and development of cracks and mass mixing effects. These problems may be solved on the basis of the Movable Cellular Automata (MCA) method, which has been successfully used for modeling fracture of the different material and structures In the paper behavior and peculiarities of failure of complex structures and materials under dynamic loading are studied on the basis of computer modeling. The results shown that sometimes even small changes of the internal structure leads to the significant increasing of the viability of the complex structures and materials. It is due to the elastic energy flux change over during the dynamical loading. This effect may be explained by the fact that elastic energy fluxes define the current stress concentration. Namely, because the area of inclusions are subjected by the largest displacement and due to less Young modulus of inclusions the loading pulses are transferred towards the other parts of the sample. This leads to "blurring" of the stress concentrators and conservation of wholeness of the structure. In its turn, this leads to essential raising up of threshold value of "injected" energy, i.e. the energy absorbed by the structure before loss of its carrying capacity. Practically, elastic energy "circulates" in the structure until a stress concentrator appears, which power will be sufficient for forming a macro-cracks. The results demonstrate a possibility of managing the fracture process under dynamic loading and raising viability of structures and heterogeneous materials by changing their internal structure, geometry, so by entering the specific inclusions.

Mechanics of the foot Part 2: A coupled solid-fluid model to investigate blood transport in the pathologic foot.

PubMed

Mithraratne, K; Ho, H; Hunter, P J; Fernandez, J W

2012-10-01

A coupled computational model of the foot consisting of a three-dimensional soft tissue continuum and a one-dimensional (1D) transient blood flow network is presented in this article. The primary aim of the model is to investigate the blood flow in major arteries of the pathologic foot where the soft tissue stiffening occurs. It has been reported in the literature that there could be up to about five-fold increase in the mechanical stiffness of the plantar soft tissues in pathologic (e.g. diabetic) feet compared with healthy ones. The increased stiffness results in higher tissue hydrostatic pressure within the plantar area of the foot when loaded. The hydrostatic pressure acts on the external surface of blood vessels and tend to reduce the flow cross-section area and hence the blood supply. The soft tissue continuum model of the foot was modelled as a tricubic Hermite finite element mesh representing all the muscles, skin and fat of the foot and treated as incompressible with transversely isotropic properties. The details of the mechanical model of soft tissue are presented in the companion paper, Part 1. The deformed state of the soft tissue continuum because of the applied ground reaction force at three foot positions (heel-strike, midstance and toe-off) was obtained by solving the Cauchy equations based on the theory of finite elasticity using the Galerkin finite element method. The geometry of the main arterial network in the foot was represented using a 1D Hermite cubic finite element mesh. The flow model consists of 1D Navier-Stokes equations and a nonlinear constitutive equation to describe vessel radius-transmural pressure relation. The latter was defined as the difference between the fluid and soft tissue hydrostatic pressure. Transient flow governing equations were numerically solved using the two-step Lax-Wendroff finite difference method. The geometry of both the soft tissue continuum and arterial network is anatomically-based and was developed using the data derived from visible human images and magnetic resonance images of a healthy male volunteer. Simulation results reveal that a two-fold increase in tissue stiffness leads to about 28% reduction in blood flow to the affected region. Copyright © 2012 John Wiley & Sons, Ltd.

Unleashing elastic energy: dynamics of energy release in rubber bands and impulsive biological systems

NASA Astrophysics Data System (ADS)

Ilton, Mark; Cox, Suzanne; Egelmeers, Thijs; Patek, S. N.; Crosby, Alfred J.

Impulsive biological systems - which include mantis shrimp, trap-jaw ants, and venus fly traps - can reach high speeds by using elastic elements to store and rapidly release energy. The material behavior and shape changes critical to achieving rapid energy release in these systems are largely unknown due to limitations of materials testing instruments operating at high speed and large displacement. In this work, we perform fundamental, proof-of-concept measurements on the tensile retraction of elastomers. Using high speed imaging, the kinematics of retraction are measured for elastomers with varying mechanical properties and geometry. Based on the kinematics, the rate of energy dissipation in the material is determined as a function of strain and strain-rate, along with a scaling relation which describes the dependence of maximum velocity on material properties. Understanding this scaling relation along with the material failure limits of the elastomer allows the prediction of material properties required for optimal performance. We demonstrate this concept experimentally by optimizing for maximum velocity in our synthetic model system, and achieve retraction velocities that exceed those in biological impulsive systems. This model system provides a foundation for future work connecting continuum performance to molecular architecture in impulsive systems.

Extracting material response from simple mechanical tests on hardening-softening-hardening viscoplastic solids

NASA Astrophysics Data System (ADS)

Mohan, Nisha

Compliant foams are usually characterized by a wide range of desirable mechanical properties. These properties include viscoelasticity at different temperatures, energy absorption, recoverability under cyclic loading, impact resistance, and thermal, electrical, acoustic and radiation-resistance. Some foams contain nano-sized features and are used in small-scale devices. This implies that the characteristic dimensions of foams span multiple length scales, rendering modeling their mechanical properties difficult. Continuum mechanics-based models capture some salient experimental features like the linear elastic regime, followed by non-linear plateau stress regime. However, they lack mesostructural physical details. This makes them incapable of accurately predicting local peaks in stress and strain distributions, which significantly affect the deformation paths. Atomistic methods are capable of capturing the physical origins of deformation at smaller scales, but suffer from impractical computational intensity. Capturing deformation at the so-called meso-scale, which is capable of describing the phenomenon at a continuum level, but with some physical insights, requires developing new theoretical approaches. A fundamental question that motivates the modeling of foams is `how to extract the intrinsic material response from simple mechanical test data, such as stress vs. strain response?' A 3D model was developed to simulate the mechanical response of foam-type materials. The novelty of this model includes unique features such as the hardening-softening-hardening material response, strain rate-dependence, and plastically compressible solids with plastic non-normality. Suggestive links from atomistic simulations of foams were borrowed to formulate a physically informed hardening material input function. Motivated by a model that qualitatively captured the response of foam-type vertically aligned carbon nanotube (VACNT) pillars under uniaxial compression [2011,"Analysis of Uniaxial Compression of Vertically Aligned Carbon Nanotubes," J. Mech.Phys. Solids, 59, pp. 2227--2237, Erratum 60, 1753-1756 (2012)], the property space exploration was advanced to three types of simple mechanical tests: 1) uniaxial compression, 2) uniaxial tension, and 3) nanoindentation with a conical and a flat-punch tip. The simulations attempt to explain some of the salient features in experimental data, like 1) The initial linear elastic response. 2) One or more nonlinear instabilities, yielding, and hardening. The model-inherent relationships between the material properties and the overall stress-strain behavior were validated against the available experimental data. The material properties include the gradient in stiffness along the height, plastic and elastic compressibility, and hardening. Each of these tests was evaluated in terms of their efficiency in extracting material properties. The uniaxial simulation results proved to be a combination of structural and material influences. Out of all deformation paths, flat-punch indentation proved to be superior since it is the most sensitive in capturing the material properties.

Gravity-driven groundwater flow and slope failure potential: 1. Elastic effective-stress model

USGS Publications Warehouse

Iverson, Richard M.; Reid, Mark E.

1992-01-01

Hilly or mountainous topography influences gravity-driven groundwater flow and the consequent distribution of effective stress in shallow subsurface environments. Effective stress, in turn, influences the potential for slope failure. To evaluate these influences, we formulate a two-dimensional, steady state, poroelastic model. The governing equations incorporate groundwater effects as body forces, and they demonstrate that spatially uniform pore pressure changes do not influence effective stresses. We implement the model using two finite element codes. As an illustrative case, we calculate the groundwater flow field, total body force field, and effective stress field in a straight, homogeneous hillslope. The total body force and effective stress fields show that groundwater flow can influence shear stresses as well as effective normal stresses. In most parts of the hillslope, groundwater flow significantly increases the Coulomb failure potential Φ, which we define as the ratio of maximum shear stress to mean effective normal stress. Groundwater flow also shifts the locus of greatest failure potential toward the slope toe. However, the effects of groundwater flow on failure potential are less pronounced than might be anticipated on the basis of a simpler, one-dimensional, limit equilibrium analysis. This is a consequence of continuity, compatibility, and boundary constraints on the two-dimensional flow and stress fields, and it points to important differences between our elastic continuum model and limit equilibrium models commonly used to assess slope stability.

Ab initio study of the Jπ=0± continuum structures in 4He

NASA Astrophysics Data System (ADS)

Aoyama, S.; Baye, D.

2018-05-01

The Jπ=0± continuum structures in 4He are investigated by using an ab initio reaction theory with the microscopic R -matrix method. In the Ex≥˜20 MeV excitation energy region of 4He, the continuum states are mainly described by the t +p , h +n , and d +d channels. The Jπ=0± elastic phase shifts of the t +p and h +n channels show an apparently resonant behavior which might indicate the existence of excited 03+ and 02- resonance states of 4He above the known 02+ and 01- ones. However, the corresponding 03+ and 02- resonances have not been observed yet, although an experimental candidate with a large decay width is reported for 02-. In this paper, by analyzing the Jπ=0± S matrices, we discuss why the observation of these states is unlikely.

Terahertz circular dichroism spectroscopy of biomolecules

NASA Astrophysics Data System (ADS)

Xu, Jing; Galan, Jhenny; Ramian, Gerald; Savvidis, Pavlos; Scopatz, Anthony; Birge, Robert R.; Allen, S. James; Plaxco, Kevin

2004-02-01

Biopolymers such as proteins, DNA and RNA fold into large, macromolecular chiral structures. As charged macromolecules, they absorb strongly in the terahertz due to large-scale collective vibrational modes; as chiral objects, this absorption should be coupled with significant circular dichroism. Terahertz circular dichroism (TCD) is potentially important as a biospecific sensor, unobscured by spectral features related to abiological material. We have constructed atomistic simulations and elastic continuum models of TCD. These models estimate the magnitude of the TCD and the relation between TCD spectroscopic signatures (zero crossings) and the structure, charge distribution and mechanical properties of biomaterials. A broad band TCD spectrometer based on a polarizing interferometer is developed to explore TCD in biomolecules in aqueous solution. Preliminary results on TCD in lysozyme in water at several terahertz frequencies is presented.

Multi-Scale Modeling of a Graphite-Epoxy-Nanotube System

NASA Technical Reports Server (NTRS)

Frankland, S. J. V.; Riddick, J. C.; Gates, T. S.

2005-01-01

A multi-scale method is utilized to determine some of the constitutive properties of a three component graphite-epoxy-nanotube system. This system is of interest because carbon nanotubes have been proposed as stiffening and toughening agents in the interlaminar regions of carbon fiber/epoxy laminates. The multi-scale method uses molecular dynamics simulation and equivalent-continuum modeling to compute three of the elastic constants of the graphite-epoxy-nanotube system: C11, C22, and C33. The 1-direction is along the nanotube axis, and the graphene sheets lie in the 1-2 plane. It was found that the C11 is only 4% larger than the C22. The nanotube therefore does have a small, but positive effect on the constitutive properties in the interlaminar region.

Hydrodynamics of Turning Flocks.

PubMed

Yang, Xingbo; Marchetti, M Cristina

2015-12-18

We present a hydrodynamic model of flocking that generalizes the familiar Toner-Tu equations to incorporate turning inertia of well-polarized flocks. The continuum equations controlled by only two dimensionless parameters, orientational inertia and alignment strength, are derived by coarse-graining the inertial spin model recently proposed by Cavagna et al. The interplay between orientational inertia and bend elasticity of the flock yields anisotropic spin waves that mediate the propagation of turning information throughout the flock. The coupling between spin-current density to the local vorticity field through a nonlinear friction gives rise to a hydrodynamic mode with angular-dependent propagation speed at long wavelengths. This mode becomes unstable as a result of the growth of bend and splay deformations augmented by the spin wave, signaling the transition to complex spatiotemporal patterns of continuously turning and swirling flocks.

Mechanostability of Proteins and Virus Capsids

NASA Astrophysics Data System (ADS)

Cieplak, Marek

2013-03-01

Molecular dynamics of proteins within coarse grained models have become a useful tool in studies of large scale systems. The talk will discuss two applications of such modeling. The first is a theoretical survey of proteins' resistance to constant speed stretching as performed for a set of 17134 simple and 318 multidomain proteins. The survey has uncovered new potent force clamps. They involve formation of cysteine slipknots or dragging of a cystine plug through the cystine ring and lead to characteristic forces that are significantly larger than the common shear-based clamp such as observed in titin. The second application involves studies of nanoindentation processes in virus capsids and elucidates their molecular aspects by showing deviations in behavior compared to the continuum shell model. Across the 35 capsids studied, both the collapse force and the elastic stiffness are observed to vary by a factor of 20. The changes in mechanical properties do not correlate simply with virus size or symmetry. There is a strong connection to the mean coordination number < z > , defined as the mean number of interactions to neighboring amino acids. The Young's modulus for thin shell capsids rises roughly quadratically with < z > - 6, where 6 is the minimum coordination for elastic stability in three dimensions. Supported by European Regional Development Fund, through Innovative Economy grant Nanobiom (POIG.01.01.02-00-008/08)

Structure of 8B from elastic and inelastic 7Be+p scattering

NASA Astrophysics Data System (ADS)

Mitchell, J. P.; Rogachev, G. V.; Johnson, E. D.; Baby, L. T.; Kemper, K. W.; Moro, A. M.; Peplowski, P.; Volya, A. S.; Wiedenhöver, I.

2013-05-01

Background: Detailed experimental knowledge of the level structure of light weakly bound nuclei is necessary to guide the development of new theoretical approaches that combine nuclear structure with reaction dynamics.Purpose: The resonant structure of 8B is studied in this work.Method: Excitation functions for elastic and inelastic 7Be+p scattering were measured using a 7Be rare isotope beam. Excitation energies ranging between 1.6 and 3.4 MeV were investigated. An R-matrix analysis of the excitation functions was performed.Results: New low-lying resonances at 1.9, 2.54, and 3.3 MeV in 8B are reported with spin-parity assignment 0+, 2+, and 1+, respectively. Comparison to the time-dependent continuum shell (TDCSM) model and ab initio no-core shell model/resonating-group method (NCSM/RGM) calculations is performed. This work is a more detailed analysis of the data first published as a Rapid Communication. J. P. Mitchell, G. V. Rogachev, E. D. Johnson, L. T. Baby, K. W. Kemper , [Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.82.011601 82, 011601(R) (2010)].Conclusions: Identification of the 0+, 2+, 1+ states that were predicted by some models at relatively low energy but never observed experimentally is an important step toward understanding the structure of 8B. Their identification was aided by having both elastic and inelastic scattering data. Direct comparison of the cross sections and phase shifts predicted by the TDCSM and ab initio no-core shell model coupled with the resonating group method is of particular interest and provides a good test for these theoretical approaches.

The Finite Strain Johnson Cook Plasticity and Damage Constitutive Model in ALEGRA.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanchez, Jason James

A finite strain formulation of the Johnson Cook plasticity and damage model and it's numerical implementation into the ALEGRA code is presented. The goal of this work is to improve the predictive material failure capability of the Johnson Cook model. The new implementation consists of a coupling of damage and the stored elastic energy as well as the minimum failure strain criteria for spall included in the original model development. This effort establishes the necessary foundation for a thermodynamically consistent and complete continuum solid material model, for which all intensive properties derive from a common energy. The motivation for developingmore » such a model is to improve upon ALEGRA's present combined model framework. Several applications of the new Johnson Cook implementation are presented. Deformation driven loading paths demonstrate the basic features of the new model formulation. Use of the model produces good comparisons with experimental Taylor impact data. Localized deformation leading to fragmentation is produced for expanding ring and exploding cylinder applications.« less

Elastic hysteresis phenomena in ULE and Zerodur optical glasses at elevated temperatures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wilkins, S.C.; Coon, D.N.; Epstein, J.S.

1988-01-01

Elastic hysteresis phenomena were observed in ULE and Zerodur glasses at elevated temperatures up to glass transition. These effects were found under load deformation testing using four-point bending. Permanent creep resulted in Zerodur at 900/degree/C and in ULE at 1000/degree/C. The deformation was monitored at mid-span of the samples with a capacitance-type transducer having 0.01 micrometer resolution. These hysteresis effects may be classified as elastic bimodulus between loading and unloading; that is, two different elastic moduli were observed between loading and unloading. Upon complete unloading, a minimal deformation state promptly returned, indicating little or no viscoelastic creep. The hysteresis effectmore » may be attributed to a change in glass structure as a function of stress state. A description of the test apparatus and procedure, test results for both glasses at several elevated temperatures, and an elementary discussion of continuum theory of constitutive behavior are included. 6 refs., 9 figs.« less

Multiscale Multiphysics and Multidomain Models I: Basic Theory

PubMed Central

Wei, Guo-Wei

2013-01-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field. PMID:25382892

Multiscale Multiphysics and Multidomain Models I: Basic Theory.

PubMed

Wei, Guo-Wei

2013-12-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.

The motion of interconnected flexible bodies

NASA Technical Reports Server (NTRS)

Hopkins, A. S.

1975-01-01

The equations of motion for an arbitrarily interconnected collection of substructures are derived. The substructures are elastic bodies which may be idealized as finite element assemblies and are subject to small deformations relative to a nominal state. Interconnections between the elastic substructures permit large relative translations and rotations between substructures, governed by Pfaffian constraints describing the connections. Screw connections (permitting rotation about and translation along a single axis) eliminate constraint forces and incorporate modal coupling. The problem of flexible spacecraft simulation is discussed. Hurty's component mode approach is extended by permitting interconnected elastic substructures large motions relative to each other and relative to inertial space. The hybrid coordinate methods are generalized by permitting all substructures to be flexible (rather than only the terminal members of a topological tree of substructures). The basic relationships of continuum mechanics are developed.

Parallel Program Systems for the Analysis of Wave Processes in Elastic-Plastic, Granular, Porous and Multi-Blocky Media

NASA Astrophysics Data System (ADS)

Sadovskaya, Oxana; Sadovskii, Vladimir

2017-04-01

Under modeling the wave propagation processes in geomaterials (granular and porous media, soils and rocks) it is necessary to take into account the structural inhomogeneity of these materials. Parallel program systems for numerical solution of 2D and 3D problems of the dynamics of deformable media with constitutive relationships of rather general form on the basis of universal mathematical model describing small strains of elastic, elastic-plastic, granular and porous materials are worked out. In the case of an elastic material, the model is reduced to the system of equations, hyperbolic by Friedrichs, written in terms of velocities and stresses in a symmetric form. In the case of an elastic-plastic material, the model is a special formulation of the Prandtl-Reuss theory in the form of variational inequality with one-sided constraints on the stress tensor. Generalization of the model to describe granularity and the collapse of pores is obtained by means of the rheological approach, taking into account different resistance of materials to tension and compression. Rotational motion of particles in the material microstructure is considered within the framework of a mathematical model of the Cosserat continuum. Computational domain may have a blocky structure, composed of an arbitrary number of layers, strips in a layer and blocks in a strip from different materials with self-consistent curvilinear interfaces. At the external boundaries of computational domain the main types of dissipative boundary conditions in terms of velocities, stresses or mixed boundary conditions can be given. Shock-capturing algorithm is proposed for implementation of the model on supercomputers with cluster architecture. It is based on the two-cyclic splitting method with respect to spatial variables and the special procedures of the stresses correction to take into account plasticity, granularity or porosity of a material. An explicit monotone ENO-scheme is applied for solving one-dimensional systems of equations at the stages of splitting method. The parallelizing of computations is carried out using the MPI library and the SPMD technology. The data exchange between processors occurs at step "predictor" of the finite-difference scheme. Program systems allow simulate the propagation of waves produced by external mechanical effects in a medium, aggregated of arbitrary number of heterogeneous blocks. Some computations of dynamic problems with and without taking into account the moment properties of a material were performed on clusters of ICM SB RAS (Krasnoyarsk) and JSCC RAS (Moscow). Parallel program systems 2Dyn_Granular, 3Dyn_Granular, 2Dyn_Cosserat, 3Dyn_Cosserat and 2Dyn_Blocks_MPI for numerical solution of 2D and 3D elastic-plastic problems of the dynamics of granular media and problems of the Cosserat elasticity theory, as well as for modeling of the dynamic processes in multi-blocky media with pliant viscoelastic, porous and fluid-saturated interlayers on cluster systems were registered by Rospatent.

Shape of a ponytail and the statistical physics of hair fiber bundles.

PubMed

Goldstein, Raymond E; Warren, Patrick B; Ball, Robin C

2012-02-17

A general continuum theory for the distribution of hairs in a bundle is developed, treating individual fibers as elastic filaments with random intrinsic curvatures. Applying this formalism to the iconic problem of the ponytail, the combined effects of bending elasticity, gravity, and orientational disorder are recast as a differential equation for the envelope of the bundle, in which the compressibility enters through an "equation of state." From this, we identify the balance of forces in various regions of the ponytail, extract a remarkably simple equation of state from laboratory measurements of human ponytails, and relate the pressure to the measured random curvatures of individual hairs.

An anatomically based patient-specific finite element model of patella articulation: towards a diagnostic tool.

PubMed

Fernandez, J W; Hunter, P J

2005-08-01

A 3D anatomically based patient-specific finite element (FE) model of patello-femoral (PF) articulation is presented to analyse the main features of patella biomechanics, namely, patella tracking (kinematics), quadriceps extensor forces, surface contact and internal patella stresses. The generic geometries are a subset from the model database of the International Union of Physiological Sciences (IUPS) (http://www.physiome.org.nz) Physiome Project with soft tissue derived from the widely used visible human dataset, and the bones digitised from an anatomically accurate physical model with muscle attachment information. The models are customised to patient magnetic resonance images using a variant of free-form deformation, called 'host-mesh' fitting. The continuum was solved using the governing equation of finite elasticity, with the multibody problem coupled through contact mechanics. Additional constraints such as tissue incompressibility are also imposed. Passive material properties are taken from the literature and implemented for deformable tissue with a non-linear micro-structurally based constitutive law. Bone and cartilage are implemented using a 'St-Venant Kirchoff' model suitable for rigid body rotations. The surface fibre directions have been estimated from anatomy images of cadaver muscle dissections and active muscle contraction was based on a steady-state calcium-tension relation. The 3D continuum model of muscle, tendon and bone is compared with experimental results from the literature, and surgical simulations performed to illustrate its clinical assessment capabilities (a Maquet procedure for reducing patella stresses and a vastus lateralis release for a bipartite patella). Finally, the model limitations, issues and future improvements are discussed.

Four-body extension of the continuum-discretized coupled-channels method

NASA Astrophysics Data System (ADS)

Descouvemont, P.

2018-06-01

I develop an extension of the continuum-discretized coupled-channels (CDCC) method to reactions where both nuclei present a low breakup threshold. This leads to a four-body model, where the only inputs are the interactions describing the colliding nuclei, and the four optical potentials between the fragments. Once these potentials are chosen, the model does not contain any additional parameter. First I briefly discuss the general formalism, and emphasize the need for dealing with large coupled-channel systems. The method is tested with existing benchmarks on 4 α bound states with the Ali-Bodmer potential. Then I apply the four-body CDCC to the 11Be+d system, where I consider the 10Be(0+,2+)+n configuration for 11Be. I show that breakup channels are crucial to reproduce the elastic cross section, but that core excitation plays a weak role. The 7Li+d system is investigated with an α +t cluster model for 7Li. I show that breakup channels significantly improve the agreement with the experimental cross section, but an additional imaginary term, simulating missing transfer channels, is necessary. The full CDCC results can be interpreted by equivalent potentials. For both systems, the real part is weakly affected by breakup channels, but the imaginary part is strongly modified. I suggest that the present wave functions could be used in future DWBA calculations.

The pH-dependent elastic properties of nanoscale DNA films and the resultant bending signals for microcantilever biosensors.

PubMed

Zhou, Mei-Hong; Meng, Wei-Lie; Zhang, Cheng-Yin; Li, Xiao-Bin; Wu, Jun-Zheng; Zhang, Neng-Hui

2018-04-25

The diverse mechanical properties of nanoscale DNA films on solid substrates have a close correlation with complex detection signals of micro-/nano-devices. This paper is devoted to formulating several multiscale models to study the effect of pH-dependent ionic inhomogeneity on the graded elastic properties of nanoscale DNA films and the resultant bending deflections of microcantilever biosensors. First, a modified inverse Debye length is introduced to improve the classical Poisson-Boltzmann equation for the electrical potential of DNA films to consider the inhomogeneous effect of hydrogen ions. Second, the graded characteristics of the particle distribution are taken into consideration for an improvement in Parsegian's mesoscopic potential for both attraction-dominated and repulsion-dominated films. Third, by the improved interchain interaction potential and the thought experiment about the compression of a macroscopic continuum DNA bar, we investigate the diversity of the elastic properties of single-stranded DNA (ssDNA) films due to pH variations. The relevant theoretical predictions quantitatively or qualitatively agree well with the relevant DNA experiments on the electrical potential, film thickness, condensation force, elastic modulus, and microcantilever deflections. The competition between attraction and repulsion among the fixed charges and the free ions endows the DNA film with mechanical properties such as a remarkable size effect and a non-monotonic behavior, and a negative elastic modulus is first revealed in the attraction-dominated ssDNA film. There exists a transition between the pH-sensitive parameter interval and the pH-insensitive one for the bending signals of microcantilevers, which is predominated by the initial stress effect in the DNA film.

Mechanics of couple-stress fluid coatings

NASA Technical Reports Server (NTRS)

Waxman, A. M.

1982-01-01

The formal development of a theory of viscoelastic surface fluids with bending resistance - their kinematics, dynamics, and rheology are discussed. It is relevant to the mechanics of fluid drops and jets coated by a thin layer of immiscible fluid with rather general rheology. This approach unifies the hydrodynamics of two-dimensional fluids with the mechanics of an elastic shell in the spirit of a Cosserat continuum. There are three distinct facets to the formulation of surface continuum mechanics. Outlined are the important ideas and results associated with each: the kinematics of evolving surface geometries, the conservation laws governing the mechanics of surface continua, and the rheological equations of state governing the surface stress and moment tensors.

A poroelastic model coupled to a fluid network with applications in lung modelling.

PubMed

Berger, Lorenz; Bordas, Rafel; Burrowes, Kelly; Grau, Vicente; Tavener, Simon; Kay, David

2016-01-01

We develop a lung ventilation model based on a continuum poroelastic representation of lung parenchyma that is strongly coupled to a pipe network representation of the airway tree. The continuous system of equations is discretized using a low-order stabilised finite element method. The framework is applied to a realistic lung anatomical model derived from computed tomography data and an artificially generated airway tree to model the conducting airway region. Numerical simulations produce physiologically realistic solutions and demonstrate the effect of airway constriction and reduced tissue elasticity on ventilation, tissue stress and alveolar pressure distribution. The key advantage of the model is the ability to provide insight into the mutual dependence between ventilation and deformation. This is essential when studying lung diseases, such as chronic obstructive pulmonary disease and pulmonary fibrosis. Thus the model can be used to form a better understanding of integrated lung mechanics in both the healthy and diseased states. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zimmerman, Jonathan A.; Jones, Reese E.; Templeton, Jeremy Alan

Materials with characteristic structures at nanoscale sizes exhibit significantly different mechani-cal responses from those predicted by conventional, macroscopic continuum theory. For example,nanocrystalline metals display an inverse Hall-Petch effect whereby the strength of the materialdecreases with decreasing grain size. The origin of this effect is believed to be a change in defor-mation mechanisms from dislocation motion across grains and pileup at grain boundaries at mi-croscopic grain sizes to rotation of grains and deformation within grain boundary interface regionsfor nanostructured materials. These rotational defects are represented by the mathematical conceptof disclinations. The ability to capture these effects within continuum theory, thereby connectingnanoscalemore » materials phenomena and macroscale behavior, has eluded the research community.The goal of our project was to develop a consistent theory to model both the evolution ofdisclinations and their kinetics. Additionally, we sought to develop approaches to extract contin-uum mechanical information from nanoscale structure to verify any developed continuum theorythat includes dislocation and disclination behavior. These approaches yield engineering-scale ex-pressions to quantify elastic and inelastic deformation in all varieties of materials, even those thatpossess highly directional bonding within their molecular structures such as liquid crystals, cova-lent ceramics, polymers and biological materials. This level of accuracy is critical for engineeringdesign and thermo-mechanical analysis is performed in micro- and nanosystems. The researchproposed here innovates on how these nanoscale deformation mechanisms should be incorporatedinto a continuum mechanical formulation, and provides the foundation upon which to develop ameans for predicting the performance of advanced engineering materials.4 AcknowledgmentThe authors acknowledge helpful discussions with Farid F. Abraham, Youping Chen, Terry J.Delph, Remi Dingreville, James W. Foulk III, Robert J. Hardy, Richard Lehoucq, Alejandro Mota,Gregory J. Wagner, Edmund B. Webb III and Xiaowang Zhou. Support for this project was pro-vided by the Enabling Predictive Simulation Investment Area of Sandia's Laboratory DirectedResearch and Development (LDRD) program.5« less

Image-based model of the spectrin cytoskeleton for red blood cell simulation.

PubMed

Fai, Thomas G; Leo-Macias, Alejandra; Stokes, David L; Peskin, Charles S

2017-10-01

We simulate deformable red blood cells in the microcirculation using the immersed boundary method with a cytoskeletal model that incorporates structural details revealed by tomographic images. The elasticity of red blood cells is known to be supplied by both their lipid bilayer membranes, which resist bending and local changes in area, and their cytoskeletons, which resist in-plane shear. The cytoskeleton consists of spectrin tetramers that are tethered to the lipid bilayer by ankyrin and by actin-based junctional complexes. We model the cytoskeleton as a random geometric graph, with nodes corresponding to junctional complexes and with edges corresponding to spectrin tetramers such that the edge lengths are given by the end-to-end distances between nodes. The statistical properties of this graph are based on distributions gathered from three-dimensional tomographic images of the cytoskeleton by a segmentation algorithm. We show that the elastic response of our model cytoskeleton, in which the spectrin polymers are treated as entropic springs, is in good agreement with the experimentally measured shear modulus. By simulating red blood cells in flow with the immersed boundary method, we compare this discrete cytoskeletal model to an existing continuum model and predict the extent to which dynamic spectrin network connectivity can protect against failure in the case of a red cell subjected to an applied strain. The methods presented here could form the basis of disease- and patient-specific computational studies of hereditary diseases affecting the red cell cytoskeleton.

Image-based model of the spectrin cytoskeleton for red blood cell simulation

PubMed Central

Stokes, David L.; Peskin, Charles S.

2017-01-01

We simulate deformable red blood cells in the microcirculation using the immersed boundary method with a cytoskeletal model that incorporates structural details revealed by tomographic images. The elasticity of red blood cells is known to be supplied by both their lipid bilayer membranes, which resist bending and local changes in area, and their cytoskeletons, which resist in-plane shear. The cytoskeleton consists of spectrin tetramers that are tethered to the lipid bilayer by ankyrin and by actin-based junctional complexes. We model the cytoskeleton as a random geometric graph, with nodes corresponding to junctional complexes and with edges corresponding to spectrin tetramers such that the edge lengths are given by the end-to-end distances between nodes. The statistical properties of this graph are based on distributions gathered from three-dimensional tomographic images of the cytoskeleton by a segmentation algorithm. We show that the elastic response of our model cytoskeleton, in which the spectrin polymers are treated as entropic springs, is in good agreement with the experimentally measured shear modulus. By simulating red blood cells in flow with the immersed boundary method, we compare this discrete cytoskeletal model to an existing continuum model and predict the extent to which dynamic spectrin network connectivity can protect against failure in the case of a red cell subjected to an applied strain. The methods presented here could form the basis of disease- and patient-specific computational studies of hereditary diseases affecting the red cell cytoskeleton. PMID:28991926

Effects of Thermal Noise on the Transitional Dynamics of an Inextensible Elastic Filament in Stagnation Flow

PubMed Central

Deng, Mingge; Grinberg, Leopold; Caswell, Bruce

2015-01-01

We investigate the dynamics of a single inextensible elastic filament subject to anisotropic friction in a viscous stagnation-point flow, by employing both a continuum model represented by Langevin type stochastic partial differential equations (SPDEs) and a Dissipative Particle Dynamics (DPD) method. Unlike previous works1, the filament is free to rotate and the tension along the filament is determined by the local inextensible constraint. The kinematics of the filament is recorded and studied with normal modes analysis. The results show that the filament displays an instability induced by negative tension, which is analogous to Euler buckling of a beam. Symmetry breaking of normal modes dynamics and stretch-coil transitions are observed above the threshold of the buckling instability point. Furthermore, both temporal and spatial noise are amplified resulting from the interaction of thermal fluctuations and nonlinear filament dynamics. Specifically, the spatial noise is amplified with even normal modes being excited due to symmetry breaking, while the temporal noise is amplified with increasing time correlation length and variance. PMID:26023834

Interrelated structures of the transport shock and collisional relaxation layer in a multitemperature, multilevel ionized gas

NASA Technical Reports Server (NTRS)

Vinolo, A. R.; Clarke, J. H.

1972-01-01

The gas dynamic structures of the transport shock and the downstream collisional relaxation layer are evaluated for partially ionized monatomic gases. Elastic and inelastic collisional nonequilibrium effects are taken into consideration. Three electronic levels are accounted for in the microscopic model of the atom. Nonequilibrium processes with respect to population of levels and species plus temperature are considered. By using an asymptotic technique the shock morphology is found on a continuum flow basis. The asymptotic procedure gives two distinct layers in which the nonequilibrium effects to be considered are different. A transport shock appears as the inner solution to an outer collisional relaxation layer in which the gas reaches local equilibrium. A family of numerical examples is displayed for different flow regimes. Argon and helium models are used in these examples.

Vector calculus in non-integer dimensional space and its applications to fractal media

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-02-01

We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

A continuum mechanics-based musculo-mechanical model for esophageal transport

NASA Astrophysics Data System (ADS)

Kou, Wenjun; Griffith, Boyce E.; Pandolfino, John E.; Kahrilas, Peter J.; Patankar, Neelesh A.

2017-11-01

In this work, we extend our previous esophageal transport model using an immersed boundary (IB) method with discrete fiber-based structural model, to one using a continuum mechanics-based model that is approximated based on finite elements (IB-FE). To deal with the leakage of flow when the Lagrangian mesh becomes coarser than the fluid mesh, we employ adaptive interaction quadrature points to deal with Lagrangian-Eulerian interaction equations based on a previous work (Griffith and Luo [1]). In particular, we introduce a new anisotropic adaptive interaction quadrature rule. The new rule permits us to vary the interaction quadrature points not only at each time-step and element but also at different orientations per element. This helps to avoid the leakage issue without sacrificing the computational efficiency and accuracy in dealing with the interaction equations. For the material model, we extend our previous fiber-based model to a continuum-based model. We present formulations for general fiber-reinforced material models in the IB-FE framework. The new material model can handle non-linear elasticity and fiber-matrix interactions, and thus permits us to consider more realistic material behavior of biological tissues. To validate our method, we first study a case in which a three-dimensional short tube is dilated. Results on the pressure-displacement relationship and the stress distribution matches very well with those obtained from the implicit FE method. We remark that in our IB-FE case, the three-dimensional tube undergoes a very large deformation and the Lagrangian mesh-size becomes about 6 times of Eulerian mesh-size in the circumferential orientation. To validate the performance of the method in handling fiber-matrix material models, we perform a second study on dilating a long fiber-reinforced tube. Errors are small when we compare numerical solutions with analytical solutions. The technique is then applied to the problem of esophageal transport. We use two fiber-reinforced models for the esophageal tissue: a bi-linear model and an exponential model. We present three cases on esophageal transport that differ in the material model and the muscle fiber architecture. The overall transport features are consistent with those observed from the previous model. We remark that the continuum-based model can handle more realistic and complicated material behavior. This is demonstrated in our third case where a spatially varying fiber architecture is included based on experimental study. We find that this unique muscle fiber architecture could generate a so-called pressure transition zone, which is a luminal pressure pattern that is of clinical interest. This suggests an important role of muscle fiber architecture in esophageal transport.

Simulations of Sea-Ice Dynamics Using the Material-Point Method

NASA Technical Reports Server (NTRS)

Sulsky, D.; Schreyer, H.; Peterson, K.; Nguyen, G.; Coon, G.; Kwok, R.

2006-01-01

In recent years, the availability of large volumes of recorded ice motion derived from high-resolution SAR data has provided an amazingly detailed look at the deformation of the ice cover. The deformation is dominated by the appearance of linear kinematic features that have been associated with the presence of leads. These remarkable data put us in a position to begin detailed evaluation of current coupled mechanical and thermodynamic models of sea ice. This presentation will describe the material point method (MPM) for solving these model equations. MPM is a numerical method for continuum mechanics that combines the best aspects of Lagrangian and Eulerian discretizations. The material points provide a Lagrangian description of the ice that models convection naturally. Thus, properties such as ice thickness and compactness are computed in a Lagrangian frame and do not suffer from errors associated with Eulerian advection schemes, such as artificial diffusion, dispersion, or oscillations near discontinuities. This desirable property is illustrated by solving transport of ice in uniform, rotational and convergent velocity fields. Moreover, the ice geometry is represented by unconnected material points rather than a grid. This representation facilitates modeling the large deformations observed in the Arctic, as well as localized deformation along leads, and admits a sharp representation of the ice edge. MPM also easily allows the use of any ice constitutive model. The versatility of MPM is demonstrated by using two constitutive models for simulations of wind-driven ice. The first model is a standard viscous-plastic model with two thickness categories. The MPM solution to the viscous-plastic model agrees with previously published results using finite elements. The second model is a new elastic-decohesive model that explicitly represents leads. The model includes a mechanism to initiate leads, and to predict their orientation and width. The elastic-decohesion model can provide similar overall deformation as the viscous-plastic model; however, explicit regions of opening and shear are predicted. Furthermore, the efficiency of MPM with the elastic-decohesive model is competitive with the current best methods for sea ice dynamics. Simulations will also be presented for an area of the Beaufort Sea, where predictions can be validated against satellite observations of the Arctic.

On the mechanics of growing thin biological membranes

NASA Astrophysics Data System (ADS)

Rausch, Manuel K.; Kuhl, Ellen

2014-02-01

Despite their seemingly delicate appearance, thin biological membranes fulfill various crucial roles in the human body and can sustain substantial mechanical loads. Unlike engineering structures, biological membranes are able to grow and adapt to changes in their mechanical environment. Finite element modeling of biological growth holds the potential to better understand the interplay of membrane form and function and to reliably predict the effects of disease or medical intervention. However, standard continuum elements typically fail to represent thin biological membranes efficiently, accurately, and robustly. Moreover, continuum models are typically cumbersome to generate from surface-based medical imaging data. Here we propose a computational model for finite membrane growth using a classical midsurface representation compatible with standard shell elements. By assuming elastic incompressibility and membrane-only growth, the model a priori satisfies the zero-normal stress condition. To demonstrate its modular nature, we implement the membrane growth model into the general-purpose non-linear finite element package Abaqus/Standard using the concept of user subroutines. To probe efficiently and robustness, we simulate selected benchmark examples of growing biological membranes under different loading conditions. To demonstrate the clinical potential, we simulate the functional adaptation of a heart valve leaflet in ischemic cardiomyopathy. We believe that our novel approach will be widely applicable to simulate the adaptive chronic growth of thin biological structures including skin membranes, mucous membranes, fetal membranes, tympanic membranes, corneoscleral membranes, and heart valve membranes. Ultimately, our model can be used to identify diseased states, predict disease evolution, and guide the design of interventional or pharmaceutic therapies to arrest or revert disease progression.

Differential geometry-based solvation and electrolyte transport models for biomolecular modeling: a review

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wei, Guowei; Baker, Nathan A.

2016-11-11

This chapter reviews the differential geometry-based solvation and electrolyte transport for biomolecular solvation that have been developed over the past decade. A key component of these methods is the differential geometry of surfaces theory, as applied to the solvent-solute boundary. In these approaches, the solvent-solute boundary is determined by a variational principle that determines the major physical observables of interest, for example, biomolecular surface area, enclosed volume, electrostatic potential, ion density, electron density, etc. Recently, differential geometry theory has been used to define the surfaces that separate the microscopic (solute) domains for biomolecules from the macroscopic (solvent) domains. In thesemore » approaches, the microscopic domains are modeled with atomistic or quantum mechanical descriptions, while continuum mechanics models (including fluid mechanics, elastic mechanics, and continuum electrostatics) are applied to the macroscopic domains. This multiphysics description is integrated through an energy functional formalism and the resulting Euler-Lagrange equation is employed to derive a variety of governing partial differential equations for different solvation and transport processes; e.g., the Laplace-Beltrami equation for the solvent-solute interface, Poisson or Poisson-Boltzmann equations for electrostatic potentials, the Nernst-Planck equation for ion densities, and the Kohn-Sham equation for solute electron density. Extensive validation of these models has been carried out over hundreds of molecules, including proteins and ion channels, and the experimental data have been compared in terms of solvation energies, voltage-current curves, and density distributions. We also propose a new quantum model for electrolyte transport.« less

On the mechanics of growing thin biological membranes

PubMed Central

Rausch, Manuel K.; Kuhl, Ellen

2013-01-01

Despite their seemingly delicate appearance, thin biological membranes fulfill various crucial roles in the human body and can sustain substantial mechanical loads. Unlike engineering structures, biological membranes are able to grow and adapt to changes in their mechanical environment. Finite element modeling of biological growth holds the potential to better understand the interplay of membrane form and function and to reliably predict the effects of disease or medical intervention. However, standard continuum elements typically fail to represent thin biological membranes efficiently, accurately, and robustly. Moreover, continuum models are typically cumbersome to generate from surface-based medical imaging data. Here we propose a computational model for finite membrane growth using a classical midsurface representation compatible with standard shell elements. By assuming elastic incompressibility and membrane-only growth, the model a priori satisfies the zero-normal stress condition. To demonstrate its modular nature, we implement the membrane growth model into the general-purpose non-linear finite element package Abaqus/Standard using the concept of user subroutines. To probe efficiently and robustness, we simulate selected benchmark examples of growing biological membranes under different loading conditions. To demonstrate the clinical potential, we simulate the functional adaptation of a heart valve leaflet in ischemic cardiomyopathy. We believe that our novel approach will be widely applicable to simulate the adaptive chronic growth of thin biological structures including skin membranes, mucous membranes, fetal membranes, tympanic membranes, corneoscleral membranes, and heart valve membranes. Ultimately, our model can be used to identify diseased states, predict disease evolution, and guide the design of interventional or pharmaceutic therapies to arrest or revert disease progression. PMID:24563551

Mesh Deformation Based on Fully Stressed Design: The Method and Two-Dimensional Examples

NASA Technical Reports Server (NTRS)

Hsu, Su-Yuen; Chang, Chau-Lyan

2007-01-01

Mesh deformation in response to redefined boundary geometry is a frequently encountered task in shape optimization and analysis of fluid-structure interaction. We propose a simple and concise method for deforming meshes defined with three-node triangular or four-node tetrahedral elements. The mesh deformation method is suitable for large boundary movement. The approach requires two consecutive linear elastic finite-element analyses of an isotropic continuum using a prescribed displacement at the mesh boundaries. The first analysis is performed with homogeneous elastic property and the second with inhomogeneous elastic property. The fully stressed design is employed with a vanishing Poisson s ratio and a proposed form of equivalent strain (modified Tresca equivalent strain) to calculate, from the strain result of the first analysis, the element-specific Young s modulus for the second analysis. The theoretical aspect of the proposed method, its convenient numerical implementation using a typical linear elastic finite-element code in conjunction with very minor extra coding for data processing, and results for examples of large deformation of two-dimensional meshes are presented in this paper. KEY WORDS: Mesh deformation, shape optimization, fluid-structure interaction, fully stressed design, finite-element analysis, linear elasticity, strain failure, equivalent strain, Tresca failure criterion

A Theoretical Analysis of the Effect of the Hydrogenation of Graphene to Graphane on Its Mechanical Properties

NASA Astrophysics Data System (ADS)

Peng, Q.; Liang, Chao; Ji, Wei; de, Suvranu

2013-03-01

We investigated the mechanical properties of graphene and graphane using first-principles calculations based on density-functional theory. A conventional unitcell containing a hexagonal ring made of carbon atoms was chosen to capture the finite wave vector ``soft modes'', which affect the the fourth and fifth elastic constants considerably. Graphane has about 2/3 ultimate strengths in all three tested deformation modes - armchair, zigzag, and biaxial- compared to graphene. However, graphane has larger ultimate strains in zigzag deformation, and smaller in armchair deformation. We obtained the second, third, fourth, and fifth order elastic constants for a rigorous continuum description of the elastic response. Graphane has a relatively low in-plane stiffness of 240 N/m which is about 2/3 of that of graphene, and a very small Poisson ratio of 0.078, 44% of that of graphene. The pressure dependence of the second order elastic constants were predicted from the third order elastic constants. The Poisson's ratio monotonically decreases with increasing pressure. Acknowledge the financial support from DTRA Grant # BRBAA08-C-2-0130, the U.S. NRCFDP # NRC-38-08-950, and U.S. DOE NEUP Grant #DE-NE0000325.

Mechanics of ultrasound elastography

PubMed Central

Li, Guo-Yang

2017-01-01

Ultrasound elastography enables in vivo measurement of the mechanical properties of living soft tissues in a non-destructive and non-invasive manner and has attracted considerable interest for clinical use in recent years. Continuum mechanics plays an essential role in understanding and improving ultrasound-based elastography methods and is the main focus of this review. In particular, the mechanics theories involved in both static and dynamic elastography methods are surveyed. They may help understand the challenges in and opportunities for the practical applications of various ultrasound elastography methods to characterize the linear elastic, viscoelastic, anisotropic elastic and hyperelastic properties of both bulk and thin-walled soft materials, especially the in vivo characterization of biological soft tissues. PMID:28413350

NASA Astrophysics Data System (ADS)

Morcelle, V.; Lichtenthäler, R.; Lépine-Szily, A.; Guimarães, V.; Pires, K. C. C.; Lubian, J.; Mendes Junior, D. R.; de Faria, P. N.; Kolata, J. J.; Becchetti, F. D.; Jiang, H.; Aguilera, E. F.; Lizcano, D.; Martinez-Quiroz, E.; Garcia, H.

2017-01-01

We present 8B 27Al elastic scattering angular distributions for the proton-halo nucleus 8B at two energies above the Coulomb barrier, namely Elab=15.3 and 21.7 MeV. The experiments were performed in the Radioactive Ion Beams in Brasil facility (RIBRAS) in São Paulo, and in the TwinSol facility at the University of Notre Dame, USA. The angular distributions were measured in the angular range of 15-80 degrees. Optical model and continuum discretized coupled channels calculations were performed, and the total reaction cross sections were derived. A comparison of the 8B+27Al total reaction cross sections with similar systems including exotic, weakly bound, and tightly bound projectiles impinging on the same target is presented.

Anticrack inclusion model for compaction bands in sandstone

NASA Astrophysics Data System (ADS)

Sternlof, Kurt R.; Rudnicki, John W.; Pollard, David D.

2005-11-01

Detailed observations of compaction bands exposed in the Aztec Sandstone of southeastern Nevada indicate that these thin, tabular, bounded features of localized porosity loss initiated at pervasive grain-scale flaws, which collapsed in response to compressive tectonic loading. From many of these Griffith-type flaws, an apparently self-sustaining progression of collapse propagated outward to form bands of compacted grains a few centimeters thick and tens of meters in planar extent. These compaction bands can be idealized as highly eccentric ellipsoidal bodies that have accommodated uniform uniaxial plastic strain parallel to their short dimension within a surrounding elastic material. They thus can be represented mechanically as contractile Eshelby inclusions, which generate near-tip compressive stress concentrations consistent with self-sustaining, in-plane propagation. The combination of extreme aspect ratio (˜10-4) and significant uniaxial plastic strain (˜10%) also justifies an approximation of the bands as anticracks: sharp boundaries across which a continuous distribution of closing mode displacement discontinuity has been accommodated. This anticrack interpretation of compaction bands is analogous to that of pressure solution surfaces, except that porosity loss takes the place of material dissolution. We find that displacement discontinuity boundary element modeling of compaction bands as anticracks within a two-dimensional linear elastic continuum can accurately represent the perturbed external stress fields they induce.

Measurements of stiff-material compliance on the nanoscale using ultrasonic force microscopy

NASA Astrophysics Data System (ADS)

Dinelli, F.; Biswas, S. K.; Briggs, G. A. D.; Kolosov, O. V.

2000-05-01

Ultrasonic force microscopy (UFM) was introduced to probe nanoscale mechanical properties of stiff materials. This was achieved by vibrating the sample far above the first resonance of the probing atomic force microscope cantilever where the cantilever becomes dynamically rigid. By operating UFM at different set force values, it is possible to directly measure the absolute values of the tip-surface contact stiffness. From this an evaluation of surface elastic properties can be carried out assuming a suitable solid-solid contact model. In this paper we present curves of stiffness as a function of the normal load in the range of 0-300 nN. The dependence of stiffness on the relative humidity has also been investigated. Materials with different elastic constants (such as sapphire lithium fluoride, and silicon) have been successfully differentiated. Continuum mechanics models cannot however explain the dependence of stiffness on the normal force and on the relative humidity. In this high-frequency regime, it is likely that viscous forces might play an important role modifying the tip-surface interaction. Plastic deformation might also occur due to the high strain rates applied when ultrasonically vibrating the sample. Another possible cause of these discrepancies might be the presence of water in between the two bodies in contact organizing in a solidlike way and partially sustaining the load.

TensorCalculator: exploring the evolution of mechanical stress in the CCMV capsid

NASA Astrophysics Data System (ADS)

Kononova, Olga; Maksudov, Farkhad; Marx, Kenneth A.; Barsegov, Valeri

2018-01-01

A new computational methodology for the accurate numerical calculation of the Cauchy stress tensor, stress invariants, principal stress components, von Mises and Tresca tensors is developed. The methodology is based on the atomic stress approach which permits the calculation of stress tensors, widely used in continuum mechanics modeling of materials properties, using the output from the MD simulations of discrete atomic and C_α -based coarse-grained structural models of biological particles. The methodology mapped into the software package TensorCalculator was successfully applied to the empty cowpea chlorotic mottle virus (CCMV) shell to explore the evolution of mechanical stress in this mechanically-tested specific example of a soft virus capsid. We found an inhomogeneous stress distribution in various portions of the CCMV structure and stress transfer from one portion of the virus structure to another, which also points to the importance of entropic effects, often ignored in finite element analysis and elastic network modeling. We formulate a criterion for elastic deformation using the first principal stress components. Furthermore, we show that von Mises and Tresca stress tensors can be used to predict the onset of a viral capsid’s mechanical failure, which leads to total structural collapse. TensorCalculator can be used to study stress evolution and dynamics of defects in viral capsids and other large-size protein assemblies.

Viscous constitutive relations of solid-liquid composites in terms of grain boundary contiguity: 1. Grain boundary diffusion control model

NASA Astrophysics Data System (ADS)

Takei, Yasuko; Holtzman, Benjamin K.

2009-06-01

Viscous constitutive relations of partially molten rocks deforming in the regime of grain boundary (GB) diffusion creep are derived theoretically on the basis of microstructural processes at the grain scale. The viscous constitutive relation developed in this study is based on contiguity as an internal state variable, which enables us to take into account the detailed effects of grain-scale melt distribution observed in experiments. Compared to the elasticities derived previously for the same microstructural model, the viscosities are much more sensitive to the presence of melt and variations in contiguity. As explored in this series of three companion papers, this "contiguity" model predicts that a very small amount of melt (ϕ < 0.01) significantly reduces the bulk and shear viscosities. Furthermore, a large anisotropy in viscosity is produced by anisotropy in contiguity, which occurs in deforming partially molten rocks. These results have important implications for deformation and melt extraction at small melt fractions, as well as for shear-induced melt segregation. The viscous and elastic constitutive relations derived in terms of contiguity bridge microscopic grain-scale and macroscopic continuum properties. These constitutive relations are essential for investigating melt migration dynamics in a forward sense on the basis of the basic equations of two-phase dynamics and in an inverse sense on the basis of seismological observations.

Generalized continuum modeling of scale-dependent crystalline plasticity

NASA Astrophysics Data System (ADS)

Mayeur, Jason R.

The use of metallic material systems (e.g. pure metals, alloys, metal matrix composites) in a wide range of engineering applications from medical devices to electronic components to automobiles continues to motivate the development of improved constitutive models to meet increased performance demands while minimizing cost. Emerging technologies often incorporate materials in which the dominant microstructural features have characteristic dimensions reaching into the submicron and nanometer regime. Metals comprised of such fine microstructures often exhibit unique and size-dependent mechanical response, and classical approaches to constitutive model development at engineering (continuum) scales, being local in nature, are inadequate for describing such behavior. Therefore, traditional modeling frameworks must be augmented and/or reformulated to account for such phenomena. Crystal plasticity constitutive models have proven quite capable of capturing first-order microstructural effects such as grain orientation (elastic/plastic anisotropy), grain morphology, phase distribution, etc. on the deformation behavior of both single and polycrystals, yet suffer from the same limitations as other local continuum theories with regard to capturing scale-dependent mechanical response. This research is focused on the development, numerical implementation, and application of a generalized (nonlocal) theory of single crystal plasticity capable of describing the scale-dependent mechanical response of both single and polycrystalline metals that arises as a result of heterogeneous deformation. This research developed a dislocation-based theory of micropolar single crystal plasticity. The majority of nonlocal crystal plasticity theories are predicated on the connection between gradients of slip and geometrically necessary dislocations. Due to the diversity of existing nonlocal crystal plasticity theories, a review, summary, and comparison of representative model classes is presented in Chapter 2 from a unified dislocation-based perspective. The discussion of the continuum crystal plasticity theories is prefaced by a brief review of discrete dislocation plasticity, which facilitates the comparison of certain model aspects and also serves as a reference for latter segments of the research which make connection to this constitutive description. Chapter 2 has utility not only as a literature review, but also as a synthesis and analysis of competing and alternative nonlocal crystal plasticity modeling strategies from a common viewpoint. The micropolar theory of single crystal plasticity is presented in Chapter 3. Two different types of flow criteria are considered - the so-called single and multicriterion theories, and several variations of the dislocation-based strength models appropriate for each theory are presented and discussed. The numerical implementation of the two-dimensional version of the constitutive theory is given in Chapter 4. A user element subroutine for the implicit commercial finite element code Abaqus/Standard is developed and validated through the solution of initial-boundary value problems with closed-form solutions. Convergent behavior of the subroutine is also demonstrated for an initial-boundary value problem exhibiting strain localization. In Chapter 5, the models are employed to solve several standard initial-boundary value problems for heterogeneously deforming single crystals including simple shearing of a semi-infinite constrained thin film, pure bending of thin films, and simple shearing of a metal matrix composite with elastic inclusions. The simulation results are compared to those obtained from the solution of equivalent boundary value problems using discrete dislocation dynamics and alternative generalized crystal plasticity theories. Comparison and calibration with respect to the former provides guidance in the specification of non-traditional material parameters that arise in the model formulation and demonstrates its effectiveness at capturing the heterogeneous deformation fields and size-dependent mechanical behavior predicted by a finer scale constitutive description. Finally, in Chapter 6, the models are applied to simulate the deformation behavior of small polycrystalline ensembles. Several grain boundary constitutive descriptions are explored and the response characteristics are analyzed with respect to experimental observations as well as results obtained from discrete dislocation dynamics and alternative nonlocal crystal plasticity theories. Particular attention is focused on how the various grain boundary descriptions serve to either locally concentrate or diffuse deformation heterogeneity as a function of grain size.

Phase transitions during compression and decompression of clots from platelet-poor plasma, platelet-rich plasma and whole blood.

PubMed

Liang, Xiaojun; Chernysh, Irina; Purohit, Prashant K; Weisel, John W

2017-09-15

Blood clots are required to stem bleeding and are subject to a variety of stresses, but they can also block blood vessels and cause heart attacks and ischemic strokes. We measured the compressive response of human platelet-poor plasma (PPP) clots, platelet-rich plasma (PRP) clots and whole blood clots and correlated these measurements with confocal and scanning electron microscopy to track changes in clot structure. Stress-strain curves revealed four characteristic regions, for compression-decompression: (1) linear elastic region; (2) upper plateau or softening region; (3) non-linear elastic region or re-stretching of the network; (4) lower plateau in which dissociation of some newly made connections occurs. Our experiments revealed that compression proceeds by the passage of a phase boundary through the clot separating rarefied and densified phases. This observation motivates a model of fibrin mechanics based on the continuum theory of phase transitions, which accounts for the pre-stress caused by platelets, the adhesion of fibrin fibers in the densified phase, the compression of red blood cells (RBCs), and the pumping of liquids through the clot during compression/decompression. Our experiments and theory provide insights into the mechanical behavior of blood clots that could have implications clinically and in the design of fibrin-based biomaterials. The objective of this paper is to measure and mathematically model the compression behavior of various human blood clots. We show by a combination of confocal and scanning electron microscopy that compression proceeds by the passage of a front through the sample that separates a densified region of the clot from a rarefied region, and that the compression/decompression response is reversible with hysteresis. These observations form the basis of a model for the compression response of clots based on the continuum theory of phase transitions. Our studies may reveal how clot rheology under large compression in vivo due to muscle contraction, platelet retraction and hydrodynamic flow varies under various pathophysiological conditions and could inform the design of fibrin based biomaterials. Copyright © 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A continuum theory of edge dislocations

NASA Astrophysics Data System (ADS)

Berdichevsky, V. L.

2017-09-01

Continuum theory of dislocation aims to describe the behavior of large ensembles of dislocations. This task is far from completion, and, most likely, does not have a "universal solution", which is applicable to any dislocation ensemble. In this regards it is important to have guiding lines set by benchmark cases, where the transition from a discrete set of dislocations to a continuum description is made rigorously. Two such cases have been considered recently: equilibrium of dislocation walls and screw dislocations in beams. In this paper one more case is studied, equilibrium of a large set of 2D edge dislocations placed randomly in a 2D bounded region. The major characteristic of interest is energy of dislocation ensemble, because it determines the structure of continuum equations. The homogenized energy functional is obtained for the periodic dislocation ensembles with a random contents of the periodic cell. Parameters of the periodic structure can change slowly on distances of order of the size of periodic cells. The energy functional is obtained by the variational-asymptotic method. Equilibrium positions are local minima of energy. It is confirmed the earlier assertion that energy density of the system is the sum of elastic energy of averaged elastic strains and microstructure energy, which is elastic energy of the neutralized dislocation system, i.e. the dislocation system placed in a constant dislocation density field making the averaged dislocation density zero. The computation of energy is reduced to solution of a variational cell problem. This problem is solved analytically. The solution is used to investigate stability of simple dislocation arrays, i.e. arrays with one dislocation in the periodic cell. The relations obtained yield two outcomes: First, there is a state parameter of the system, dislocation polarization; averaged stresses affect only dislocation polarization and cannot change other characteristics of the system. Second, the structure of dislocation phase space is strikingly simple. Dislocation phase space is split in a family of subspaces corresponding to constant values of dislocation polarizations; in each equipolarization subspace there are many local minima of energy; for zero external stresses the system is stuck in a local minimum of energy; for non-zero slowly changing external stress, dislocation polarization evolves, while the system moves over local energy minima of equipolarization subspaces. Such a simple picture of dislocation dynamics is due to the presence of two time scales, slow evolution of dislocation polarization and fast motion of the system over local minima of energy. The existence of two time scales is justified for a neutral system of edge dislocations.

Molecular-dynamics Simulation-based Cohesive Zone Representation of Intergranular Fracture Processes in Aluminum

NASA Technical Reports Server (NTRS)

Yamakov, Vesselin I.; Saether, Erik; Phillips, Dawn R.; Glaessgen, Edward H.

2006-01-01

A traction-displacement relationship that may be embedded into a cohesive zone model for microscale problems of intergranular fracture is extracted from atomistic molecular-dynamics simulations. A molecular-dynamics model for crack propagation under steady-state conditions is developed to analyze intergranular fracture along a flat 99 [1 1 0] symmetric tilt grain boundary in aluminum. Under hydrostatic tensile load, the simulation reveals asymmetric crack propagation in the two opposite directions along the grain boundary. In one direction, the crack propagates in a brittle manner by cleavage with very little or no dislocation emission, and in the other direction, the propagation is ductile through the mechanism of deformation twinning. This behavior is consistent with the Rice criterion for cleavage vs. dislocation blunting transition at the crack tip. The preference for twinning to dislocation slip is in agreement with the predictions of the Tadmor and Hai criterion. A comparison with finite element calculations shows that while the stress field around the brittle crack tip follows the expected elastic solution for the given boundary conditions of the model, the stress field around the twinning crack tip has a strong plastic contribution. Through the definition of a Cohesive-Zone-Volume-Element an atomistic analog to a continuum cohesive zone model element - the results from the molecular-dynamics simulation are recast to obtain an average continuum traction-displacement relationship to represent cohesive zone interaction along a characteristic length of the grain boundary interface for the cases of ductile and brittle decohesion. Keywords: Crack-tip plasticity; Cohesive zone model; Grain boundary decohesion; Intergranular fracture; Molecular-dynamics simulation

Does the continuum theory of dynamic fracture work?

NASA Astrophysics Data System (ADS)

Kessler, David A.; Levine, Herbert

2003-09-01

We investigate the validity of the linear elastic fracture mechanics approach to dynamic fracture. We first test the predictions in a lattice simulation, using a formula of Eshelby for the time-dependent stress intensity factor. Excellent agreement with the theory is found. We then use the same method to analyze the experiment of Sharon and Fineberg. The data here are not consistent with the theoretical expectation.

Co- and post-seismic shallow fault physics from near-field geodesy, seismic tomography, and mechanical modeling

NASA Astrophysics Data System (ADS)

Nevitt, J.; Brooks, B. A.; Catchings, R.; Goldman, M.; Criley, C.; Chan, J. H.; Glennie, C. L.; Ericksen, T. L.; Madugo, C. M.

2017-12-01

The physics governing near-surface fault slip and deformation are largely unknown, introducing significant uncertainty into seismic hazard models. Here we combine near-field measurements of surface deformation from the 2014 M6.0 South Napa earthquake with high-resolution seismic imaging and finite element models to investigate the effects of rupture speed, elastic heterogeneities, and plasticity on shallow faulting. We focus on two sites that experienced either predominantly co-seismic or post-seismic slip. We measured surface deformation with mobile laser scanning of deformed vine rows within 300 m of the fault at 1 week and 1 month after the event. Shear strain profiles for the co- and post-seismic sites are similar, with maxima of 0.012 and 0.013 and values exceeding 0.002 occurring within 26 m- and 18 m-wide zones, respectively. That the rupture remained buried at the two sites and produced similar deformation fields suggests that permanent deformation due to dynamic stresses did not differ significantly from the quasi-static case, which might be expected if the rupture decelerated as it approached the surface. Active-source seismic surveys, 120 m in length with 1 m geophone/shot spacing, reveal shallow compliant zones of reduced shear modulus. For the co- and post-seismic sites, the tomographic anomaly (Vp/Vs > 5) at 20 m depth has a width of 80 m and 50 m, respectively, much wider than the observed surface displacement fields. We investigate this discrepancy with a suite of finite element models in which a planar fault is buried 5 m below the surface. The model continuum is defined by either homogeneous or heterogeneous elastic properties, with or without Drucker-Prager plastic yielding, with properties derived from lab testing of similar near-surface materials. We find that plastic yielding can greatly narrow the surface displacement zone, but that the width of this zone is largely insensitive to changes in the elastic structure (i.e., the presence of a compliant zone).

Single-cell mechanics--An experimental-computational method for quantifying the membrane-cytoskeleton elasticity of cells.

PubMed

Tartibi, M; Liu, Y X; Liu, G-Y; Komvopoulos, K

2015-11-01

The membrane-cytoskeleton system plays a major role in cell adhesion, growth, migration, and differentiation. F-actin filaments, cross-linkers, binding proteins that bundle F-actin filaments to form the actin cytoskeleton, and integrins that connect the actin cytoskeleton network to the cell plasma membrane and extracellular matrix are major cytoskeleton constituents. Thus, the cell cytoskeleton is a complex composite that can assume different shapes. Atomic force microscopy (AFM)-based techniques have been used to measure cytoskeleton material properties without much attention to cell shape. A recently developed surface chemical patterning method for long-term single-cell culture was used to seed individual cells on circular patterns. A continuum-based cell model, which uses as input the force-displacement response obtained with a modified AFM setup and relates the membrane-cytoskeleton elastic behavior to the cell geometry, while treating all other subcellular components suspended in the cytoplasmic liquid (gel) as an incompressible fluid, is presented and validated by experimental results. The developed analytical-experimental methodology establishes a framework for quantifying the membrane-cytoskeleton elasticity of live cells. This capability may have immense implications in cell biology, particularly in studies seeking to establish correlations between membrane-cytoskeleton elasticity and cell disease, mortality, differentiation, and migration, and provide insight into cell infiltration through nonwoven fibrous scaffolds. The present method can be further extended to analyze membrane-cytoskeleton viscoelasticity, examine the role of other subcellular components (e.g., nucleus envelope) in cell elasticity, and elucidate the effects of mechanical stimuli on cell differentiation and motility. This is the first study to decouple the membrane-cytoskeleton elasticity from cell stiffness and introduce an effective approach for measuring the elastic modulus. The novelty of this study is the development of new technology for quantifying the elastic stiffness of the membrane-cytoskeleton system of cells. This capability could have immense implications in cell biology, particularly in establishing correlations between various cell diseases, mortality, and differentiation with membrane-cytoskeleton elasticity, examining through-tissue cell migration, and understanding cell infiltration in porous scaffolds. The present method can be further extended to analyze membrane-cytoskeleton viscous behavior, identify the contribution of other subcellular components (e.g., nucleus envelope) to load sharing, and elucidate mechanotransduction effects due to repetitive compressive loading and unloading on cell differentiation and motility. Copyright © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The geometry of discombinations and its applications to semi-inverse problems in anelasticity

PubMed Central

Yavari, Arash; Goriely, Alain

2014-01-01

The geometrical formulation of continuum mechanics provides us with a powerful approach to understand and solve problems in anelasticity where an elastic deformation is combined with a non-elastic component arising from defects, thermal stresses, growth effects or other effects leading to residual stresses. The central idea is to assume that the material manifold, prescribing the reference configuration for a body, has an intrinsic, non-Euclidean, geometrical structure. Residual stresses then naturally arise when this configuration is mapped into Euclidean space. Here, we consider the problem of discombinations (a new term that we introduce in this paper), that is, a combined distribution of fields of dislocations, disclinations and point defects. Given a discombination, we compute the geometrical characteristics of the material manifold (curvature, torsion, non-metricity), its Cartan's moving frames and structural equations. This identification provides a powerful algorithm to solve semi-inverse problems with non-elastic components. As an example, we calculate the residual stress field of a cylindrically symmetric distribution of discombinations in an infinite circular cylindrical bar made of an incompressible hyperelastic isotropic elastic solid. PMID:25197257

Continuum modeling of large lattice structures: Status and projections

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Mikulas, Martin M., Jr.

1988-01-01

The status and some recent developments of continuum modeling for large repetitive lattice structures are summarized. Discussion focuses on a number of aspects including definition of an effective substitute continuum; characterization of the continuum model; and the different approaches for generating the properties of the continuum, namely, the constitutive matrix, the matrix of mass densities, and the matrix of thermal coefficients. Also, a simple approach is presented for generating the continuum properties. The approach can be used to generate analytic and/or numerical values of the continuum properties.

Dynamics of cancerous tissue correlates with invasiveness

NASA Astrophysics Data System (ADS)

West, Ann-Katrine Vransø; Wullkopf, Lena; Christensen, Amalie; Leijnse, Natascha; Tarp, Jens Magelund; Mathiesen, Joachim; Erler, Janine Terra; Oddershede, Lene Broeng

2017-03-01

Two of the classical hallmarks of cancer are uncontrolled cell division and tissue invasion, which turn the disease into a systemic, life-threatening condition. Although both processes are studied, a clear correlation between cell division and motility of cancer cells has not been described previously. Here, we experimentally characterize the dynamics of invasive and non-invasive breast cancer tissues using human and murine model systems. The intrinsic tissue velocities, as well as the divergence and vorticity around a dividing cell correlate strongly with the invasive potential of the tissue, thus showing a distinct correlation between tissue dynamics and aggressiveness. We formulate a model which treats the tissue as a visco-elastic continuum. This model provides a valid reproduction of the cancerous tissue dynamics, thus, biological signaling is not needed to explain the observed tissue dynamics. The model returns the characteristic force exerted by an invading cell and reveals a strong correlation between force and invasiveness of breast cancer cells, thus pinpointing the importance of mechanics for cancer invasion.

A viscoelastic-stochastic model of the effects of cytoskeleton remodelling on cell adhesion.

PubMed

Li, Long; Zhang, Wenyan; Wang, Jizeng

2016-10-01

Cells can adapt their mechanical properties through cytoskeleton remodelling in response to external stimuli when the cells adhere to the extracellular matrix (ECM). Many studies have investigated the effects of cell and ECM elasticity on cell adhesion. However, experiments determined that cells are viscoelastic and exhibiting stress relaxation, and the mechanism behind the effect of cellular viscoelasticity on the cell adhesion behaviour remains unclear. Therefore, we propose a theoretical model of a cluster of ligand-receptor bonds between two dissimilar viscoelastic media subjected to an applied tensile load. In this model, the distribution of interfacial traction is assumed to follow classical continuum viscoelastic equations, whereas the rupture and rebinding of individual molecular bonds are governed by stochastic equations. On the basis of this model, we determined that viscosity can significantly increase the lifetime, stability and dynamic strength of the adhesion cluster of molecular bonds, because deformation relaxation attributed to the viscoelastic property can increase the rebinding probability of each open bond and reduce the stress concentration in the adhesion area.

Efficient rolling texture predictions and texture-sensitive properties of α-uranium foils

DOE PAGES

Steiner, Matthew A.; Klein, Robert W.; Calhoun, Christopher A.; ...

2017-01-01

Here, finite element (FE) analysis was used to simulate the strain history of an α-uranium foil during cold-rolling, with the sheet modeled as an isotropic elastoplastic continuum. The resulting strain history was then used as input for a viscoplastic self-consistent (VPSC) polycrystal plasticity model to simulate crystallographic texture evolution. Mid-plane textures predicted via the combined FE→VPSC approach show alignment of the (010) poles along the rolling direction (RD), and the (001) poles along the normal direction (ND) with a symmetric splitting along RD. The surface texture is similar to that of the mid-plane, but with a shear-induced asymmetry that favorsmore » one of the RD split features of the (001) pole figure. Both the mid-plane and surface textures predicted by the FE→VPSC approach agree with published experimental results for cold-rolled α-uranium plates, as well as predictions made by a more computationally intensive full-field crystal plasticity based finite element model. α-uranium foils produced by cold-rolling must typically undergo a final recrystallization anneal to restore ductility prior to their final application, resulting in significant texture evolution from the cold-rolled plate deformation texture. Using the texture measured from a foil in the final recrystallized state, coefficients of the thermal expansion and elastic stiffness tensors were calculated using a thermo-elastic self-consistent model, and the anisotropic yield loci and flow curves along the RD, TD, and ND were predicted using the VPSC code.« less

Efficient rolling texture predictions and texture-sensitive properties of α-uranium foils

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steiner, Matthew A.; Klein, Robert W.; Calhoun, Christopher A.

Here, finite element (FE) analysis was used to simulate the strain history of an α-uranium foil during cold-rolling, with the sheet modeled as an isotropic elastoplastic continuum. The resulting strain history was then used as input for a viscoplastic self-consistent (VPSC) polycrystal plasticity model to simulate crystallographic texture evolution. Mid-plane textures predicted via the combined FE→VPSC approach show alignment of the (010) poles along the rolling direction (RD), and the (001) poles along the normal direction (ND) with a symmetric splitting along RD. The surface texture is similar to that of the mid-plane, but with a shear-induced asymmetry that favorsmore » one of the RD split features of the (001) pole figure. Both the mid-plane and surface textures predicted by the FE→VPSC approach agree with published experimental results for cold-rolled α-uranium plates, as well as predictions made by a more computationally intensive full-field crystal plasticity based finite element model. α-uranium foils produced by cold-rolling must typically undergo a final recrystallization anneal to restore ductility prior to their final application, resulting in significant texture evolution from the cold-rolled plate deformation texture. Using the texture measured from a foil in the final recrystallized state, coefficients of the thermal expansion and elastic stiffness tensors were calculated using a thermo-elastic self-consistent model, and the anisotropic yield loci and flow curves along the RD, TD, and ND were predicted using the VPSC code.« less

Efficient rolling texture predictions and texture-sensitive thermomechanical properties of α-uranium foils

NASA Astrophysics Data System (ADS)

Steiner, Matthew A.; Klein, Robert W.; Calhoun, Christopher A.; Knezevic, Marko; Garlea, Elena; Agnew, Sean R.

2017-11-01

Finite element (FE) analysis was used to simulate the strain history of an α-uranium foil during cold straight-rolling, with the sheet modeled as an isotropic elastoplastic continuum. The resulting strain history was then used as input for a viscoplastic self-consistent (VPSC) polycrystal plasticity model to simulate crystallographic texture evolution. Mid-plane textures predicted via the combined FE→VPSC approach show alignment of the (010) poles along the rolling direction (RD), and the (001) poles along the normal direction (ND) with a symmetric splitting along RD. The surface texture is similar to that of the mid-plane, but with a shear-induced asymmetry that favors one of the RD split features of the (001) pole figure. Both the mid-plane and surface textures predicted by the FE→VPSC approach agree with published experimental results for cold straight-rolled α-uranium plates, as well as predictions made by a more computationally intensive full-field crystal plasticity based finite element model. α-uranium foils produced by cold-rolling must typically undergo a recrystallization anneal to restore ductility prior to their final application, resulting in significant texture evolution from the cold-rolled plate deformation texture. Using the texture measured from a foil in the final recrystallized state, coefficients of thermal expansion and the elastic stiffness tensors were calculated using a thermo-elastic self-consistent model, and the anisotropic yield loci and flow curves along the RD, TD, and ND were predicted using the VPSC code.

Fluctuation Pressure Assisted Ejection of DNA From Bacteriophage

NASA Astrophysics Data System (ADS)

Harrison, Michael J.

2011-03-01

The role of thermal pressure fluctuations excited within tightly packaged DNA while it is ejected from protein capsid shells is discussed in a model calculation. At equilibrium before ejection we assume the DNA is folded many times into a bundle of parallel segments that forms an equilibrium conformation at minimum free energy, which presses tightly against capsid walls. Using a canonical ensemble at temperature T we calculate internal pressure fluctuations against a slowly moving or static capsid mantle for an elastic continuum model of the folded DNA bundle. It is found that fluctuating pressures on the capsid from thermal excitation of longitudinal acoustic vibrations in the bundle whose wavelengths are exceeded by the bend persistence length may have root-mean-square values that are several tens of atmospheres for typically small phage dimensions. Comparisons are given with measured data on three mutants of lambda phage with different base pair lengths and total genome ejection pressures.

Two-dimensional strain gradient damage modeling: a variational approach

NASA Astrophysics Data System (ADS)

Placidi, Luca; Misra, Anil; Barchiesi, Emilio

2018-06-01

In this paper, we formulate a linear elastic second gradient isotropic two-dimensional continuum model accounting for irreversible damage. The failure is defined as the condition in which the damage parameter reaches 1, at least in one point of the domain. The quasi-static approximation is done, i.e., the kinetic energy is assumed to be negligible. In order to deal with dissipation, a damage dissipation term is considered in the deformation energy functional. The key goal of this paper is to apply a non-standard variational procedure to exploit the damage irreversibility argument. As a result, we derive not only the equilibrium equations but, notably, also the Karush-Kuhn-Tucker conditions. Finally, numerical simulations for exemplary problems are discussed as some constitutive parameters are varying, with the inclusion of a mesh-independence evidence. Element-free Galerkin method and moving least square shape functions have been employed.

Mathematical Physics in Italy in the XIX Century: The Theory of Elasticity

NASA Astrophysics Data System (ADS)

Capecchi, Danilo

In the second half of the nineteenth century there was in Italy an important group of mathematicians who focused their attention on mathematical physics. The most prominent of them were Enrico Betti, Eugenio Beltrami, Gregorio Ricci-Curbastro and some others (Vito Volterra, Carlo Somigliana and Tullio Levi Civita) whose activity persevered for many years in the twentieth century. In this article, I will write about the contribution of this group to the theory of elasticity. The best representative writing on continuum mechanics and elasticity as theories of mathematical physics is presented in the book Teoria della elasticità by Enrico Betti. The book is interesting not only for the particular results found but also for its structure which became paradigmatic for the development of subsequent texts on elasticity, not only those in Italian. Betti's interest was concentrated on the mathematical aspects of a physical theory. Physical principles are not discussed; they are only exposed in the most formal way possible. The objective is to arrive, without discussing epistemological or empirical problems, at the formulation and solution of differential equations that rule elasticity, as had become classic in the emerging mathematical physics. Beltrami wrote no complete books on elasticity; however, his contribution to this field was perhaps more original than that of Betti. A similar consideration holds true for Volterra and Somigliana.

Finite gradient elasticity and plasticity: a constitutive thermodynamical framework

NASA Astrophysics Data System (ADS)

Bertram, Albrecht

2016-05-01

In Bertram (Continuum Mech Thermodyn. doi: 10.1007/s00161-014-0387-0 , 2015), a mechanical framework for finite gradient elasticity and plasticity has been given. In the present paper, this is extended to thermodynamics. The mechanical theory is only briefly repeated here. A format for a rather general constitutive theory including all thermodynamic fields is given in a Euclidian invariant setting. The plasticity theory is rate-independent and unconstrained. The Clausius-Duhem inequality is exploited to find necessary and sufficient conditions for thermodynamic consistency. The residual dissipation inequality restricts the flow and hardening rules in combination with the yield criterion.

Effect of surface on the dissociation of perfect dislocations into Shockley partials describing the herringbone Au(1\\xA01\\xA01) surface reconstruction

NASA Astrophysics Data System (ADS)

Ait-Oubba, A.; Coupeau, C.; Durinck, J.; Talea, M.; Grilhé, J.

2018-06-01

In the framework of the continuum elastic theory, the equilibrium positions of Shockley partial dislocations have been determined as a function of their distance from the free surface. It is found that the dissociation width decreases with the decreasing depth, except for a depth range very close to the free surface for which the dissociation width is enlarged. A similar behaviour is also predicted when Shockley dislocation pairs are regularly arranged, whatever the wavelength. These results derived from the elastic theory are compared to STM observations of the reconstructed (1 1 1) surface in gold, which is usually described by a Shockley dislocations network.

Effective elastic properties of a van der Waals molecular monolayer at a metal surface

NASA Astrophysics Data System (ADS)

Sun, Dezheng; Kim, Dae-Ho; Le, Duy; Borck, Øyvind; Berland, Kristian; Kim, Kwangmoo; Lu, Wenhao; Zhu, Yeming; Luo, Miaomiao; Wyrick, Jonathan; Cheng, Zhihai; Einstein, T. L.; Rahman, Talat S.; Hyldgaard, Per; Bartels, Ludwig

2010-11-01

Adsorbing anthracene on a Cu(111) surface results in a wide range of complex and intriguing superstructures spanning a coverage range from 1 per 17 to 1 per 15 substrate atoms. In accompanying first-principles density-functional theory calculations we show the essential role of van der Waals interactions in estimating the variation in anthracene adsorption energy and height across the sample. We can thereby evaluate the compression of the anthracene film in terms of continuum elastic properties, which results in an effective Young’s modulus of 1.5 GPa and a Poisson ratio ≈0.1 . These values suggest interpretation of the molecular monolayer as a porous material—in marked congruence with our microscopic observations.

Continuum Fatigue Damage Modeling for Use in Life Extending Control

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.

1994-01-01

This paper develops a simplified continuum (continuous wrp to time, stress, etc.) fatigue damage model for use in Life Extending Controls (LEC) studies. The work is based on zero mean stress local strain cyclic damage modeling. New nonlinear explicit equation forms of cyclic damage in terms of stress amplitude are derived to facilitate the continuum modeling. Stress based continuum models are derived. Extension to plastic strain-strain rate models are also presented. Application of these models to LEC applications is considered. Progress toward a nonzero mean stress based continuum model is presented. Also, new nonlinear explicit equation forms in terms of stress amplitude are also derived for this case.

Towards thermomechanics of fractal media

NASA Astrophysics Data System (ADS)

Ostoja-Starzewski, Martin

2007-11-01

Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.

Competing nucleation of islands and nanopits in zinc-blend Ill-nitride quaternary material system

NASA Astrophysics Data System (ADS)

Gambaryan, K. M.; Aroutiounian, V. M.; Simonyan, A. K.; Yeranyan, L. S.

2016-10-01

The growth mechanism of quantum dots (QDs), nanopits and collaborative QDs- nanopits structures in GaN-InN-AlN material system is theoretically investigated using the continuum elasticity model. The islands energy versus their volume, as well as the critical energy and volume versus the island and wetting layer lattice constants relative mismatch ratio (strain s), are calculated. It is shown that when the zinc-blend GaN is used as a substrate and when the strain between the wetting layer and a substrate overcomes critical ε* = 0.039 value, instead of QDs nucleation, the formation of nanopits becomes energetically preferable. Revealed feature is critical and has to be taking into account at QDs engineering in GaInAlN material system.

The relaxed-polar mechanism of locally optimal Cosserat rotations for an idealized nanoindentation and comparison with 3D-EBSD experiments

NASA Astrophysics Data System (ADS)

Fischle, Andreas; Neff, Patrizio; Raabe, Dierk

2017-08-01

The rotation {{polar}}(F) \\in {{SO}}(3) arises as the unique orthogonal factor of the right polar decomposition F = {{polar}}(F) U of a given invertible matrix F \\in {{GL}}^+(3). In the context of nonlinear elasticity Grioli (Boll Un Math Ital 2:252-255, 1940) discovered a geometric variational characterization of {{polar}}(F) as a unique energy-minimizing rotation. In preceding works, we have analyzed a generalization of Grioli's variational approach with weights (material parameters) μ > 0 and μ _c ≥ 0 (Grioli: μ = μ _c). The energy subject to minimization coincides with the Cosserat shear-stretch contribution arising in any geometrically nonlinear, isotropic and quadratic Cosserat continuum model formulated in the deformation gradient field F :=\

Exploiting NiTi shape memory alloy films in design of tunable high frequency microcantilever resonators

NASA Astrophysics Data System (ADS)

Stachiv, I.; Sittner, P.; Olejnicek, J.; Landa, M.; Heller, L.

2017-11-01

Shape memory alloy (SMA) films are very attractive materials for microactuators because of their high energy density. However, all currently developed SMA actuators utilize martensitic transformation activated by periodically generated heating and cooling; therefore, they have a slow actuation speed, just a few Hz, which restricts their use in most of the nanotechnology applications such as high frequency microcantilever based physical and chemical sensors, atomic force microscopes, or RF filters. Here, we design tunable high frequency SMA microcantilevers for nanotechnology applications. They consist of a phase transforming NiTi SMA film sputtered on the common elastic substrate material; in our case, it is a single-crystal silicon. The reversible tuning of microcantilever resonant frequencies is then realized by intentionally changing the Young's modulus and the interlayer stress of the NiTi film by temperature, while the elastic substrate guarantees the high frequency actuation (up to hundreds of kHz) of the microcantilever. The experimental results qualitatively agree with predictions obtained from the dedicated model based on the continuum mechanics theory and a phase characteristic of NiTi. The present design of SMA microcantilevers expands the capability of current micro-/nanomechanical resonators by enabling tunability of several consecutive resonant frequencies.

Asymmetric shape transitions of epitaxial quantum dots

PubMed Central

2016-01-01

We construct a two-dimensional continuum model to describe the energetics of shape transitions in fully faceted epitaxial quantum dots (strained islands) via minimization of elastic energy and surface energy at fixed volume. The elastic energy of the island is based on a third-order approximation, enabling us to consider shape transitions between pyramids, domes, multifaceted domes and asymmetric intermediate states. The energetics of the shape transitions are determined by numerically calculating the facet lengths that minimize the energy of a given island type of prescribed island volume. By comparing the energy of different island types with the same volume and analysing the energy surface as a function of the island shape parameters, we determine the bifurcation diagram of equilibrium solutions and their stability, as well as the lowest barrier transition pathway for the island shape as a function of increasing volume. The main result is that the shape transition from pyramid to dome to multifaceted dome occurs through sequential nucleation of facets and involves asymmetric metastable transition shapes. We also explicitly determine the effect of corner energy (facet edge energy) on shape transitions and interpret the results in terms of the relative stability of asymmetric island shapes as observed in experiment. PMID:27436989

Integrated Force Method for Indeterminate Structures

NASA Technical Reports Server (NTRS)

Hopkins, Dale A.; Halford, Gary R.; Patnaik, Surya N.

2008-01-01

Two methods of solving indeterminate structural-mechanics problems have been developed as products of research on the theory of strain compatibility. In these methods, stresses are considered to be the primary unknowns (in contrast to strains and displacements being considered as the primary unknowns in some prior methods). One of these methods, denoted the integrated force method (IFM), makes it possible to compute stresses, strains, and displacements with high fidelity by use of modest finite-element models that entail relatively small amounts of computation. The other method, denoted the completed Beltrami Mitchell formulation (CBMF), enables direct determination of stresses in an elastic continuum with general boundary conditions, without the need to first calculate displacements as in traditional methods. The equilibrium equation, the compatibility condition, and the material law are the three fundamental concepts of the theory of structures. For almost 150 years, it has been commonly supposed that the theory is complete. However, until now, the understanding of the compatibility condition remained incomplete, and the compatibility condition was confused with the continuity condition. Furthermore, the compatibility condition as applied to structures in its previous incomplete form was inconsistent with the strain formulation in elasticity.

A modified Gurson-type plasticity model at finite strains: formulation, numerical analysis and phase-field coupling

NASA Astrophysics Data System (ADS)

Aldakheel, Fadi; Wriggers, Peter; Miehe, Christian

2017-12-01

The modeling of failure in ductile materials must account for complex phenomena at the micro-scale, such as nucleation, growth and coalescence of micro-voids, as well as the final rupture at the macro-scale, as rooted in the work of Gurson (J Eng Mater Technol 99:2-15, 1977). Within a top-down viewpoint, this can be achieved by the combination of a micro-structure-informed elastic-plastic model for a porous medium with a concept for the modeling of macroscopic crack discontinuities. The modeling of macroscopic cracks can be achieved in a convenient way by recently developed continuum phase field approaches to fracture, which are based on the regularization of sharp crack discontinuities, see Miehe et al. (Comput Methods Appl Mech Eng 294:486-522, 2015). This avoids the use of complex discretization methods for crack discontinuities, and can account for complex crack patterns. In this work, we develop a new theoretical and computational framework for the phase field modeling of ductile fracture in conventional elastic-plastic solids under finite strain deformation. It combines modified structures of Gurson-Tvergaard-Needelman GTN-type plasticity model outlined in Tvergaard and Needleman (Acta Metall 32:157-169, 1984) and Nahshon and Hutchinson (Eur J Mech A Solids 27:1-17, 2008) with a new evolution equation for the crack phase field. An important aspect of this work is the development of a robust Explicit-Implicit numerical integration scheme for the highly nonlinear rate equations of the enhanced GTN model, resulting with a low computational cost strategy. The performance of the formulation is underlined by means of some representative examples, including the development of the experimentally observed cup-cone failure mechanism.

Porous media modeling and micro-structurally motivated material moduli determination via the micro-dilatation theory

NASA Astrophysics Data System (ADS)

Jeong, J.; Ramézani, H.; Sardini, P.; Kondo, D.; Ponson, L.; Siitari-Kauppi, M.

2015-07-01

In the present contribution, the porous material modeling and micro-structural material parameters determination are scrutinized via the micro-dilatation theory. The main goal is to take advantage of the micro-dilatation theory which belongs to the generalized continuum media. In the first stage, the thermodynamic laws are entirely revised to reach the energy balance relation using three variables, deformation, porosity change and its gradient underlying the porous media as described in the micro-dilatation theory or so-called void elasticity. Two experiments over cement mortar specimens are performed in order to highlight the material parameters related to the pore structure. The shrinkage due to CO2 carbonation, porosity and its gradient are calculated. The extracted values are verified via 14C-PMMA radiographic image method. The modeling of swelling phenomenon of Delayed Ettringite Formation (DEF) is studied later on. This issue is performed via the crystallization pressure application using the micro-dilatation theory.

Viscoelastic Waves Simulation in a Blocky Medium with Fluid-Saturated Interlayers Using High-Performance Computing

NASA Astrophysics Data System (ADS)

Sadovskii, Vladimir; Sadovskaya, Oxana

2017-04-01

A thermodynamically consistent approach to the description of linear and nonlinear wave processes in a blocky medium, which consists of a large number of elastic blocks interacting with each other via pliant interlayers, is proposed. The mechanical properties of interlayers are defined by means of the rheological schemes of different levels of complexity. Elastic interaction between the blocks is considered in the framework of the linear elasticity theory [1]. The effects of viscoelastic shear in the interblock interlayers are taken into consideration using the Pointing-Thomson rheological scheme. The model of an elastic porous material is used in the interlayers, where the pores collapse if an abrupt compressive stress is applied. On the basis of the Biot equations for a fluid-saturated porous medium, a new mathematical model of a blocky medium is worked out, in which the interlayers provide a convective fluid motion due to the external perturbations. The collapse of pores is modeled within the generalized rheological approach, wherein the mechanical properties of a material are simulated using four rheological elements. Three of them are the traditional elastic, viscous and plastic elements, the fourth element is the so-called rigid contact [2], which is used to describe the behavior of materials with different resistance to tension and compression. Thermodynamic consistency of the equations in interlayers with the equations in blocks guarantees fulfillment of the energy conservation law for a blocky medium in a whole, i.e. kinetic and potential energy of the system is the sum of kinetic and potential energies of the blocks and interlayers. As a result of discretization of the equations of the model, robust computational algorithm is constructed, that is stable because of the thermodynamic consistency of the finite difference equations at a discrete level. The splitting method by the spatial variables and the Godunov gap decay scheme are used in the blocks, the dissipationless finite difference Ivanov scheme is applied in the interlayers. The parallel program is designed, using the MPI technology. By means of this software, nonlinear wave processes in the case of initial rotation of the central block in a rock mass as well as in the case of concentrated couple stress load, applied at the boundary of a rock mass, are analyzed. Results of computations on the multiprocessor computer systems demonstrate the strong anisotropy of a blocky medium. This work was supported by the Complex Fundamental Research Program no. II.2P "Integration and Development" of Siberian Branch of the Russian Academy of Sciences. References 1. Sadovskii V.M., Sadovskaya O.V. Modeling of Elastic Waves in a Blocky Medium Based on Equations of the Cosserat Continuum // Wave Motion. 2015. V. 52. P. 138-150. 2. Sadovskaya O., Sadovskii V. Mathematical Modeling in Mechanics of Granular Materials. Ser.: Advanced Structured Materials, V. 21. Heidelberg - New York - Dordrecht - London, Springer, 2012. 390 p.

CCKT Calculation of e-H Total Cross Sections

NASA Technical Reports Server (NTRS)

Bhatia, Aaron K.; Schneider, B. I.; Temkin, A.; Fisher, Richard R. (Technical Monitor)

2002-01-01

We are in the process of carrying out calculations of e-H total cross sections using the 'complex-correlation Kohn-T' (CCKT) method. In a later paper, we described the methodology more completely, but confined calculations to the elastic scattering region, with definitive, precision results for S-wave phase shifts. Here we extend the calculations to the (low) continuum (1 much less than k(exp 2) much less than 3) using a Green's function formulation. This avoids having to solve integro-differential equations; rather we evaluate indefinite integrals involving appropriate Green's functions and the (complex) optical potential to find the scattering function u(r). From the asymptotic form of u(r) we extract a T(sub L) which is a complex number. From T(sub L), elastic sigma(sub L)(elastic) = 4pi(2L+1)((absolute value of T(sub L))(exp 2)), and total sigma (sub L)(total) = 4pi/k(2L+1)Im(T(sub L)) cross sections follow.

Elastic Instability of Slender Rods in Steady Shear Flow Yields Positive First Normal Stress Differences

NASA Astrophysics Data System (ADS)

Becker, Leif E.; Shelley, Michael J.

2000-11-01

First normal stress differences in shear flow are a fundamental property of Non-Newtonian fluids. Experiments involving dilute suspensions of slender fibers exhibit a sharp transition to non-zero normal stress differences beyond a critical shear rate, but existing continuum theories for rigid rods predict neither this transition nor the corresponding magnitude of this effect. We present the first conclusive evidence that elastic instabilities are predominantly responsible for observed deviations from the dilute suspension theory of rigid rods. Our analysis is based on slender body theory and the equilibrium equations of elastica. A straight slender body executing its Jeffery orbit in Couette flow is subject to axial fluid forcing, alternating between compression and tension. We present a stability analysis showing that elastic instabilities are possible for strong flows. Simulations give the fully non-linear evolution of this shape instability, and show that flexibility of the fibers alone is sufficient to cause both shear-thinning and significant first normal stress differences.

Segmentation in cohesive systems constrained by elastic environments

NASA Astrophysics Data System (ADS)

Novak, I.; Truskinovsky, L.

2017-04-01

The complexity of fracture-induced segmentation in elastically constrained cohesive (fragile) systems originates from the presence of competing interactions. The role of discreteness in such phenomena is of interest in a variety of fields, from hierarchical self-assembly to developmental morphogenesis. In this paper, we study the analytically solvable example of segmentation in a breakable mass-spring chain elastically linked to a deformable lattice structure. We explicitly construct the complete set of local minima of the energy in this prototypical problem and identify among them the states corresponding to the global energy minima. We show that, even in the continuum limit, the dependence of the segmentation topology on the stretching/pre-stress parameter in this problem takes the form of a devil's type staircase. The peculiar nature of this staircase, characterized by locking in rational microstructures, is of particular importance for biological applications, where its structure may serve as an explanation of the robustness of stress-driven segmentation. This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

Delamination Analysis Of Composite Curved Bars

NASA Technical Reports Server (NTRS)

Ko, William L.; Jackson, Raymond H.

1990-01-01

Classical anisotropic elasticity theory used to construct "multilayer" composite semicircular curved bar subjected to end forces and end moments. Radial location and intensity of open-mode delamination stress calculated and compared with results obtained from anisotropic continuum theory and from finite element method. Multilayer theory gave more accurate predictions of location and intensity of open-mode delamination stress. Currently being applied to predict open-mode delamination stress concentrations in horse-shoe-shaped composite test coupons.

Mission Command: Elasticity, Equilibrium, Culture, and Intent

DTIC Science & Technology

2006-11-01

évidence « l’élasticité » de l’organisation. Comparativement à l’organisation décentralisée, une force centralisée possède une réserve beaucoup plus...avoir une faible intention implicite potentiel comparativement à une autre. La mesure dans laquelle la culture de commandement de l’organisation...is that the organisation is optimised, by design , to operate at this point on the continuum. Centralised Decentralised Shared Intent Implicit

Constitutive modelling of composite biopolymer networks.

PubMed

Fallqvist, B; Kroon, M

2016-04-21

The mechanical behaviour of biopolymer networks is to a large extent determined at a microstructural level where the characteristics of individual filaments and the interactions between them determine the response at a macroscopic level. Phenomena such as viscoelasticity and strain-hardening followed by strain-softening are observed experimentally in these networks, often due to microstructural changes (such as filament sliding, rupture and cross-link debonding). Further, composite structures can also be formed with vastly different mechanical properties as compared to the individual networks. In this present paper, we present a constitutive model presented in a continuum framework aimed at capturing these effects. Special care is taken to formulate thermodynamically consistent evolution laws for dissipative effects. This model, incorporating possible anisotropic network properties, is based on a strain energy function, split into an isochoric and a volumetric part. Generalisation to three dimensions is performed by numerical integration over the unit sphere. Model predictions indicate that the constitutive model is well able to predict the elastic and viscoelastic response of biological networks, and to an extent also composite structures. Copyright © 2016 Elsevier Ltd. All rights reserved.

Application of the cohesive zone model for the evaluation of stiffness losses in a rotor with a transverse breathing crack

NASA Astrophysics Data System (ADS)

Toni Liong, Rugerri; Proppe, Carsten

2013-04-01

The breathing mechanism of a transversely cracked rotor and its influence on a rotor system that appears due to shaft weight and inertia forces is studied. A method is proposed for the evaluation of the stiffness losses in the cross-section that contains the crack. This method is based on a cohesive zone model (CZM) instead of linear elastic fracture mechanics (LEFM). The CZM is developed for mode-I plane strain conditions and accounts explicitly for triaxiality of the stress state by using constitutive relations. The breathing crack is modelled by a parabolic shape. As long as the relative crack depth is small, a crack closure straight line model may be used, while the crack closure parabolic line should be used in the case of a deep crack. The CZM is also implemented in a one-dimensional continuum rotor model by means of finite element (FE) discretisation in order to predict and to analyse the dynamic behavior of a cracked rotor. The proposed method provides a useful tool for the analysis of rotor systems containing cracks.

The effect of spontaneous curvature on a two-phase vesicle

PubMed Central

Cox, Geoffrey; Lowengrub, John

2015-01-01

Vesicles are membrane-bound structures commonly known for their roles in cellular transport and the shape of a vesicle is determined by its surrounding membrane (lipid bilayer). When the membrane is composed of different lipids, it is natural for the lipids of similar molecular structure to migrate towards one another (via spinodal decomposition), creating a multi-phase vesicle. In this article, we consider a two-phase vesicle model which is driven by nature’s propensity to maintain a minimal state of elastic energy. The model assumes a continuum limit, thereby treating the membrane as a closed three-dimensional surface. The main purpose of this study is to reveal the complexity of the Helfrich two-phase vesicle model with non-zero spontaneous curvature and provide further evidence to support the relevance of spontaneous curvature as a modelling parameter. In this paper, we illustrate the complexity of the Helfrich two-phase model by providing multiple examples of undocumented solutions and energy hysteresis. We also investigate the influence of spontaneous curvature on morphological effects and membrane phenomena such as budding and fusion. PMID:26097287

Continuum-Scale Modeling of Shear Banding in Bulk Metallic Glass-Matrix Composites

NASA Astrophysics Data System (ADS)

Gibbons, Michael

Metallic glasses represent a relatively new class of materials that have demonstrated enormous potential for functional and structural applications due to the unique set of properties attributed to them as a result of the disordered isotropic structure with metallically bonded elements. Amorphous metals benefit from the strong nature of the metallic bonds, but lack the crystallographic structure and polycrystalline nature of traditional metals which unsurprisingly has huge implications on the material properties, as all deformation mechanisms associated with a lattice are suppressed. This results in excellent strength, a high elastic strain limit, exceptional hardness, and improved corrosion and wear resistance. "Bulk" metallic glasses (BMG) represent the amorphous metals which can be produced at the cm length-scale, thus greatly expanding their applicability for structural applications. However, due to the catastrophic nature of the failure produced upon yielding, monolithic metallic glasses are seldomly used for structural applications. Bulk metallic glass-matrix composites (BMGMCs), however, are able to combine the excellent strength, hardness, and elastic strain limit of amorphous metallic glass with a ductile crystalline phase to achieve extraordinary toughness with minimal degradation in strength. In order to explore the mechanical interactions between the amorphous and crystalline phases, a full-field micromechanical model which couples the free-volume based constitutive behavior for the matrix phase with standard rate-dependent crystal plasticity for the dendrites, and its implementation via an elastic-viscoplastic Fast-Fourier Transform (FFT) solver. The model is calibrated to macroscale stress-strain data for Ti-Zr-V-Cu-Be BMGMCs with varying composition and furthermore by comparing the deformation behavior associated with the shear bands predicted by the model, to the artifacts observed from characterization microscopy analysis on the same failed BMGMC tensile specimens in which the macroscopic composite behavior predicted by the model was validated with. The FFT-based deformation modeling is then exercised to study the nature and origin of shear bands in metallic glass composites. Synthetic 3D microstructures were produced using images of real BMGMCs, and then subjected to uniaxial tension deformation simulations. The findings indicate that in BMGMCs, local inhomogeneities in the glass phase are less influential on the mechanical performance than the contrast in individual phase properties and the spatial distribution of the microstructure. Due to the strong contrast in mechanical properties between the phases, highly heterogeneous stress fields develop, contributing to regionally confined free-volume generation, localized flow and softening in the glass. These softened regions can link and plastic flow then rapidly localizes into a thin shear band with planar like geometry. The availability of finely resolved (spatially and temporally) 3D deformation maps allow for the determination of the mechanism corresponding with these macroscopic stick-slip oscillations apparent in the stress-strain curves. In addition to shedding light on the nature of shear banding in bulk metallic glass-matrix composites, this work also demonstrates the feasibility of using a spectral-based continuum-scale model to efficiently predict the microstructure and individual phase properties that lead to new materials, superior to those found using only experimental techniques.

On the Possibility of Elastic Strain Localisation in a Fault

NASA Astrophysics Data System (ADS)

Pasternak, E.; Mühlhaus, H.-B.; Dyskin, A. V.

2004-12-01

The phenomenon of strain localisation is often observed in shear deformation of particulate materials, e.g., fault gouge. This phenomenon is usually attributed to special types of plastic behaviour of the material (e.g., strain softening or mismatch between dilatancy and pressure sensitivity or both). Observations of strain localisation in situ or in experiments are usually based on displacement measurements and subsequent computation of the displacement gradient. While in conventional continua the symmetric part of the displacement gradient is equal to the strain, it is no longer the case in the more realistic descriptions within the framework of generalised continua. In such models the rotations of the gouge particles are considered as independent degrees of freedom the values of which usually differ from the rotation of an infinitesimal volume element of the continuum, the latter being described for infinitesimal deformations by the non-symmetric part of the displacement gradient. As a model for gouge material we propose a continuum description for an assembly of spherical particles of equal radius in which the particle rotation is treated as an independent degree of freedom. Based on this model we consider simple shear deformations of the fault gouge. We show that there exist values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-layers of the fault, even in the absence of inelasticity. Inelastic effects are neglected in order to highlight the role of the independent rotations and the associated additional parameters. The localisation-like behaviour occurs if (a) the particle rotations on the boundary of the shear layer are constrained (this type of boundary condition does not exist in a standard continuum) and (b) the contact moment—or bending stiffness is much smaller than the product of the effective shear modulus of the granulate and the square of the width of the gouge layer. It should be noted however that the virtual work functional is positive definite over the range of physically meaningful parameters (here: contact stiffnesses, solid volume fraction and coordination number) so that strictly speaking we are not dealing with a material instability.

Equivalent-Continuum Modeling With Application to Carbon Nanotubes

NASA Technical Reports Server (NTRS)

Odegard, Gregory M.; Gates, Thomas S.; Nicholson, Lee M.; Wise, Kristopher E.

2002-01-01

A method has been proposed for developing structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with equivalent-continuum models. It has been shown that this substitution may be accomplished by equating the vibrational potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As important examples with direct application to the development and characterization of single-walled carbon nanotubes and the design of nanotube-based devices, the modeling technique has been applied to determine the effective-continuum geometry and bending rigidity of a graphene sheet. A representative volume element of the chemical structure of graphene has been substituted with equivalent-truss and equivalent continuum models. As a result, an effective thickness of the continuum model has been determined. This effective thickness has been shown to be significantly larger than the interatomic spacing of graphite. The effective thickness has been shown to be significantly larger than the inter-planar spacing of graphite. The effective bending rigidity of the equivalent-continuum model of a graphene sheet was determined by equating the vibrational potential energy of the molecular model of a graphene sheet subjected to cylindrical bending with the strain energy of an equivalent continuum plate subjected to cylindrical bending.

Noise Propagation and Uncertainty Quantification in Hybrid Multiphysics Models: Initiation and Reaction Propagation in Energetic Materials

DTIC Science & Technology

2016-05-23

general model for heterogeneous granular media under compaction and (ii) the lack of a reliable multiscale discrete -to-continuum framework for...dynamics. These include a continuum- discrete model of heat dissipation/diffusion and a continuum- discrete model of compaction of a granular material with...the lack of a general model for het- erogeneous granular media under compac- tion and (ii) the lack of a reliable multi- scale discrete -to-continuum

Theory, modeling, and simulation of structural and functional materials: Micromechanics, microstructures, and properties

NASA Astrophysics Data System (ADS)

Jin, Yongmei

In recent years, theoretical modeling and computational simulation of microstructure evolution and materials property has been attracting much attention. While significant advances have been made, two major challenges remain. One is the integration of multiple physical phenomena for simulation of complex materials behavior, the other is the bridging over multiple length and time scales in materials modeling and simulation. The research presented in this Thesis is focused mainly on tackling the first major challenge. In this Thesis, a unified Phase Field Microelasticity (PFM) approach is developed. This approach is an advanced version of the phase field method that takes into account the exact elasticity of arbitrarily anisotropic, elastically and structurally inhomogeneous systems. The proposed theory and models are applicable to infinite solids, elastic half-space, and finite bodies with arbitrary-shaped free surfaces, which may undergo various concomitant physical processes. The Phase Field Microelasticity approach is employed to formulate the theories and models of martensitic transformation, dislocation dynamics, and crack evolution in single crystal and polycrystalline solids. It is also used to study strain relaxation in heteroepitaxial thin films through misfit dislocation and surface roughening. Magnetic domain evolution in nanocrystalline thin films is also investigated. Numerous simulation studies are performed. Comparison with analytical predictions and experimental observations are presented. Agreement verities the theory and models as realistic simulation tools for computational materials science and engineering. The same Phase Field Microelasticity formalism of individual models of different physical phenomena makes it easy to integrate multiple physical processes into one unified simulation model, where multiple phenomena are treated as various relaxation modes that together act as one common cooperative phenomenon. The model does not impose a priori constraints on possible microstructure evolution paths. This gives the model predicting power, where material system itself "chooses" the optimal path for multiple processes. The advances made in this Thesis present a significant step forward to overcome the first challenge, mesoscale multi-physics modeling and simulation of materials. At the end of this Thesis, the way to tackle the second challenge, bridging over multiple length and time scales in materials modeling and simulation, is discussed based on connection between the mesoscale Phase Field Microelasticity modeling and microscopic atomistic calculation as well as macroscopic continuum theory.

Reproducing the nonlinear dynamic behavior of a structured beam with a generalized continuum model

NASA Astrophysics Data System (ADS)

Vila, J.; Fernández-Sáez, J.; Zaera, R.

2018-04-01

In this paper we study the coupled axial-transverse nonlinear vibrations of a kind of one dimensional structured solids by application of the so called Inertia Gradient Nonlinear continuum model. To show the accuracy of this axiomatic model, previously proposed by the authors, its predictions are compared with numeric results from a previously defined finite discrete chain of lumped masses and springs, for several number of particles. A continualization of the discrete model equations based on Taylor series allowed us to set equivalent values of the mechanical properties in both discrete and axiomatic continuum models. Contrary to the classical continuum model, the inertia gradient nonlinear continuum model used herein is able to capture scale effects, which arise for modes in which the wavelength is comparable to the characteristic distance of the structured solid. The main conclusion of the work is that the proposed generalized continuum model captures the scale effects in both linear and nonlinear regimes, reproducing the behavior of the 1D nonlinear discrete model adequately.

Discrete-to-continuum simulation approach to polymer chain systems: Subdiffusion, segregation, and chain folding

NASA Astrophysics Data System (ADS)

Foo, Grace M.; Pandey, R. B.

1998-05-01

A discrete-to-continuum approach is introduced to study the static and dynamic properties of polymer chain systems with a bead-spring chain model in two dimensions. A finitely extensible nonlinear elastic potential is used for the bond between the consecutive beads with the Lennard-Jones (LJ) potential with smaller (Rc=21/6σ=0.95) and larger (Rc=2.5σ=2.1) values of the upper cutoff for the nonbonding interaction among the neighboring beads. We find that chains segregate at temperature T=1.0 with Rc=2.1 and remain desegregated with Rc=0.95. At low temperature (T=0.2), chains become folded, in a ribbonlike conformation, unlike random and self-avoiding walk conformations at T=1.0. The power-law dependence of the rms displacements of the center of mass (Rc.m.) of the chains and their center node (Rcn) with time are nonuniversal, with the range of exponents ν1~=0.45-0.25 and ν2~=0.30-0.10, respectively. Both radius of gyration (Rg) and average bond length () decrease on increasing the range of interaction (Rc), consistent with the extended state in good solvent to collapsed state in poor solvent description of the polymer chains. Analysis of the radial distribution function supports these observations.

Elastic layer under axisymmetric indentation and surface energy effects

NASA Astrophysics Data System (ADS)

Intarit, Pong-in; Senjuntichai, Teerapong; Rungamornrat, Jaroon

2018-04-01

In this paper, a continuum-based approach is adopted to investigate the contact problem of an elastic layer with finite thickness and rigid base subjected to axisymmetric indentation with the consideration of surface energy effects. A complete Gurtin-Murdoch surface elasticity is employed to consider the influence of surface stresses. The indentation problem of a rigid frictionless punch with arbitrary axisymmetric profiles is formulated by employing the displacement Green's functions, derived with the aid of Hankel integral transform technique. The problem is solved by assuming the contact pressure distribution in terms of a linear combination of admissible functions and undetermined coefficients. Those coefficients are then obtained by employing a collocation technique and an efficient numerical quadrature scheme. The accuracy of proposed solution technique is verified by comparing with existing solutions for rigid indentation on an elastic half-space. Selected numerical results for the indenters with flat-ended cylindrical and paraboloidal punch profiles are presented to portray the influence of surface energy effects on elastic fields of the finite layer. It is found that the presence of surface stresses renders the layer stiffer, and the size-dependent behavior of elastic fields is observed in the present solutions. In addition, the surface energy effects become more pronounced with smaller contact area; thus, the influence of surface energy cannot be ignored in the analysis of indentation problem especially when the indenter size is very small such as in the case of nanoindentation.

Vibrations of single-crystal gold nanorods and nanowires

NASA Astrophysics Data System (ADS)

Saviot, L.

2018-04-01

The vibrations of gold nanowires and nanorods are investigated numerically in the framework of continuum elasticity using the Rayleigh-Ritz variational method. Special attention is paid to identify the vibrations relevant in Raman scattering experiments. A comprehensive description of the vibrations of nanorods is proposed by determining their symmetry, comparing with standing waves in the corresponding nanowires, and estimating their Raman intensity. The role of experimentally relevant parameters such as the anisotropic cubic lattice structure, the presence of faceted lateral surfaces, and the shape of the ends of the nanorods is evaluated. Elastic anisotropy is shown to play a significant role contrarily to the presence of facets. Localized vibrations are found for nanorods with flat ends. Their evolution as the shape of the ends is changed to half-spheres is discussed.

A High-Rate, Single-Crystal Model for Cyclotrimethylene Trinitramine including Phase Transformations and Plastic Slip

DOE PAGES

Addessio, Francis L.; Luscher, Darby Jon; Cawkwell, Marc Jon; ...

2017-05-14

A continuum model for the high-rate, thermo-mechanical deformation of single-crystal cyclotrimethylene trinitramine (RDX) is developed. The model includes the effects of anisotropy, large deformations, nonlinear thermo-elasticity, phase transformations, and plastic slip. A multiplicative decomposition of the deformation gradient is used. The volumetric elastic component of the deformation is accounted for through a free-energy based equation of state for the low- (α) and high-pressure (γ) polymorphs of RDX. Crystal plasticity is addressed using a phenomenological thermal activation model. The deformation gradient for the phase transformation is based on an approach that has been applied to martensitic transformations. Simulations were conducted andmore » compared to high-rate, impact loading of oriented RDX single crystals. The simulations considered multiple orientations of the crystal relative to the direction of shock loading and multiple sample thicknesses. Thirteen slip systems, which were inferred from indentation and x-ray topography, were used to model the α-polymorph. It is shown that by increasing the number of slip systems from the previously considered number of six (6) to thirteen (13) in the α-polymorph, better comparisons with data may be obtained. Simulations of impact conditions in the vicinity of the α- to γ-polymorph transformation (3.8 GPa) are considered. Eleven of the simulations, which were at pressures below the transformation value (3.0 GPa), were compared to experimental data. Comparison of the model was also made with available data for one experiment above the transformation pressure (4.4 GPa). Also, simulations are provided for a nominal pressure of 7.5 GPa to demonstrate the effect of the transformation kinetics on the deformation of a high-rate plate impact problem.« less

Three-dimensional analysis of a faulted CO 2 reservoir using an Eshelby-Mori-Tanaka approach to rock elastic properties and fault permeability

DOE PAGES

Nguyen, Ba Nghiep; Hou, Zhangshuan; Last, George V.; ...

2016-09-29

This work develops a three-dimensional multiscale model to analyze a complex CO 2 faulted reservoir that includes some key geological features of the San Andreas and nearby faults southwest of the Kimberlina site. The model uses the STOMP-CO 2 code for flow modeling that is coupled to the ABAQUS® finite element package for geomechanical analysis. A 3D ABAQUS® finite element model is developed that contains a large number of 3D solid elements with two nearly parallel faults whose damage zones and cores are discretized using the same continuum elements. Five zones with different mineral compositions are considered: shale, sandstone, faultmore » damaged sandstone, fault damaged shale, and fault core. Rocks’ elastic properties that govern their poroelastic behavior are modeled by an Eshelby-Mori-Tanka approach (EMTA). EMTA can account for up to 15 mineral phases. The permeability of fault damage zones affected by crack density and orientations is also predicted by an EMTA formulation. A STOMP-CO 2 grid that exactly maps the ABAQUS® finite element model is built for coupled hydro-mechanical analyses. Simulations of the reservoir assuming three different crack pattern situations (including crack volume fraction and orientation) for the fault damage zones are performed to predict the potential leakage of CO 2 due to cracks that enhance the permeability of the fault damage zones. Here, the results illustrate the important effect of the crack orientation on fault permeability that can lead to substantial leakage along the fault attained by the expansion of the CO 2 plume. Potential hydraulic fracture and the tendency for the faults to slip are also examined and discussed in terms of stress distributions and geomechanical properties.« less

Three-dimensional analysis of a faulted CO 2 reservoir using an Eshelby-Mori-Tanaka approach to rock elastic properties and fault permeability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nguyen, Ba Nghiep; Hou, Zhangshuan; Last, George V.

This work develops a three-dimensional multiscale model to analyze a complex CO 2 faulted reservoir that includes some key geological features of the San Andreas and nearby faults southwest of the Kimberlina site. The model uses the STOMP-CO 2 code for flow modeling that is coupled to the ABAQUS® finite element package for geomechanical analysis. A 3D ABAQUS® finite element model is developed that contains a large number of 3D solid elements with two nearly parallel faults whose damage zones and cores are discretized using the same continuum elements. Five zones with different mineral compositions are considered: shale, sandstone, faultmore » damaged sandstone, fault damaged shale, and fault core. Rocks’ elastic properties that govern their poroelastic behavior are modeled by an Eshelby-Mori-Tanka approach (EMTA). EMTA can account for up to 15 mineral phases. The permeability of fault damage zones affected by crack density and orientations is also predicted by an EMTA formulation. A STOMP-CO 2 grid that exactly maps the ABAQUS® finite element model is built for coupled hydro-mechanical analyses. Simulations of the reservoir assuming three different crack pattern situations (including crack volume fraction and orientation) for the fault damage zones are performed to predict the potential leakage of CO 2 due to cracks that enhance the permeability of the fault damage zones. Here, the results illustrate the important effect of the crack orientation on fault permeability that can lead to substantial leakage along the fault attained by the expansion of the CO 2 plume. Potential hydraulic fracture and the tendency for the faults to slip are also examined and discussed in terms of stress distributions and geomechanical properties.« less

A High-Rate, Single-Crystal Model for Cyclotrimethylene Trinitramine including Phase Transformations and Plastic Slip

DOE Office of Scientific and Technical Information (OSTI.GOV)

Addessio, Francis L.; Luscher, Darby Jon; Cawkwell, Marc Jon

A continuum model for the high-rate, thermo-mechanical deformation of single-crystal cyclotrimethylene trinitramine (RDX) is developed. The model includes the effects of anisotropy, large deformations, nonlinear thermo-elasticity, phase transformations, and plastic slip. A multiplicative decomposition of the deformation gradient is used. The volumetric elastic component of the deformation is accounted for through a free-energy based equation of state for the low- (α) and high-pressure (γ) polymorphs of RDX. Crystal plasticity is addressed using a phenomenological thermal activation model. The deformation gradient for the phase transformation is based on an approach that has been applied to martensitic transformations. Simulations were conducted andmore » compared to high-rate, impact loading of oriented RDX single crystals. The simulations considered multiple orientations of the crystal relative to the direction of shock loading and multiple sample thicknesses. Thirteen slip systems, which were inferred from indentation and x-ray topography, were used to model the α-polymorph. It is shown that by increasing the number of slip systems from the previously considered number of six (6) to thirteen (13) in the α-polymorph, better comparisons with data may be obtained. Simulations of impact conditions in the vicinity of the α- to γ-polymorph transformation (3.8 GPa) are considered. Eleven of the simulations, which were at pressures below the transformation value (3.0 GPa), were compared to experimental data. Comparison of the model was also made with available data for one experiment above the transformation pressure (4.4 GPa). Also, simulations are provided for a nominal pressure of 7.5 GPa to demonstrate the effect of the transformation kinetics on the deformation of a high-rate plate impact problem.« less

How does a three-dimensional continuum muscle model affect the kinematics and muscle strains of a finite element neck model compared to a discrete muscle model in rear-end, frontal, and lateral impacts.

PubMed

Hedenstierna, Sofia; Halldin, Peter

2008-04-15

A finite element (FE) model of the human neck with incorporated continuum or discrete muscles was used to simulate experimental impacts in rear, frontal, and lateral directions. The aim of this study was to determine how a continuum muscle model influences the impact behavior of a FE human neck model compared with a discrete muscle model. Most FE neck models used for impact analysis today include a spring element musculature and are limited to discrete geometries and nodal output results. A solid-element muscle model was thought to improve the behavior of the model by adding properties such as tissue inertia and compressive stiffness and by improving the geometry. It would also predict the strain distribution within the continuum elements. A passive continuum muscle model with nonlinear viscoelastic materials was incorporated into the KTH neck model together with active spring muscles and used in impact simulations. The resulting head and vertebral kinematics was compared with the results from a discrete muscle model as well as volunteer corridors. The muscle strain prediction was compared between the 2 muscle models. The head and vertebral kinematics were within the volunteer corridors for both models when activated. The continuum model behaved more stiffly than the discrete model and needed less active force to fit the experimental results. The largest difference was seen in the rear impact. The strain predicted by the continuum model was lower than for the discrete model. The continuum muscle model stiffened the response of the KTH neck model compared with a discrete model, and the strain prediction in the muscles was improved.

Finsler geometry of nonlinear elastic solids with internal structure

NASA Astrophysics Data System (ADS)

Clayton, J. D.

2017-02-01

Concepts from Finsler differential geometry are applied towards a theory of deformable continua with internal structure. The general theory accounts for finite deformation, nonlinear elasticity, and various kinds of structural features in a solid body. The general kinematic structure of the theory includes macroscopic and microscopic displacement fields-i.e., a multiscale representation-whereby the latter are represented mathematically by the director vector of pseudo-Finsler space, not necessarily of unit magnitude. A physically appropriate fundamental (metric) tensor is introduced, leading to affine and nonlinear connections. A deformation gradient tensor is defined via differentiation of the macroscopic motion field, and another metric indicative of strain in the body is a function of this gradient. A total energy functional of strain, referential microscopic coordinates, and horizontal covariant derivatives of the latter is introduced. Variational methods are applied to derive Euler-Lagrange equations and Neumann boundary conditions. The theory is shown to encompass existing continuum physics models such as micromorphic, micropolar, strain gradient, phase field, and conventional nonlinear elasticity models, and it can reduce to such models when certain assumptions on geometry, kinematics, and energy functionals are imposed. The theory is applied to analyze two physical problems in crystalline solids: shear localization/fracture in a two-dimensional body and cavitation in a spherical body. In these examples, a conformal or Weyl-type transformation of the fundamental tensor enables a description of dilatation associated, respectively, with cleavage surface roughness and nucleation of voids or vacancies. For the shear localization problem, the Finsler theory is able to accurately reproduce the surface energy of Griffith's fracture mechanics, and it predicts dilatation-induced toughening as observed in experiments on brittle crystals. For the cavitation problem, the Finsler theory is able to accurately reproduce the vacancy formation energy at a nanoscale resolution, and various solutions describe localized cavitation at the core of the body and/or distributed dilatation and softening associated with amorphization as observed in atomic simulations, with relative stability of solutions depending on the regularization length.

Role of microstructure and thermal pressurization on the energy budget of an earthquake

NASA Astrophysics Data System (ADS)

Rattez, H.; Stefanou, I.; Sulem, J.

2017-12-01

The common understanding for earthquakes mechanics is that they occur by sudden slippage along a pre-existing fault (Brace and Byerlee, 1966). They are, thus, considered as frictional instabilities and can be explained by a simple spring-slider model. In this model, the stability of the block is determined by the difference between the stiffness of the spring, proxy for the elastic properties of the surrounding rock mass, and the rate of decrease of the frictional resisting force along with sliding. Therefore, it is primordial to correctly capture the softening behavior of the fault. Exhumed samples and outcrops show the presence of a principal slip zone (PSZ) inside the gouge that accommodates most of the slip in the fault. The localization process is associated with a strong weakening of the fault zone. In this study, the gouge is modelled as a saturated infinite sheared layer under thermo-hydro-mechanical couplings with Cosserat continuum. The nonlinear system of equations is integrated numerically using a Finite Element Code to study the softening regime. The use of Cosserat enables to regularizes the problem of localization and obtain a shear band thickness, and thus a softening behavior, that depends only on the constitutive parameters of the model. Cosserat continuum is also particularly interesting as it can explicitly take into account for the grain size of the fault gouge, which is an information accessible from exhumed samples (Sulem et al., 2011). From these simulations, we can estimate the evolution of fracture energy with slip and investigate the influence of the size of the microstructure or the thermal pressurization coefficient on its value. The results are compared with seismological and laboratory estimates of fracture energy under coseismic slip conditions (Viesca and Garagash, 2015).

Dynamics in a one-dimensional ferrogel model: relaxation, pairing, shock-wave propagation.

PubMed

Goh, Segun; Menzel, Andreas M; Löwen, Hartmut

2018-05-23

Ferrogels are smart soft materials, consisting of a polymeric network and embedded magnetic particles. Novel phenomena, such as the variation of the overall mechanical properties by external magnetic fields, emerge consequently. However, the dynamic behavior of ferrogels remains largely unveiled. In this paper, we consider a one-dimensional chain consisting of magnetic dipoles and elastic springs between them as a simple model for ferrogels. The model is evaluated by corresponding simulations. To probe the dynamics theoretically, we investigate a continuum limit of the energy governing the system and the corresponding equation of motion. We provide general classification scenarios for the dynamics, elucidating the touching/detachment dynamics of the magnetic particles along the chain. In particular, it is verified in certain cases that the long-time relaxation corresponds to solutions of shock-wave propagation, while formations of particle pairs underlie the initial stage of the dynamics. We expect that these results will provide insight into the understanding of the dynamics of more realistic models with randomness in parameters and time-dependent magnetic fields.

Muscle-driven finite element simulation of human foot movements.

PubMed

Spyrou, L A; Aravas, N

2012-01-01

This paper describes a finite element scheme for realistic muscle-driven simulation of human foot movements. The scheme is used to simulate human ankle plantar flexion. A three-dimensional anatomically detailed finite element model of human foot and lower leg is developed and the idea of generating natural foot movement based entirely on the contraction of the plantar flexor muscles is used. The bones, ligaments, articular cartilage, muscles, tendons, as well as the rest soft tissues of human foot and lower leg are included in the model. A realistic three-dimensional continuum constitutive model that describes the biomechanical behaviour of muscles and tendons is used. Both the active and passive properties of muscle tissue are accounted for. The materials for bones and ligaments are considered as homogeneous, isotropic and linearly elastic, whereas the articular cartilage and the rest soft tissues (mainly fat) are defined as hyperelastic materials. The model is used to estimate muscle tissue deformations as well as stresses and strains that develop in the lower leg muscles during plantar flexion of the ankle. Stresses and strains that develop in Achilles tendon during such a movement are also investigated.

A viscoelastic–stochastic model of the effects of cytoskeleton remodelling on cell adhesion

PubMed Central

Li, Long; Zhang, Wenyan

2016-01-01

Cells can adapt their mechanical properties through cytoskeleton remodelling in response to external stimuli when the cells adhere to the extracellular matrix (ECM). Many studies have investigated the effects of cell and ECM elasticity on cell adhesion. However, experiments determined that cells are viscoelastic and exhibiting stress relaxation, and the mechanism behind the effect of cellular viscoelasticity on the cell adhesion behaviour remains unclear. Therefore, we propose a theoretical model of a cluster of ligand–receptor bonds between two dissimilar viscoelastic media subjected to an applied tensile load. In this model, the distribution of interfacial traction is assumed to follow classical continuum viscoelastic equations, whereas the rupture and rebinding of individual molecular bonds are governed by stochastic equations. On the basis of this model, we determined that viscosity can significantly increase the lifetime, stability and dynamic strength of the adhesion cluster of molecular bonds, because deformation relaxation attributed to the viscoelastic property can increase the rebinding probability of each open bond and reduce the stress concentration in the adhesion area. PMID:27853571

A Coupled/Uncoupled Computational Scheme for Deformation and Fatigue Damage Analysis of Unidirectional Metal-Matrix Composites

NASA Technical Reports Server (NTRS)

Wilt, Thomas E.; Arnold, Steven M.; Saleeb, Atef F.

1997-01-01

A fatigue damage computational algorithm utilizing a multiaxial, isothermal, continuum-based fatigue damage model for unidirectional metal-matrix composites has been implemented into the commercial finite element code MARC using MARC user subroutines. Damage is introduced into the finite element solution through the concept of effective stress that fully couples the fatigue damage calculations with the finite element deformation solution. Two applications using the fatigue damage algorithm are presented. First, an axisymmetric stress analysis of a circumferentially reinforced ring, wherein both the matrix cladding and the composite core were assumed to behave elastic-perfectly plastic. Second, a micromechanics analysis of a fiber/matrix unit cell using both the finite element method and the generalized method of cells (GMC). Results are presented in the form of S-N curves and damage distribution plots.

The application of an atomistic J-integral to a ductile crack.

PubMed

Zimmerman, Jonathan A; Jones, Reese E

2013-04-17

In this work we apply a Lagrangian kernel-based estimator of continuum fields to atomic data to estimate the J-integral for the emission dislocations from a crack tip. Face-centered cubic (fcc) gold and body-centered cubic (bcc) iron modeled with embedded atom method (EAM) potentials are used as example systems. The results of a single crack with a K-loading compare well to an analytical solution from anisotropic linear elastic fracture mechanics. We also discovered that in the post-emission of dislocations from the crack tip there is a loop size-dependent contribution to the J-integral. For a system with a finite width crack loaded in simple tension, the finite size effects for the systems that were feasible to compute prevented precise agreement with theory. However, our results indicate that there is a trend towards convergence.

Predicting the Influence of Nano-Scale Material Structure on the In-Plane Buckling of Orthotropic Plates

NASA Technical Reports Server (NTRS)

Gates, Thomas S.; Odegard, Gregory M.; Nemeth, Michael P.; Frankland, Sarah-Jane V.

2004-01-01

A multi-scale analysis of the structural stability of a carbon nanotube-polymer composite material is developed. The influence of intrinsic molecular structure, such as nanotube length, volume fraction, orientation and chemical functionalization, is investigated by assessing the relative change in critical, in-plane buckling loads. The analysis method relies on elastic properties predicted using the hierarchical, constitutive equations developed from the equivalent-continuum modeling technique applied to the buckling analysis of an orthotropic plate. The results indicate that for the specific composite materials considered in this study, a composite with randomly orientated carbon nanotubes consistently provides the highest values of critical buckling load and that for low volume fraction composites, the non-functionalized nanotube material provides an increase in critical buckling stability with respect to the functionalized system.

Equivalent-Continuum Modeling of Nano-Structured Materials

NASA Technical Reports Server (NTRS)

Odegard, Gregory M.; Gates, Thomas S.; Nicholson, Lee M.; Wise, Kristopher E.

2001-01-01

A method has been developed for modeling structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with an equivalent-continuum model. It has been shown that this substitution may be accomplished by equating the vibrational potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As an important example with direct application to the development and characterization of single-walled carbon nanotubes, the model has been applied to determine the effective continuum geometry of a graphene sheet. A representative volume element of the equivalent-continuum model has been developed with an effective thickness. This effective thickness has been shown to be similar to, but slightly smaller than, the interatomic spacing of graphite.

Ab Initio Studies of Shock-Induced Chemical Reactions of Inter-Metallics

NASA Astrophysics Data System (ADS)

Zaharieva, Roussislava; Hanagud, Sathya

2009-06-01

Shock-induced and shock assisted chemical reactions of intermetallic mixtures are studied by many researchers, using both experimental and theoretical techniques. The theoretical studies are primarily at continuum scales. The model frameworks include mixture theories and meso-scale models of grains of porous mixtures. The reaction models vary from equilibrium thermodynamic model to several non-equilibrium thermodynamic models. The shock-effects are primarily studied using appropriate conservation equations and numerical techniques to integrate the equations. All these models require material constants from experiments and estimates of transition states. Thus, the objective of this paper is to present studies based on ab initio techniques. The ab inito studies, to date, use ab inito molecular dynamics. This paper presents a study that uses shock pressures, and associated temperatures as starting variables. Then intermetallic mixtures are modeled as slabs. The required shock stresses are created by straining the lattice. Then, ab initio binding energy calculations are used to examine the stability of the reactions. Binding energies are obtained for different strain components super imposed on uniform compression and finite temperatures. Then, vibrational frequencies and nudge elastic band techniques are used to study reactivity and transition states. Examples include Ni and Al.

Effects of continuum breakdown on hypersonic aerothermodynamics for reacting flow

NASA Astrophysics Data System (ADS)

Holman, Timothy D.; Boyd, Iain D.

2011-02-01

This study investigates the effects of continuum breakdown on the surface aerothermodynamic properties (pressure, stress, and heat transfer rate) of a sphere in a Mach 25 flow of reacting air in regimes varying from continuum to a rarefied gas. Results are generated using both continuum [computational fluid dynamics (CFD)] and particle [direct simulation Monte Carlo (DSMC)] approaches. The DSMC method utilizes a chemistry model that calculates the backward rates from an equilibrium constant. A preferential dissociation model is modified in the CFD method to better compare with the vibrationally favored dissociation model that is utilized in the DSMC method. Tests of these models are performed to confirm their validity and to compare the chemistry models in both numerical methods. This study examines the effect of reacting air flow on continuum breakdown and the surface properties of the sphere. As the global Knudsen number increases, the amount of continuum breakdown in the flow and on the surface increases. This increase in continuum breakdown significantly affects the surface properties, causing an increase in the differences between CFD and DSMC. Explanations are provided for the trends observed.

Revisiting the continuum model of tendon pathology: what is its merit in clinical practice and research?

PubMed Central

Cook, J L; Rio, E; Purdam, C R; Docking, S I

2016-01-01

The pathogenesis of tendinopathy and the primary biological change in the tendon that precipitates pathology have generated several pathoaetiological models in the literature. The continuum model of tendon pathology, proposed in 2009, synthesised clinical and laboratory-based research to guide treatment choices for the clinical presentations of tendinopathy. While the continuum has been cited extensively in the literature, its clinical utility has yet to be fully elucidated. The continuum model proposed a model for staging tendinopathy based on the changes and distribution of disorganisation within the tendon. However, classifying tendinopathy based on structure in what is primarily a pain condition has been challenged. The interplay between structure, pain and function is not yet fully understood, which has partly contributed to the complex clinical picture of tendinopathy. Here we revisit and assess the merit of the continuum model in the context of new evidence. We (1) summarise new evidence in tendinopathy research in the context of the continuum, (2) discuss tendon pain and the relevance of a model based on structure and (3) describe relevant clinical elements (pain, function and structure) to begin to build a better understanding of the condition. Our goal is that the continuum model may help guide targeted treatments and improved patient outcomes. PMID:27127294

Wrinkle-free design of thin membrane structures using stress-based topology optimization

NASA Astrophysics Data System (ADS)

Luo, Yangjun; Xing, Jian; Niu, Yanzhuang; Li, Ming; Kang, Zhan

2017-05-01

Thin membrane structures would experience wrinkling due to local buckling deformation when compressive stresses are induced in some regions. Using the stress criterion for membranes in wrinkled and taut states, this paper proposed a new stress-based topology optimization methodology to seek the optimal wrinkle-free design of macro-scale thin membrane structures under stretching. Based on the continuum model and linearly elastic assumption in the taut state, the optimization problem is defined as to maximize the structural stiffness under membrane area and principal stress constraints. In order to make the problem computationally tractable, the stress constraints are reformulated into equivalent ones and relaxed by a cosine-type relaxation scheme. The reformulated optimization problem is solved by a standard gradient-based algorithm with the adjoint-variable sensitivity analysis. Several examples with post-bulking simulations and experimental tests are given to demonstrate the effectiveness of the proposed optimization model for eliminating stress-related wrinkles in the novel design of thin membrane structures.

Finite-size effect on the dynamic and sensing performances of graphene resonators: the role of edge stress.

PubMed

Kim, Chang-Wan; Dai, Mai Duc; Eom, Kilho

2016-01-01

We have studied the finite-size effect on the dynamic behavior of graphene resonators and their applications in atomic mass detection using a continuum elastic model such as modified plate theory. In particular, we developed a model based on von Karman plate theory with including the edge stress, which arises from the imbalance between the coordination numbers of bulk atoms and edge atoms of graphene. It is shown that as the size of a graphene resonator decreases, the edge stress depending on the edge structure of a graphene resonator plays a critical role on both its dynamic and sensing performances. We found that the resonance behavior of graphene can be tuned not only through edge stress but also through nonlinear vibration, and that the detection sensitivity of a graphene resonator can be controlled by using the edge stress. Our study sheds light on the important role of the finite-size effect in the effective design of graphene resonators for their mass sensing applications.

Multilayer theory for delamination analysis of a composite curved bar subjected to end forces and end moments

NASA Technical Reports Server (NTRS)

Ko, William L.; Jackson, Raymond H.

1989-01-01

A composite test specimen in the shape of a semicircular curved bar subjected to bending offers an excellent stress field for studying the open-mode delamination behavior of laminated composite materials. This is because the open-mode delamination nucleates at the midspan of the curved bar. The classical anisotropic elasticity theory was used to construct a 'multilayer' theory for the calculations of the stress and deformation fields induced in the multilayered composite semicircular curved bar subjected to end forces and end moments. The radial location and intensity of the open-mode delamination stress were calculated and were compared with the results obtained from the anisotropic continuum theory and from the finite element method. The multilayer theory gave more accurate predictions of the location and the intensity of the open-mode delamination stress than those calculated from the anisotropic continuum theory.

Multilayer theory for delamination analysis of a composite curved bar subjected to end forces and end moments

NASA Technical Reports Server (NTRS)

Ko, William L.; Jackson, Raymond H.

1989-01-01

A composite test specimen in the shape of a semicircular curved bar subjected to bending offers an excellent stress field for studying the open-mode delamination behavior of laminated composite materials. This is because the open-mode delamination nucleates at the midspan of the curved bar. The classical anisotropic elasticity theory was used to construct a multilayer theory for the calculations of the stress and deformation fields induced in the multilayered composite semicircular curved bar subjected to end forces and end moments. The radial location and intensity of the open-mode delamination stress were calculated and were compared with the results obtained from the anisotropic continuum theory and from the finite element method. The multilayer theory gave more accurate predictions of the location and the intensity of the open-mode delamination stress than those calculated from the anisotropic continuum theory.

Rigid proteins and softening of biological membranes-with application to HIV-induced cell membrane softening.

PubMed

Agrawal, Himani; Zelisko, Matthew; Liu, Liping; Sharma, Pradeep

2016-05-06

A key step in the HIV-infection process is the fusion of the virion membrane with the target cell membrane and the concomitant transfer of the viral RNA. Experimental evidence suggests that the fusion is preceded by considerable elastic softening of the cell membranes due to the insertion of fusion peptide in the membrane. What are the mechanisms underpinning the elastic softening of the membrane upon peptide insertion? A broader question may be posed: insertion of rigid proteins in soft membranes ought to stiffen the membranes not soften them. However, experimental observations perplexingly appear to show that rigid proteins may either soften or harden membranes even though conventional wisdom only suggests stiffening. In this work, we argue that regarding proteins as merely non-specific rigid inclusions is flawed, and each protein has a unique mechanical signature dictated by its specific interfacial coupling to the surrounding membrane. Predicated on this hypothesis, we have carried out atomistic simulations to investigate peptide-membrane interactions. Together with a continuum model, we reconcile contrasting experimental data in the literature including the case of HIV-fusion peptide induced softening. We conclude that the structural rearrangements of the lipids around the inclusions cause the softening or stiffening of the biological membranes.

Wall effects in Stokes experiment with a liquid foam

NASA Astrophysics Data System (ADS)

Gao, Haijing; Subramani, Hariprasad; Harris, Michael; Basaran, Osman

2011-11-01

Liquid foams are widely used in numerous applications ranging from the oil and gas industry to beauty, healthcare, and household products industries. A fundamental understanding of the relationships between the properties of liquid foams and their flow responses is, however, still in its infancy compared to that involving the fluid dynamics of simple fluids. In this talk, the flow of a dry liquid foam around a spherical bead, i.e. the Stokes problem for liquid foams, is studied experimentally. In contrast to previous work (cf. Cantat 2006), the focus of the present research is to probe the effect of a solid wall that is located a few bubble radii from the bead. The new experimental results show that the elastic modulus of dry liquid foams is directly proportional to the surface tension of the foaming agents and inversely proportional to the average bubble size in the foams, in agreement with previous theoretical and experimental studies. The experiments further show that the close proximity of the solid wall causes profound structural changes to the gas bubbles as the foam flows past the bead. A good understanding of these structural changes and how they can affect the elastic modulus of foams can be indispensable in formulating improved models for accurately describing the dynamical response of foams within the realm of continuum mechanics.

Antimonide-based membranes synthesis integration and strain engineering

PubMed Central

Anwar, Farhana; Klein, Brianna A.; Rasoulof, Amin; Dawson, Noel M.; Schuler-Sandy, Ted; Deneke, Christoph F.; Ferreira, Sukarno O.; Cavallo, Francesca; Krishna, Sanjay

2017-01-01

Antimonide compounds are fabricated in membrane form to enable materials combinations that cannot be obtained by direct growth and to support strain fields that are not possible in the bulk. InAs/(InAs,Ga)Sb type II superlattices (T2SLs) with different in-plane geometries are transferred from a GaSb substrate to a variety of hosts, including Si, polydimethylsiloxane, and metal-coated substrates. Electron microscopy shows structural integrity of transferred membranes with thickness of 100 nm to 2.5 μm and lateral sizes from 24×24μm2 to 1×1 cm2. Electron microscopy reveals the excellent quality of the membrane interface with the new host. The crystalline structure of the T2SL is not altered by the fabrication process, and a minimal elastic relaxation occurs during the release step, as demonstrated by X-ray diffraction and mechanical modeling. A method to locally strain-engineer antimonide-based membranes is theoretically illustrated. Continuum elasticity theory shows that up to ∼3.5% compressive strain can be induced in an InSb quantum well through external bending. Photoluminescence spectroscopy and characterization of an IR photodetector based on InAs/GaSb bonded to Si demonstrate the functionality of transferred membranes in the IR range. PMID:27986953

Rigid proteins and softening of biological membranes—with application to HIV-induced cell membrane softening

NASA Astrophysics Data System (ADS)

Agrawal, Himani; Zelisko, Matthew; Liu, Liping; Sharma, Pradeep

2016-05-01

A key step in the HIV-infection process is the fusion of the virion membrane with the target cell membrane and the concomitant transfer of the viral RNA. Experimental evidence suggests that the fusion is preceded by considerable elastic softening of the cell membranes due to the insertion of fusion peptide in the membrane. What are the mechanisms underpinning the elastic softening of the membrane upon peptide insertion? A broader question may be posed: insertion of rigid proteins in soft membranes ought to stiffen the membranes not soften them. However, experimental observations perplexingly appear to show that rigid proteins may either soften or harden membranes even though conventional wisdom only suggests stiffening. In this work, we argue that regarding proteins as merely non-specific rigid inclusions is flawed, and each protein has a unique mechanical signature dictated by its specific interfacial coupling to the surrounding membrane. Predicated on this hypothesis, we have carried out atomistic simulations to investigate peptide-membrane interactions. Together with a continuum model, we reconcile contrasting experimental data in the literature including the case of HIV-fusion peptide induced softening. We conclude that the structural rearrangements of the lipids around the inclusions cause the softening or stiffening of the biological membranes.

Generalized Finsler geometric continuum physics with applications in fracture and phase transformations

NASA Astrophysics Data System (ADS)

Clayton, J. D.

2017-02-01

A theory of deformation of continuous media based on concepts from Finsler differential geometry is presented. The general theory accounts for finite deformations, nonlinear elasticity, and changes in internal state of the material, the latter represented by elements of a state vector of generalized Finsler space whose entries consist of one or more order parameter(s). Two descriptive representations of the deformation gradient are considered. The first invokes an additive decomposition and is applied to problems involving localized inelastic deformation mechanisms such as fracture. The second invokes a multiplicative decomposition and is applied to problems involving distributed deformation mechanisms such as phase transformations or twinning. Appropriate free energy functions are posited for each case, and Euler-Lagrange equations of equilibrium are derived. Solutions are obtained for specific problems of tensile fracture of an elastic cylinder and for amorphization of a crystal under spherical and uniaxial compression. The Finsler-based approach is demonstrated to be more general and potentially more physically descriptive than existing hyperelasticity models couched in Riemannian geometry or Euclidean space, without incorporation of supplementary ad hoc equations or spurious fitting parameters. Predictions for single crystals of boron carbide ceramic agree qualitatively, and in many instances quantitatively, with results from physical experiments and atomic simulations involving structural collapse and failure of the crystal along its c-axis.

Earthquakes in the Laboratory: Continuum-Granular Interactions

NASA Astrophysics Data System (ADS)

Ecke, Robert; Geller, Drew; Ward, Carl; Backhaus, Scott

2013-03-01

Earthquakes in nature feature large tectonic plate motion at large scales of 10-100 km and local properties of the earth on the scale of the rupture width, of the order of meters. Fault gouge often fills the gap between the large slipping plates and may play an important role in the nature and dynamics of earthquake events. We have constructed a laboratory scale experiment that represents a similitude scale model of this general earthquake description. Two photo-elastic plates (50 cm x 25 cm x 1 cm) confine approximately 3000 bi-disperse nylon rods (diameters 0.12 and 0.16 cm, height 1 cm) in a gap of approximately 1 cm. The plates are held rigidly along their outer edges with one held fixed while the other edge is driven at constant speed over a range of about 5 cm. The local stresses exerted on the plates are measured using their photo-elastic response, the local relative motions of the plates, i.e., the local strains, are determined by the relative motion of small ball bearings attached to the top surface, and the configurations of the nylon rods are investigated using particle tracking tools. We find that this system has properties similar to real earthquakes and are exploring these ``lab-quake'' events with the quantitative tools we have developed.

Strain-dependent Damage Evolution and Velocity Reduction in Fault Zones Induced by Earthquake Rupture

NASA Astrophysics Data System (ADS)

Zhong, J.; Duan, B.

2009-12-01

Low-velocity fault zones (LVFZs) with reduced seismic velocities relative to the surrounding wall rocks are widely observed around active faults. The presence of such a zone will affect rupture propagation, near-field ground motion, and off-fault damage in subsequent earth-quakes. In this study, we quantify the reduction of seismic velocities caused by dynamic rup-ture on a 2D planar fault surrounded by a low-velocity fault zone. First, we implement the damage rheology (Lyakhovsky et al. 1997) in EQdyna (Duan and Oglesby 2006), an explicit dynamic finite element code. We further extend this damage rheology model to include the dependence of strains on crack density. Then, we quantify off-fault continuum damage distribution and velocity reduction induced by earthquake rupture with the presence of a preexisting LVFZ. We find that the presence of a LVFZ affects the tempo-spatial distribu-tions of off-fault damage. Because lack of constraint in some damage parameters, we further investigate the relationship between velocity reduction and these damage prameters by a large suite of numerical simulations. Slip velocity, slip, and near-field ground motions computed from damage rheology are also compared with those from off-fault elastic or elastoplastic responses. We find that the reduction in elastic moduli during dynamic rupture has profound impact on these quantities.

Poisson's ratio over two centuries: challenging hypotheses

PubMed Central

Greaves, G. Neville

2013-01-01

This article explores Poisson's ratio, starting with the controversy concerning its magnitude and uniqueness in the context of the molecular and continuum hypotheses competing in the development of elasticity theory in the nineteenth century, moving on to its place in the development of materials science and engineering in the twentieth century, and concluding with its recent re-emergence as a universal metric for the mechanical performance of materials on any length scale. During these episodes France lost its scientific pre-eminence as paradigms switched from mathematical to observational, and accurate experiments became the prerequisite for scientific advance. The emergence of the engineering of metals followed, and subsequently the invention of composites—both somewhat separated from the discovery of quantum mechanics and crystallography, and illustrating the bifurcation of technology and science. Nowadays disciplines are reconnecting in the face of new scientific demands. During the past two centuries, though, the shape versus volume concept embedded in Poisson's ratio has remained invariant, but its application has exploded from its origins in describing the elastic response of solids and liquids, into areas such as materials with negative Poisson's ratio, brittleness, glass formation, and a re-evaluation of traditional materials. Moreover, the two contentious hypotheses have been reconciled in their complementarity within the hierarchical structure of materials and through computational modelling. PMID:24687094

Mechanical Properties of Plant Cell Walls Probed by Relaxation Spectra1[W][OA

PubMed Central

Hansen, Steen Laugesen; Ray, Peter Martin; Karlsson, Anders Ola; Jørgensen, Bodil; Borkhardt, Bernhard; Petersen, Bent Larsen; Ulvskov, Peter

2011-01-01

Transformants and mutants with altered cell wall composition are expected to display a biomechanical phenotype due to the structural role of the cell wall. It is often quite difficult, however, to distinguish the mechanical behavior of a mutant's or transformant's cell walls from that of the wild type. This may be due to the plant’s ability to compensate for the wall modification or because the biophysical method that is often employed, determination of simple elastic modulus and breakstrength, lacks the resolving power necessary for detecting subtle mechanical phenotypes. Here, we apply a method, determination of relaxation spectra, which probes, and can separate, the viscoelastic properties of different cell wall components (i.e. those properties that depend on the elastic behavior of load-bearing wall polymers combined with viscous interactions between them). A computer program, BayesRelax, that deduces relaxation spectra from appropriate rheological measurements is presented and made accessible through a Web interface. BayesRelax models the cell wall as a continuum of relaxing elements, and the ability of the method to resolve small differences in cell wall mechanical properties is demonstrated using tuber tissue from wild-type and transgenic potatoes (Solanum tuberosum) that differ in rhamnogalacturonan I side chain structure. PMID:21075961

Simulation of elastic wave propagation using cellular automata and peridynamics, and comparison with experiments

DOE PAGES

Nishawala, Vinesh V.; Ostoja-Starzewski, Martin; Leamy, Michael J.; ...

2015-09-10

Peridynamics is a non-local continuum mechanics formulation that can handle spatial discontinuities as the governing equations are integro-differential equations which do not involve gradients such as strains and deformation rates. This paper employs bond-based peridynamics. Cellular Automata is a local computational method which, in its rectangular variant on interior domains, is mathematically equivalent to the central difference finite difference method. However, cellular automata does not require the derivation of the governing partial differential equations and provides for common boundary conditions based on physical reasoning. Both methodologies are used to solve a half-space subjected to a normal load, known as Lamb’smore » Problem. The results are compared with theoretical solution from classical elasticity and experimental results. Furthermore, this paper is used to validate our implementation of these methods.« less

Folding and faulting of an elastic continuum

NASA Astrophysics Data System (ADS)

Bigoni, Davide; Gourgiotis, Panos A.

2016-03-01

Folding is a process in which bending is localized at sharp edges separated by almost undeformed elements. This process is rarely encountered in Nature, although some exceptions can be found in unusual layered rock formations (called `chevrons') and seashell patterns (for instance Lopha cristagalli). In mechanics, the bending of a three-dimensional elastic solid is common (for example, in bulk wave propagation), but folding is usually not achieved. In this article, the route leading to folding is shown for an elastic solid obeying the couple-stress theory with an extreme anisotropy. This result is obtained with a perturbation technique, which involves the derivation of new two-dimensional Green's functions for applied concentrated force and moment. While the former perturbation reveals folding, the latter shows that a material in an extreme anisotropic state is also prone to a faulting instability, in which a displacement step of finite size emerges. Another failure mechanism, namely the formation of dilation/compaction bands, is also highlighted. Finally, a geophysical application to the mechanics of chevron formation shows how the proposed approach may explain the formation of natural structures.

Folding and faulting of an elastic continuum

PubMed Central

Gourgiotis, Panos A.

2016-01-01

Folding is a process in which bending is localized at sharp edges separated by almost undeformed elements. This process is rarely encountered in Nature, although some exceptions can be found in unusual layered rock formations (called ‘chevrons’) and seashell patterns (for instance Lopha cristagalli). In mechanics, the bending of a three-dimensional elastic solid is common (for example, in bulk wave propagation), but folding is usually not achieved. In this article, the route leading to folding is shown for an elastic solid obeying the couple-stress theory with an extreme anisotropy. This result is obtained with a perturbation technique, which involves the derivation of new two-dimensional Green's functions for applied concentrated force and moment. While the former perturbation reveals folding, the latter shows that a material in an extreme anisotropic state is also prone to a faulting instability, in which a displacement step of finite size emerges. Another failure mechanism, namely the formation of dilation/compaction bands, is also highlighted. Finally, a geophysical application to the mechanics of chevron formation shows how the proposed approach may explain the formation of natural structures. PMID:27118925

Segmentation in cohesive systems constrained by elastic environments

PubMed Central

Novak, I.

2017-01-01

The complexity of fracture-induced segmentation in elastically constrained cohesive (fragile) systems originates from the presence of competing interactions. The role of discreteness in such phenomena is of interest in a variety of fields, from hierarchical self-assembly to developmental morphogenesis. In this paper, we study the analytically solvable example of segmentation in a breakable mass–spring chain elastically linked to a deformable lattice structure. We explicitly construct the complete set of local minima of the energy in this prototypical problem and identify among them the states corresponding to the global energy minima. We show that, even in the continuum limit, the dependence of the segmentation topology on the stretching/pre-stress parameter in this problem takes the form of a devil's type staircase. The peculiar nature of this staircase, characterized by locking in rational microstructures, is of particular importance for biological applications, where its structure may serve as an explanation of the robustness of stress-driven segmentation. This article is part of the themed issue ‘Patterning through instabilities in complex media: theory and applications.’ PMID:28373383

On the elastic–plastic decomposition of crystal deformation at the atomic scale

DOE PAGES

Stukowski, Alexander; Arsenlis, A.

2012-03-02

Given two snapshots of an atomistic system, taken at different stages of the deformation process, one can compute the incremental deformation gradient field, F, as defined by continuum mechanics theory, from the displacements of atoms. However, such a kinematic analysis of the total deformation does not reveal the respective contributions of elastic and plastic deformation. We develop a practical technique to perform the multiplicative decomposition of the deformation field, F = F eF p, into elastic and plastic parts for the case of crystalline materials. The described computational analysis method can be used to quantify plastic deformation in a materialmore » due to crystal slip-based mechanisms in molecular dynamics and molecular statics simulations. The knowledge of the plastic deformation field, F p, and its variation with time can provide insight into the number, motion and localization of relevant crystal defects such as dislocations. As a result, the computed elastic field, F e, provides information about inhomogeneous lattice strains and lattice rotations induced by the presence of defects.« less

Integrating qPLM and biomechanical test data with an anisotropic fiber distribution model and predictions of TGF-β1 and IGF-1 regulation of articular cartilage fiber modulus

PubMed Central

Stender, Michael E.; Raub, Christopher B.; Yamauchi, Kevin A.; Shirazi, Reza; Vena, Pasquale; Sah, Robert L.; Hazelwood, Scott J.; Klisch, Stephen M.

2013-01-01

A continuum mixture model with distinct collagen (COL) and glycosaminoglycan (GAG) elastic constituents was developed for the solid matrix of immature bovine articular cartilage. A continuous COL fiber volume fraction distribution function and a true COL fiber elastic modulus (Ef) were used. Quantitative polarized light microscopy (qPLM) methods were developed to account for the relatively high cell density of immature articular cartilage and used with a novel algorithm that constructs a 3D distribution function from 2D qPLM data. For specimens untreated and cultured in vitro, most model parameters were specified from qPLM analysis and biochemical assay results; consequently, Ef was predicted using an optimization to measured mechanical properties in uniaxial tension and unconfined compression. Analysis of qPLM data revealed a highly anisotropic fiber distribution, with principal fiber orientation parallel to the surface layer. For untreated samples, predicted Ef values were 175 and 422 MPa for superficial (S) and middle (M) zone layers, respectively. TGF-β1 treatment was predicted to increase and decrease Ef values for the S and M layers to 281 and 309 MPa, respectively. IGF-1 treatment was predicted to decrease Ef values for the S and M layers to 22 and 26 MPa, respectively. A novel finding was that distinct native depth-dependent fiber modulus properties were modulated to nearly homogeneous values by TGF-β1 and IGF-1 treatments, with modulated values strongly dependent on treatment. PMID:23266906

Alignment of nematic liquid crystals by inhomogeneous surfaces

NASA Astrophysics Data System (ADS)

Ong, Hiap Liew; Hurd, Alan J.; Meyer, Robert B.

1985-01-01

Variable oblique alignment of nematic liquid crystals has been achieved on microscopically inhomogeneous surfaces. The surfaces consist of small patches favoring vertical (homeotropic) alignment surrounded by a matrix favoring a planar alignment. The construction of these surfaces employs randomly distributed microscopic metal islands formed by certain metals as vapor-deposited films. Larger scale periodic patterns were made as well to verify the techniques. The results are interpreted in terms of a continuum elasticity theory and azimuthal degeneracy is also discussed.

Strain field determination in III-V heteroepitaxy coupling finite elements with experimental and theoretical techniques at the nanoscale

NASA Astrophysics Data System (ADS)

Florini, Nikoletta; Dimitrakopulos, George P.; Kioseoglou, Joseph; Pelekanos, Nikos T.; Kehagias, Thomas

2017-04-01

We are briefly reviewing the current status of elastic strain field determination in III-V heteroepitaxial nanostructures, linking finite elements (FE) calculations with quantitative nanoscale imaging and atomistic calculation techniques. III-V semiconductor nanostructure systems of various dimensions are evaluated in terms of their importance in photonic and microelectronic devices. As elastic strain distribution inside nano-heterostructures has a significant impact on the alloy composition, and thus their electronic properties, it is important to accurately map its components both at the interface plane and along the growth direction. Therefore, we focus on the determination of the stress-strain fields in III-V heteroepitaxial nanostructures by experimental and theoretical methods with emphasis on the numerical FE method by means of anisotropic continuum elasticity (CE) approximation. Subsequently, we present our contribution to the field by coupling FE simulations on InAs quantum dots (QDs) grown on (211)B GaAs substrate, either uncapped or buried, and GaAs/AlGaAs core-shell nanowires (NWs) grown on (111) Si, with quantitative high-resolution transmission electron microscopy (HRTEM) methods and atomistic molecular dynamics (MD) calculations. Full determination of the elastic strain distribution can be exploited for band gap tailoring of the heterostructures by controlling the content of the active elements, and thus influence the emitted radiation.

NASA Workshop on Distributed Parameter Modeling and Control of Flexible Aerospace Systems

NASA Technical Reports Server (NTRS)

Marks, Virginia B. (Compiler); Keckler, Claude R. (Compiler)

1994-01-01

Although significant advances have been made in modeling and controlling flexible systems, there remains a need for improvements in model accuracy and in control performance. The finite element models of flexible systems are unduly complex and are almost intractable to optimum parameter estimation for refinement using experimental data. Distributed parameter or continuum modeling offers some advantages and some challenges in both modeling and control. Continuum models often result in a significantly reduced number of model parameters, thereby enabling optimum parameter estimation. The dynamic equations of motion of continuum models provide the advantage of allowing the embedding of the control system dynamics, thus forming a complete set of system dynamics. There is also increased insight provided by the continuum model approach.

Predicting dynamics and rheology of blood flow: A comparative study of multiscale and low-dimensional models of red blood cells

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Wenxiao; Fedosov, Dmitry A.; Caswell, Bruce

In this work we compare the predictive capability of two mathematical models for red blood cells (RBCs) focusing on blood flow in capillaries and arterioles. Both RBC models as well as their corresponding blood flows are based on the dissipative particle dynamics (DPD) method, a coarse-grained molecular dynamics approach. The first model employs a multiscale description of the RBC (MS-RBC), with its membrane represented by hundreds or even thousands of DPD-particles connected by springs into a triangular network in combination with out-of-plane elastic bending resistance. Extra dissipation within the network accounts for membrane viscosity, while the characteristic biconcave RBC shapemore » is achieved by imposition of constraints for constant membrane area and constant cell volume. The second model is based on a low-dimensional description (LD-RBC) constructed as a closed torus-like ring of only 10 large DPD colloidal particles. They are connected into a ring by worm-like chain (WLC) springs combined with bending resistance. The LD-RBC model can be fitted to represent the entire range of nonlinear elastic deformations as measured by optical-tweezers for healthy and for infected RBCs in malaria. MS-RBCs suspensions model the dynamics and rheology of blood flow accurately for any size vessel but this approach is computationally expensive above 100 microns. Surprisingly, the much more economical suspensions of LD-RBCs also capture the blood flow dynamics and rheology accurately except for vessels with sizes comparable to RBC diameter. In particular, the LD-RBC suspensions are shown to properly capture the experimental data for the apparent viscosity of blood and its cell-free layer (CFL) in tube flow. Taken together, these findings suggest a hierarchical approach in modeling blood flow in the arterial tree, whereby the MS-RBC model should be employed for capillaries and arterioles below 100 microns, the LD-RBC model for arterioles, and the continuum description for arteries.« less

Theory of equilibria of elastic 2-braids with interstrand interaction

NASA Astrophysics Data System (ADS)

Starostin, E. L.; van der Heijden, G. H. M.

2014-03-01

Motivated by continuum models for DNA supercoiling we formulate a theory for equilibria of 2-braids, i.e., structures formed by two elastic rods winding around each other in continuous contact and subject to a local interstrand interaction. No assumption is made on the shape of the contact curve. The theory is developed in terms of a moving frame of directors attached to one of the strands. The other strand is tracked by including in this frame the normalised closest-approach chord connecting the two strands. The kinematic constant-distance constraint is formulated at strain level through the introduction of what we call braid strains. As a result the total potential energy involves arclength derivatives of these strains, thus giving rise to a second-order variational problem. The Euler-Lagrange equations for this problem give balance equations for the overall braid force and moment referred to the moving frame as well as differential equations that can be interpreted as effective constitutive relations encoding the effect that the second strand has on the first as the braid deforms under the action of end loads. Hard contact models are used to obtain the normal contact pressure between strands that has to be non-negative for a physically realisable solution without the need for external devices such as clamps or glue to keep the strands together. The theory is first illustrated by a number of problems that can be solved analytically and then applied to several new problems that have not hitherto been treated.

The significance of turbulent flow representation in single-continuum models

USGS Publications Warehouse

Reimann, T.; Rehrl, C.; Shoemaker, W.B.; Geyer, T.; Birk, S.

2011-01-01

Karst aquifers exhibit highly conductive features caused from rock dissolution processes. Flow within these structures can become turbulent and therefore can be expressed by nonlinear gradient functions. One way to account for these effects is by coupling a continuum model with a conduit network. Alternatively, turbulent flow can be considered by adapting the hydraulic conductivity within the continuum model. Consequently, the significance of turbulent flow on the dynamic behavior of karst springs is investigated by an enhanced single-continuum model that results in conduit-type flow in continuum cells (CTFC). The single-continuum approach CTFC represents laminar and turbulent flow as well as more complex hybrid models that require additional programming and numerical efforts. A parameter study is conducted to investigate the effects of turbulent flow on the response of karst springs to recharge events using the new CTFC approach, existing hybrid models, and MODFLOW-2005. Results reflect the importance of representing (1) turbulent flow in karst conduits and (2) the exchange between conduits and continuum cells. More specifically, laminar models overestimate maximum spring discharge and underestimate hydraulic gradients within the conduit. It follows that aquifer properties inferred from spring hydrographs are potentially impaired by ignoring flow effects due to turbulence. The exchange factor used for hybrid models is necessary to account for the scale dependency between hydraulic properties of the matrix continuum and conduits. This functionality, which is not included in CTFC, can be mimicked by appropriate use of the Horizontal Flow Barrier package for MODFLOW. Copyright 2011 by the American Geophysical Union.

Modeling plasticity by non-continuous deformation

NASA Astrophysics Data System (ADS)

Ben-Shmuel, Yaron; Altus, Eli

2017-10-01

Plasticity and failure theories are still subjects of intense research. Engineering constitutive models on the macroscale which are based on micro characteristics are very much in need. This study is motivated by the observation that continuum assumptions in plasticity in which neighbour material elements are inseparable at all-time are physically impossible, since local detachments, slips and neighbour switching must operate, i.e. non-continuous deformation. Material microstructure is modelled herein by a set of point elements (particles) interacting with their neighbours. Each particle can detach from and/or attach with its neighbours during deformation. Simulations on two- dimensional configurations subjected to uniaxial compression cycle are conducted. Stochastic heterogeneity is controlled by a single "disorder" parameter. It was found that (a) macro response resembles typical elasto-plastic behaviour; (b) plastic energy is proportional to the number of detachments; (c) residual plastic strain is proportional to the number of attachments, and (d) volume is preserved, which is consistent with macro plastic deformation. Rigid body displacements of local groups of elements are also observed. Higher disorder decreases the macro elastic moduli and increases plastic energy. Evolution of anisotropic effects is obtained with no additional parameters.

Nonlinear force propagation, anisotropic stiffening and non-affine relaxation in a model cytoskeleton

NASA Astrophysics Data System (ADS)

Mizuno, Daisuke; Head, David; Ikebe, Emi; Nakamasu, Akiko; Kinoshita, Suguru; Peijuan, Zhang; Ando, Shoji

2013-03-01

Forces are generated heterogeneously in living cells and transmitted through cytoskeletal networks that respond highly non-linearly. Here, we carry out high-bandwidth passive microrheology on vimentin networks reconstituted in vitro, and observe the nonlinear mechanical response due to forces propagating from a local source applied by an optical tweezer. Since the applied force is constant, the gel becomes equilibrated and the fluctuation-dissipation theorem can be employed to deduce the viscoelasticity of the local environment from the thermal fluctuations of colloidal probes. Our experiments unequivocally demonstrate the anisotropic stiffening of the cytoskeletal network behind the applied force, with greater stiffening in the parallel direction. Quantitative agreement with an affine continuum model is obtained, but only for the response at certain frequency ~ 10-1000 Hz which separates the high-frequency power law and low-frequency elastic behavior of the network. We argue that the failure of the model at lower frequencies is due to the presence of non-affinity, and observe that zero-frequency changes in particle separation can be fitted when an independently-measured, empirical nonaffinity factor is applied.

Categorical prototyping: incorporating molecular mechanisms into 3D printing.

PubMed

Brommer, Dieter B; Giesa, Tristan; Spivak, David I; Buehler, Markus J

2016-01-15

We apply the mathematical framework of category theory to articulate the precise relation between the structure and mechanics of a nanoscale system in a macroscopic domain. We maintain the chosen molecular mechanical properties from the nanoscale to the continuum scale. Therein we demonstrate a procedure to 'protoype a model', as category theory enables us to maintain certain information across disparate fields of study, distinct scales, or physical realizations. This process fits naturally with prototyping, as a prototype is not a complete product but rather a reduction to test a subset of properties. To illustrate this point, we use large-scale multi-material printing to examine the scaling of the elastic modulus of 2D carbon allotropes at the macroscale and validate our printed model using experimental testing. The resulting hand-held materials can be examined more readily, and yield insights beyond those available in the original digital representations. We demonstrate this concept by twisting the material, a test beyond the scope of the original model. The method developed can be extended to other methods of additive manufacturing.

Polymer-induced forces at interfaces

NASA Astrophysics Data System (ADS)

Rangarajan, Murali

This dissertation concerns studies of forces generated by confined and physisorbed flexible polymers using lattice mean-field theories, and those generated by confined and clamped semiflexible polymers modeled as slender elastic rods. Lattice mean-field theories have been used in understanding and predicting the behavior of polymeric interfacial systems. In order to efficiently tailor such systems for various applications of interest, one has to understand the forces generated in the interface due to the polymer molecules. The present work examines the abilities and limitations of lattice mean-field theories in predicting the structure of physisorbed polymer layers and the resultant forces. Within the lattice mean-field theory, a definition of normal force of compression as the negative derivative of the partition-function-based excess free energy with surface separation gives misleading results because the theory does not explicitly account for the normal stresses involved in the system. Correct expressions for normal and tangential forces are obtained from a continuum-mechanics-based formulation. Preliminary comparisons with lattice Monte Carlo simulations show that mean-field theories fail to predict significant attractive forces when the surfaces are undersaturated, as one would expect. The corrections to the excluded volume (non-reversal chains) and the mean-field (anisotropic field) approximations improve the predictions of layer structure, but not the forces. Bending of semiflexible polymer chains (elastic rods) is considered for two boundary conditions---where the chain is hinged on both ends and where the chain is clamped on one end and hinged on the other. For the former case, the compressive forces and chain shapes obtained are consistent with the inflexional elastica published by Love. For the latter, multiple and higher-order solutions are observed for the hinged-end position for a given force. Preliminary studies are conducted on actin-based motility of Listeria monocytogenes by treating actin filaments as elastic rods, using the actoclampin model. The results show qualitative agreement with calculations where the filaments are modeled as Hookean springs. The feasibility of the actoclampin model to address long length-scale rotation of Listeria during actin-based motility is addressed.

Helium segregation on surfaces of plasma-exposed tungsten

DOE PAGES

Maroudas, Dimitrios; Blondel, Sophie; Hu, Lin; ...

2016-01-21

Here we report a hierarchical multi-scale modeling study of implanted helium segregation on surfaces of tungsten, considered as a plasma facing component in nuclear fusion reactors. We employ a hierarchy of atomic-scale simulations based on a reliable interatomic interaction potential, including molecular-statics simulations to understand the origin of helium surface segregation, targeted molecular-dynamics (MD) simulations of near-surface cluster reactions, and large-scale MD simulations of implanted helium evolution in plasma-exposed tungsten. We find that small, mobile He-n (1 <= n <= 7) clusters in the near-surface region are attracted to the surface due to an elastic interaction force that provides themore » thermodynamic driving force for surface segregation. Elastic interaction force induces drift fluxes of these mobile Hen clusters, which increase substantially as the migrating clusters approach the surface, facilitating helium segregation on the surface. Moreover, the clusters' drift toward the surface enables cluster reactions, most importantly trap mutation, in the near-surface region at rates much higher than in the bulk material. Moreover, these near-surface cluster dynamics have significant effects on the surface morphology, near-surface defect structures, and the amount of helium retained in the material upon plasma exposure. We integrate the findings of such atomic-scale simulations into a properly parameterized and validated spatially dependent, continuum-scale reaction-diffusion cluster dynamics model, capable of predicting implanted helium evolution, surface segregation, and its near-surface effects in tungsten. This cluster-dynamics model sets the stage for development of fully atomistically informed coarse-grained models for computationally efficient simulation predictions of helium surface segregation, as well as helium retention and surface morphological evolution, toward optimal design of plasma facing components.« less

Helium segregation on surfaces of plasma-exposed tungsten

NASA Astrophysics Data System (ADS)

Maroudas, Dimitrios; Blondel, Sophie; Hu, Lin; Hammond, Karl D.; Wirth, Brian D.

2016-02-01

We report a hierarchical multi-scale modeling study of implanted helium segregation on surfaces of tungsten, considered as a plasma facing component in nuclear fusion reactors. We employ a hierarchy of atomic-scale simulations based on a reliable interatomic interaction potential, including molecular-statics simulations to understand the origin of helium surface segregation, targeted molecular-dynamics (MD) simulations of near-surface cluster reactions, and large-scale MD simulations of implanted helium evolution in plasma-exposed tungsten. We find that small, mobile He n (1  ⩽  n  ⩽  7) clusters in the near-surface region are attracted to the surface due to an elastic interaction force that provides the thermodynamic driving force for surface segregation. This elastic interaction force induces drift fluxes of these mobile He n clusters, which increase substantially as the migrating clusters approach the surface, facilitating helium segregation on the surface. Moreover, the clusters’ drift toward the surface enables cluster reactions, most importantly trap mutation, in the near-surface region at rates much higher than in the bulk material. These near-surface cluster dynamics have significant effects on the surface morphology, near-surface defect structures, and the amount of helium retained in the material upon plasma exposure. We integrate the findings of such atomic-scale simulations into a properly parameterized and validated spatially dependent, continuum-scale reaction-diffusion cluster dynamics model, capable of predicting implanted helium evolution, surface segregation, and its near-surface effects in tungsten. This cluster-dynamics model sets the stage for development of fully atomistically informed coarse-grained models for computationally efficient simulation predictions of helium surface segregation, as well as helium retention and surface morphological evolution, toward optimal design of plasma facing components.

Application of Mortar Coupling in Multiscale Modelling of Coupled Flow, Transport, and Biofilm Growth in Porous Media

NASA Astrophysics Data System (ADS)

Laleian, A.; Valocchi, A. J.; Werth, C. J.

2017-12-01

Multiscale models of reactive transport in porous media are capable of capturing complex pore-scale processes while leveraging the efficiency of continuum-scale models. In particular, porosity changes caused by biofilm development yield complex feedbacks between transport and reaction that are difficult to quantify at the continuum scale. Pore-scale models, needed to accurately resolve these dynamics, are often impractical for applications due to their computational cost. To address this challenge, we are developing a multiscale model of biofilm growth in which non-overlapping regions at pore and continuum spatial scales are coupled with a mortar method providing continuity at interfaces. We explore two decompositions of coupled pore-scale and continuum-scale regions to study biofilm growth in a transverse mixing zone. In the first decomposition, all reaction is confined to a pore-scale region extending the transverse mixing zone length. Only solute transport occurs in the surrounding continuum-scale regions. Relative to a fully pore-scale result, we find the multiscale model with this decomposition has a reduced run time and consistent result in terms of biofilm growth and solute utilization. In the second decomposition, reaction occurs in both an up-gradient pore-scale region and a down-gradient continuum-scale region. To quantify clogging, the continuum-scale model implements empirical relations between porosity and continuum-scale parameters, such as permeability and the transverse dispersion coefficient. Solutes are sufficiently mixed at the end of the pore-scale region, such that the initial reaction rate is accurately computed using averaged concentrations in the continuum-scale region. Relative to a fully pore-scale result, we find accuracy of biomass growth in the multiscale model with this decomposition improves as the interface between pore-scale and continuum-scale regions moves downgradient where transverse mixing is more fully developed. Also, this decomposition poses additional challenges with respect to mortar coupling. We explore these challenges and potential solutions. While recent work has demonstrated growing interest in multiscale models, further development is needed for their application to field-scale subsurface contaminant transport and remediation.

Growth on demand: Reviewing the mechanobiology of stretched skin

PubMed Central

Zöllner, Alexander M.; Holland, Maria A.; Honda, Kord S.; Gosain, Arun K.; Kuhl, Ellen

2013-01-01

Skin is a highly dynamic, autoregulated, living system that responds to mechanical stretch through a net gain in skin surface area. Tissue expansion uses the concept of controlled overstretch to grow extra skin for defect repair in situ. While the short-term mechanics of stretched skin have been studied intensely by testing explanted tissue samples ex vivo, we know very little about the long-term biomechanics and mechanobiology of living skin in vivo. redHere we explore the long-term effects of mechanical stretch on the characteristics of living skin using a mathematical model for skin growth. We review the molecular mechanisms by which skin responds to mechanical loading and model their effects collectively in a single scalar-valued internal variable, the surface area growth. redThis allows us to adopt a continuum model for growing skin based on the multiplicative decomposition of the deformation gradient into a reversible elastic and an irreversible growth part.redTo demonstrate the inherent modularity of this approach, we implement growth as a user-defined constitutive subroutine into the general purpose implicit finite element program Abaqus/Standard. To illustrate the features of the model, we simulate the controlled area growth of skin in response to tissue expansion with multiple filling points in time. Our results demonstrate that the field theories of continuum mechanics can reliably predict the manipulation of thin biological membranes through mechanical overstretch. Our model could serve as a valuable tool to rationalize clinical process parameters such as expander geometry, expander size, filling volume, filling pressure, and inflation timing to minimize tissue necrosis and maximize patient comfort in plastic and reconstructive surgery. While initially developed for growing skin, our model can easily be generalized to arbitrary biological structures to explore the physiology and pathology of stretch-induced growth of other living systems such as hearts, arteries, bladders, intestines, ureters, muscles, and nerves. PMID:23623569

SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-08-01

This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. Themore » notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.« less

Nondestructive Characterization Techniques Used for Ceramic Matrix Composite Life Determination

NASA Technical Reports Server (NTRS)

Effinger, Michael; Koenig, John; Ellingson, Bill; Spohnholtz, Todd

2000-01-01

Recent results indicate that the specific damping capacity and resonant frequency measurements taken periodically during a component's lifetime is able to quantify the mechanical fatigue of CMCS. This gives hope for the potential of determining the actual and residual life of CMC materials using a combination of nondestructive techniques. If successful, then this new paradigm for life prediction of CMCs could revolutionize the approach for designing and servicing CMC components, thereby significantly reducing costs for design, development, health monitoring, and maintenance of CMC components and systems. The Nondestructive Characterization (NDC) life prediction approach would complement life prediction using micromechanics and continuum finite element models. This paper reports on the initial concept of NDC life prediction, a review of the C/SiC blisk damping data, and how changes in the specific damping capacity & ultrasonic elastic modulus data have established the concept as a possibility.

Concept for Determining the Life of Ceramic Matrix Composites Using Nondestructive Characterization Techniques

NASA Technical Reports Server (NTRS)

Effinger, Michael; Ellingson, Bill; Spohnholtz, Todd; Koenig, John

2000-01-01

Damping measurements have been taken on ceramic matrix composite (CMC) turbopump blisks in the as fabricated, post proof testing, and post turbopump testing conditions. These results indicate that damping is able to quantify fatigue of the CMC blisk. This gives hope for the potential of determining the actual and residual life of CMC materials using a combination of nondestructive techniques. If successful, then this new paradigm for life prediction of CMCs could revolutionize the approach for designing and servicing CMC components, thereby significantly reducing costs for design, development, health monitoring, and maintenance of CMC components and systems. The Nondestructive Characterization (NDC) life prediction approach would complement life prediction using micromechanics and continuum finite element models. This paper reports on the initial concept of NDC life prediction and how changes in damping and ultrasonic elastic modulus data have established the concept as a possibility.

``The Princess and the Pea'' at the Nanoscale: Wrinkling and Delamination of Graphene on Nanoparticles

NASA Astrophysics Data System (ADS)

Yamamoto, Mahito; Pierre-Louis, Olivier; Huang, Jia; Fuhrer, Michael S.; Einstein, Theodore L.; Cullen, William G.

2012-10-01

Thin membranes exhibit complex responses to external forces or geometrical constraints. A familiar example is the wrinkling, exhibited by human skin, plant leaves, and fabrics, that results from the relative ease of bending versus stretching. Here, we study the wrinkling of graphene, the thinnest and stiffest known membrane, deposited on a silica substrate decorated with silica nanoparticles. At small nanoparticle density, monolayer graphene adheres to the substrate, detached only in small regions around the nanoparticles. With increasing nanoparticle density, we observe the formation of wrinkles which connect nanoparticles. Above a critical nanoparticle density, the wrinkles form a percolating network through the sample. As the graphene membrane is made thicker, global delamination from the substrate is observed. The observations can be well understood within a continuum-elastic model and have important implications for strain-engineering the electronic properties of graphene.

Continuum Reconfigurable Parallel Robots for Surgery: Shape Sensing and State Estimation with Uncertainty.

PubMed

Anderson, Patrick L; Mahoney, Arthur W; Webster, Robert J

2017-07-01

This paper examines shape sensing for a new class of surgical robot that consists of parallel flexible structures that can be reconfigured inside the human body. Known as CRISP robots, these devices provide access to the human body through needle-sized entry points, yet can be configured into truss-like structures capable of dexterous movement and large force application. They can also be reconfigured as needed during a surgical procedure. Since CRISP robots are elastic, they will deform when subjected to external forces or other perturbations. In this paper, we explore how to combine sensor information with mechanics-based models for CRISP robots to estimate their shapes under applied loads. The end result is a shape sensing framework for CRISP robots that will enable future research on control under applied loads, autonomous motion, force sensing, and other robot behaviors.

A computational procedure for multibody systems including flexible beam dynamics

NASA Technical Reports Server (NTRS)

Downer, J. D.; Park, K. C.; Chiou, J. C.

1990-01-01

A computational procedure suitable for the solution of equations of motions for flexible multibody systems has been developed. A fully nonlinear continuum approach capable of accounting for both finite rotations and large deformations has been used to model a flexible beam component. The beam kinematics are referred directly to an inertial reference frame such that the degrees of freedom embody both the rigid and flexible deformation motions. As such, the beam inertia expression is identical to that of rigid body dynamics. The nonlinear coupling between gross body motion and elastic deformation is contained in the internal force expression. Numerical solution procedures for the integration of spatial kinematic systems can be directily applied to the generalized coordinates of both the rigid and flexible components. An accurate computation of the internal force term which is invariant to rigid motions is incorporated into the general solution procedure.

Coupling discrete and continuum concentration particle models for multiscale and hybrid molecular-continuum simulations

NASA Astrophysics Data System (ADS)

Petsev, Nikolai D.; Leal, L. Gary; Shell, M. Scott

2017-12-01

Hybrid molecular-continuum simulation techniques afford a number of advantages for problems in the rapidly burgeoning area of nanoscale engineering and technology, though they are typically quite complex to implement and limited to single-component fluid systems. We describe an approach for modeling multicomponent hydrodynamic problems spanning multiple length scales when using particle-based descriptions for both the finely resolved (e.g., molecular dynamics) and coarse-grained (e.g., continuum) subregions within an overall simulation domain. This technique is based on the multiscale methodology previously developed for mesoscale binary fluids [N. D. Petsev, L. G. Leal, and M. S. Shell, J. Chem. Phys. 144, 084115 (2016)], simulated using a particle-based continuum method known as smoothed dissipative particle dynamics. An important application of this approach is the ability to perform coupled molecular dynamics (MD) and continuum modeling of molecularly miscible binary mixtures. In order to validate this technique, we investigate multicomponent hybrid MD-continuum simulations at equilibrium, as well as non-equilibrium cases featuring concentration gradients.

Design, analysis, and applications of cellular contact-aided compliant mechanisms

NASA Astrophysics Data System (ADS)

Mehta, Vipul

A new class of compliant mechanisms utilizing the benefits of cellular geometry and contact are addressed in this work. The design, analysis, fabrication and testing of such structures for high-strain and high-strength applications is the focus of the present research. Cellular structures have relatively good strength-to-weight ratios. They also have a higher strain capability than solid structures. Contact during deformation reduces failure-causing bending stresses through stress relief, thereby enabling such cellular structures to be stretched more than the corresponding structures without contact. Both analytical and numerical models are developed to represent one specific mechanism. Several candidate materials are investigated for such mechanisms. Although the allowable strain of all these materials is small, the overall strain of the contact-aided cellular mechanisms is at least an order of magnitude greater than that of the constitutive material. Application of contact to different materials yields an improvement in the global strain capacity by more than 100% relative to cellular structures without contact. Experiments are conducted to validate the models, and good agreement is found. Size optimization is carried out to maximize the stress relief and the overall strain. Two main applications are considered in the present work. One application consists of a morphing aircraft skin for adaptive structures. Different material models such as linearly elastic and multi-linear elastic are examined. For linearly elastic materials, contact-induced stress-relief is advantageous and for nonlinear elastic materials, reduction of transverse deflection due to contact is useful. The proposed contact-aided skin structure is compared with a cellular skin without contact. The contact mechanism helps to increase the morphing capacity while decreasing the structural mass. Using contact-aided cellular mechanisms, the global strain capability is increased by as much as 37%. For a fixed global strain, the optimum contact-aided structure is 15% lighter than an optimum non-contact structure. Another application involves investigation of meso-scaled cellular structures. Two different materials are considered---nanoparticulate zirconia and particulate stainless steel. The lost mold rapid infiltration forming process is utilized to fabricate free standing cellular mechanisms. The analytical model is employed to address the tradeoffs between the manufacturing constraints and to design suitable contact-aided cellular mechanisms. A custom rig is developed to test these meso-scaled parts. Force displacement characteristics are experimentally obtained and compared against those found using the analytical model. Topology optimization tools are applied to the design of compliant cellular mechanisms with and without a contact mechanism. A two-step procedure is developed. For cellular structures without contact, an inverse homogenization method is employed. The compliant mechanism is optimized to yield prescribed elasticity coefficients and achieve a large effective elastic strain. To implement a contact mechanism in the second step, the continuum model of a non-contact structure is converted into a frame model. Only the non-overlapping designs are investigated exhaustively for stress relief. A differential evolution optimizer is used to maximize the stress relief. Four cell topologies are found for different effective properties corresponding to different structural requirements. For each such topology, a contact mechanism is devised that demonstrates stress relief. One such topology resulted a stress relief as high as 36%.

Soil compaction: Evaluation of stress transmission and resulting soil structure

NASA Astrophysics Data System (ADS)

Naveed, Muhammad; Schjønning, Per; Keller, Thomas; Lamande, Mathieu

2016-04-01

Accurate estimation of stress transmission and resultant deformation in soil profiles is a prerequisite for the development of predictive models and decision support tools for preventing soil compaction. Numerous studies have been carried out on the effects of soil compaction, whilst relatively few studies have focused on the cause (mode of stress transmission in the soil). We have coupled both cause and effects together in the present study by carrying out partially confined compression tests on (1) wet aggregates, (2) air dry aggregates, and (3) intact soils to quantify stress transmission and compaction-resulted soil structure at the same time. Stress transmission was quantified using both X-ray CT and Tactilus sensor mat, and soil-pore structure was quantified using X-ray CT. Our results imply that stress transmission through soil highly depends on the magnitude of applied load and aggregate strength. As soon as the applied load is lower than the aggregate strength, the mode of stress transmission is discrete as stresses were mainly transmitted through chain of aggregates. With increasing applied load soil aggregates start deforming that transformed heterogeneous soil into homogenous, as a result stress transmission mode was shifted from discrete towards more like a continuum. Continuum-like stress transmission mode was better simulated with Boussinesq (1885) model based on theory of elasticity compared to discrete. The soil-pore structure was greatly affected by increasing applied stresses. Total porosity was reduced 5-16% and macroporosity 50-85% at 620 kPa applied stress for the intact soils. Similarly, significant changes in the morphological indices of the macropore space were also observed with increasing applied stresses.

Applicability of the Continuum-Shell Theories to the Mechanics of Carbon Nanotubes

NASA Technical Reports Server (NTRS)

Harik, V. M.; Gates, T. S.; Nemeth, M. P.

2002-01-01

Validity of the assumptions relating the applicability of continuum shell theories to the global mechanical behavior of carbon nanotubes is examined. The present study focuses on providing a basis that can be used to qualitatively assess the appropriateness of continuum-shell models for nanotubes. To address the effect of nanotube structure on their deformation, all nanotube geometries are divided into four major classes that require distinct models. Criteria for the applicability of continuum models are presented. The key parameters that control the buckling strains and deformation modes of these classes of nanotubes are determined. In an analogy with continuum mechanics, mechanical laws of geometric similitude are presented. A parametric map is constructed for a variety of nanotube geometries as a guide for the applicability of different models. The continuum assumptions made in representing a nanotube as a homogeneous thin shell are analyzed to identify possible limitations of applying shell theories and using their bifurcation-buckling equations at the nano-scale.

Considerations for the Development of a Substance-Related Care and Prevention Continuum Model

PubMed Central

Perlman, David C.; Jordan, Ashly E.

2017-01-01

There are significant gaps in the identification and engagement in care and prevention services of people who use illicit substances. Care continuum models have proven to be useful tools in the evaluation of care for HIV and other conditions; numerous issues in substance-related care and prevention resemble those identified in other continua models. Systems of care for substance misuse and substance use disorders (SUDs) can be viewed as consisting of a prevention and care continuum, reflecting incidence and prevalence of substance misuse and SUDs, screening and identification, medical and psychosocial evaluation for treatment, engagement in evidence-based treatment, treatment retention, relapse prevention, timeliness of step completion, and measures of overall and substance use-related specific morbidity and mortality. Care and prevention continuum models could potentially be applied at program, local, regional, state, and national levels. We discuss important lessons that can be drawn from applications of continuum models in other fields. The development and use of a substance-related care and prevention continuum may yield significant patient care, program evaluation and improvement, and population-level benefits. PMID:28770195

High strength, low stiffness, porous NiTi with superelastic properties.

PubMed

Greiner, Christian; Oppenheimer, Scott M; Dunand, David C

2005-11-01

Near-stoichiometric NiTi with up to 18% closed porosity was produced by expansion at 1200 degrees C of argon-filled pores trapped by powder metallurgy within a NiTi billet. When optimally heat-treated, NiTi with 6-16% porosity exhibits superelasticity, with recoverable compressive strains up to 6% at a maximum compressive stress up to 1700 MPa. The apparent Young's modulus of NiTi with 16% porosity, measured during uniaxial compression, is in the range of 15-25 GPa (similar to human bone), but is much lower than measured ultrasonically (approximately 40 GPa), or predicted from continuum elastic mechanics. This effect is attributed to the reversible stress-induced transformation contributing to the linear elastic deformation of porous NiTi. The unique combination of low stiffness, high strength, high recoverable strains and large energy absorption of porous superelastic NiTi, together with the known biocompatibility of NiTi, makes this material attractive for bone-implant applications.

D-Wave Electron-H, -He+, and -Li2+ Elastic Scattering and Photoabsorption in P States of Two-Electron Systems

NASA Technical Reports Server (NTRS)

Bhatia, A. K.

2014-01-01

In previous papers [A. K. Bhatia, Phys. Rev. A 85, 052708 (2012); 86, 032709 (2012); 87, 042705 (2013)] electron-H, -He+, and -Li2+ P-wave scattering phase shifts were calculated using the variational polarized orbital theory. This method is now extended to the singlet and triplet D-wave scattering in the elastic region. The long-range correlations are included in the Schrodinger equation by using the method of polarized orbitals variationally. Phase shifts are compared to those obtained by other methods. The present calculation provides results which are rigorous lower bonds to the exact phase shifts. Using the presently calculated D-wave and previously calculated S-wave continuum functions, photoionization of singlet and triplet P states of He and Li+ are also calculated, along with the radiative recombination rate coefficients at various electron temperatures.

How the continents deform: The evidence from tectonic geodesy

USGS Publications Warehouse

Thatcher, Wayne R.

2009-01-01

Space geodesy now provides quantitative maps of the surface velocity field within tectonically active regions, supplying constraints on the spatial distribution of deformation, the forces that drive it, and the brittle and ductile properties of continental lithosphere. Deformation is usefully described as relative motions among elastic blocks and is block-like because major faults are weaker than adjacent intact crust. Despite similarities, continental block kinematics differs from global plate tectonics: blocks are much smaller, typically ∼100–1000 km in size; departures from block rigidity are sometimes measurable; and blocks evolve over ∼1–10 Ma timescales, particularly near their often geometrically irregular boundaries. Quantitatively relating deformation to the forces that drive it requires simplifying assumptions about the strength distribution in the lithosphere. If brittle/elastic crust is strongest, interactions among blocks control the deformation. If ductile lithosphere is the stronger, its flow properties determine the surface deformation, and a continuum approach is preferable.

Surface phonons and elastic surface waves

NASA Astrophysics Data System (ADS)

Büscher, H.; Klein-Heßling, W.; Ludwig, W.

Theoretical investigations on the dynamics of the (001), (110) and (111) surfaces of some cubic metals (Ag, Cu, Ni) will be reviewed. Both, lattice dynamical and continuum theoretical results are obtained via a Green's function formalism. The main attitude of this paper is the comparison of our results with experiments and with results obtained via slab-calculations. The calculation of elastic surface waves has been performed using a modified surface-green-function-matching method. We have used two different approaches of calculation the bulk Green's function (a) using the spectral representation and (b) a method, what works on residues. The investigations are carried out using shortrange phenomenological potentials. The atomic force constants in the first surface layers are modified to describe surface phonon anomalies, observed by experiments. In the case of Ag (100) and Ag(110) we conclude that the detection of odd symmetry shear modes by Erskine et al. [1 a, b] was not very accurate.

Computational strategies in the dynamic simulation of constrained flexible MBS

NASA Technical Reports Server (NTRS)

Amirouche, F. M. L.; Xie, M.

1993-01-01

This research focuses on the computational dynamics of flexible constrained multibody systems. At first a recursive mapping formulation of the kinematical expressions in a minimum dimension as well as the matrix representation of the equations of motion are presented. The method employs Kane's equation, FEM, and concepts of continuum mechanics. The generalized active forces are extended to include the effects of high temperature conditions, such as creep, thermal stress, and elastic-plastic deformation. The time variant constraint relations for rolling/contact conditions between two flexible bodies are also studied. The constraints for validation of MBS simulation of gear meshing contact using a modified Timoshenko beam theory are also presented. The last part deals with minimization of vibration/deformation of the elastic beam in multibody systems making use of time variant boundary conditions. The above methodologies and computational procedures developed are being implemented in a program called DYAMUS.

Realistic Gamow shell model for resonance and continuum in atomic nuclei

NASA Astrophysics Data System (ADS)

Xu, F. R.; Sun, Z. H.; Wu, Q.; Hu, B. S.; Dai, S. J.

2018-02-01

The Gamow shell model can describe resonance and continuum for atomic nuclei. The model is established in the complex-moment (complex-k) plane of the Berggren coordinates in which bound, resonant and continuum states are treated on equal footing self-consistently. In the present work, the realistic nuclear force, CD Bonn, has been used. We have developed the full \\hat{Q}-box folded-diagram method to derive the realistic effective interaction in the model space which is nondegenerate and contains resonance and continuum channels. The CD-Bonn potential is renormalized using the V low-k method. With choosing 16O as the inert core, we have applied the Gamow shell model to oxygen isotopes.

Hybrid plasma modeling.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hopkins, Matthew Morgan; DeChant, Lawrence Justin.; Piekos, Edward Stanley

2009-02-01

This report summarizes the work completed during FY2007 and FY2008 for the LDRD project ''Hybrid Plasma Modeling''. The goal of this project was to develop hybrid methods to model plasmas across the non-continuum-to-continuum collisionality spectrum. The primary methodology to span these regimes was to couple a kinetic method (e.g., Particle-In-Cell) in the non-continuum regions to a continuum PDE-based method (e.g., finite differences) in continuum regions. The interface between the two would be adjusted dynamically ased on statistical sampling of the kinetic results. Although originally a three-year project, it became clear during the second year (FY2008) that there were not sufficientmore » resources to complete the project and it was terminated mid-year.« less

Elastohydrodynamic synchronization of adjacent beating flagella

NASA Astrophysics Data System (ADS)

Goldstein, Raymond E.; Lauga, Eric; Pesci, Adriana I.; Proctor, Michael R. E.

2016-11-01

It is now well established that nearby beating pairs of eukaryotic flagella or cilia typically synchronize in phase. A substantial body of evidence supports the hypothesis that hydrodynamic coupling between the active filaments, combined with waveform compliance, provides a robust mechanism for synchrony. This elastohydrodynamic mechanism has been incorporated into bead-spring models in which the beating flagella are represented by microspheres tethered by radial springs as they are driven about orbits by internal forces. While these low-dimensional models reproduce the phenomenon of synchrony, their parameters are not readily relatable to those of the filaments they represent. More realistic models, which reflect the underlying elasticity of the axonemes and the active force generation, take the form of fourth-order nonlinear partial differential equations (PDEs). While computational studies have shown the occurrence of synchrony, the effects of hydrodynamic coupling between nearby filaments governed by such continuum models have been examined theoretically only in the regime of interflagellar distances d large compared to flagellar length L . Yet in many biological situations d /L ≪1 . Here we present an asymptotic analysis of the hydrodynamic coupling between two extended filaments in the regime d /L ≪1 and find that the form of the coupling is independent of the microscopic details of the internal forces that govern the motion of the individual filaments. The analysis is analogous to that yielding the localized induction approximation for vortex filament motion, extended to the case of mutual induction. In order to understand how the elastohydrodynamic coupling mechanism leads to synchrony of extended objects, we introduce a heuristic model of flagellar beating. The model takes the form of a single fourth-order nonlinear PDE whose form is derived from symmetry considerations, the physics of elasticity, and the overdamped nature of the dynamics. Analytical and numerical studies of this model illustrate how synchrony between a pair of filaments is achieved through the asymptotic coupling.

Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices.

PubMed

Español, Malena I; Golovaty, Dmitry; Wilber, J Patrick

2018-01-01

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

Role of Brittle Behaviour of Soft Calcarenites Under Low Confinement: Laboratory Observations and Numerical Investigation

NASA Astrophysics Data System (ADS)

Lollino, Piernicola; Andriani, Gioacchino Francesco

2017-07-01

The strength decay that occurs in the post-peak stage, under low confinement stress, represents a key factor of the stress-strain behaviour of rocks. However, for soft rocks this issue is generally underestimated or even neglected in the solution of boundary value problems, as for example those concerning the stability of underground cavities or rocky cliffs. In these cases, the constitutive models frequently used in limit equilibrium analyses or more sophisticated numerical calculations are, respectively, rigid-plastic or elastic-perfectly plastic. In particular, most of commercial continuum-based numerical codes propose a variety of constitutive models, including elasticity, elasto-plasticity, strain-softening and elasto-viscoplasticity, which are not exhaustive in simulating the progressive failure mechanisms affecting brittle rock materials, these being characterized by material detachment and crack opening and propagation. As a consequence, a numerical coupling with mechanical joint propagation is needed to cope with fracture mechanics. Therefore, continuum-based applications that treat the simulation of the failure processes of intact rock masses at low stress levels may need the adoption of numerical techniques capable of implementing fracture mechanics and rock brittleness concepts, as it is shown in this paper. This work is aimed at highlighting, for some applications of rock mechanics, the essential role of post-peak brittleness of soft rocks by means of the application of a hybrid finite-discrete element method. This method allows for a proper simulation of the brittle rock behaviour and the related mechanism of fracture propagation. In particular, the paper presents two ideal problems, represented by a shallow underground cave and a vertical cliff, for which the evolution of the stability conditions is investigated by comparing the solutions obtained implementing different brittle material responses with those resulting from the assumption of perfectly plastic behaviour. To this purpose, a series of petrophysical and mechanical tests were conducted on samples of soft calcarenite belonging to the Calcarenite di Gravina Fm. (Apulia, Southern Italy), focusing specific attention on the post-peak behaviour of the material under three types of loading (compression, indirect tension and shear). Typical geometrical features representative of real rock engineering problems observed in Southern Italy were assumed in the problems examined. The numerical results indicate the impact of soft rock brittleness in the assessment of stability and highlight the need for the adoption of innovative numerical techniques to analyse these types of problems properly.

Modelling fragmentations of aminoacids after resonant electron attachment: quantum evidence of possible direct -OH detachment

NASA Astrophysics Data System (ADS)

Panosetti, C.; Baccarelli, I.; Sebastianelli, F.; Gianturco, F. A.

2010-10-01

We investigate some aspects of the radiation damage mechanisms in biomolecules, focusing on the modelling of resonant fragmentation caused by the attachment of low-energy electrons (LEEs) initially ejected by biological tissues when exposed to ionizing radiation. Scattering equations are formulated within a symmetry-adapted, single-center expansion of both continuum and bound electrons, and the interaction forces are obtained from a combination of ab initio calculations and a nonempirical model of exchange and correlation effects developped in our group. We present total elastic scattering cross-sections and resonance features obtained for the equilibrium geometries of glycine, alanine, proline and valine. Our results at those geometries of the target molecules are briefly shown to qualitatively explain some of the fragmentation patterns obtained in experiments. We further carry out a one-dimensional (1D) modeling for the dynamics of intramolecular energy transfers mediated by the vibrational activation of selected bonds: our calculations indicate that resonant electron attachment to glycine can trigger direct, dissociative evolution of the complex into (Gly-OH)- and -OH losses, while they also find that the same process does not occur via a direct, 1D dissociative path in the larger aminoacids of the present study.

Comprehensive Micromechanics-Analysis Code - Version 4.0

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Bednarcyk, B. A.

2005-01-01

Version 4.0 of the Micromechanics Analysis Code With Generalized Method of Cells (MAC/GMC) has been developed as an improved means of computational simulation of advanced composite materials. The previous version of MAC/GMC was described in "Comprehensive Micromechanics-Analysis Code" (LEW-16870), NASA Tech Briefs, Vol. 24, No. 6 (June 2000), page 38. To recapitulate: MAC/GMC is a computer program that predicts the elastic and inelastic thermomechanical responses of continuous and discontinuous composite materials with arbitrary internal microstructures and reinforcement shapes. The predictive capability of MAC/GMC rests on a model known as the generalized method of cells (GMC) - a continuum-based model of micromechanics that provides closed-form expressions for the macroscopic response of a composite material in terms of the properties, sizes, shapes, and responses of the individual constituents or phases that make up the material. Enhancements in version 4.0 include a capability for modeling thermomechanically and electromagnetically coupled ("smart") materials; a more-accurate (high-fidelity) version of the GMC; a capability to simulate discontinuous plies within a laminate; additional constitutive models of materials; expanded yield-surface-analysis capabilities; and expanded failure-analysis and life-prediction capabilities on both the microscopic and macroscopic scales.

Rupture Propagation for Stochastic Fault Models

NASA Astrophysics Data System (ADS)

Favreau, P.; Lavallee, D.; Archuleta, R.

2003-12-01

The inversion of strong motion data of large earhquakes give the spatial distribution of pre-stress on the ruptured faults and it can be partially reproduced by stochastic models, but a fundamental question remains: how rupture propagates, constrained by the presence of spatial heterogeneity? For this purpose we investigate how the underlying random variables, that control the pre-stress spatial variability, condition the propagation of the rupture. Two stochastic models of prestress distributions are considered, respectively based on Cauchy and Gaussian random variables. The parameters of the two stochastic models have values corresponding to the slip distribution of the 1979 Imperial Valley earthquake. We use a finite difference code to simulate the spontaneous propagation of shear rupture on a flat fault in a 3D continuum elastic body. The friction law is the slip dependent friction law. The simulations show that the propagation of the rupture front is more complex, incoherent or snake-like for a prestress distribution based on Cauchy random variables. This may be related to the presence of a higher number of asperities in this case. These simulations suggest that directivity is stronger in the Cauchy scenario, compared to the smoother rupture of the Gauss scenario.

Applications of Artificial Neural Networks in Structural Engineering with Emphasis on Continuum Models

NASA Technical Reports Server (NTRS)

Kapania, Rakesh K.; Liu, Youhua

1998-01-01

The use of continuum models for the analysis of discrete built-up complex aerospace structures is an attractive idea especially at the conceptual and preliminary design stages. But the diversity of available continuum models and hard-to-use qualities of these models have prevented them from finding wide applications. In this regard, Artificial Neural Networks (ANN or NN) may have a great potential as these networks are universal approximators that can realize any continuous mapping, and can provide general mechanisms for building models from data whose input-output relationship can be highly nonlinear. The ultimate aim of the present work is to be able to build high fidelity continuum models for complex aerospace structures using the ANN. As a first step, the concepts and features of ANN are familiarized through the MATLAB NN Toolbox by simulating some representative mapping examples, including some problems in structural engineering. Then some further aspects and lessons learned about the NN training are discussed, including the performances of Feed-Forward and Radial Basis Function NN when dealing with noise-polluted data and the technique of cross-validation. Finally, as an example of using NN in continuum models, a lattice structure with repeating cells is represented by a continuum beam whose properties are provided by neural networks.

Huygens-Fresnel picture for electron-molecule elastic scattering★

NASA Astrophysics Data System (ADS)

Baltenkov, Arkadiy S.; Msezane, Alfred Z.

2017-11-01

The elastic scattering cross sections for a slow electron by C2 and H2 molecules have been calculated within the framework of the non-overlapping atomic potential model. For the amplitudes of the multiple electron scattering by a target the wave function of the molecular continuum is represented as a combination of a plane wave and two spherical waves generated by the centers of atomic spheres. This wave function obeys the Huygens-Fresnel principle according to which the electron wave scattering by a system of two centers is accompanied by generation of two spherical waves; their interaction creates a diffraction pattern far from the target. Each of the Huygens waves, in turn, is a superposition of the partial spherical waves with different orbital angular momenta l and their projections m. The amplitudes of these partial waves are defined by the corresponding phases of electron elastic scattering by an isolated atomic potential. In numerical calculations the s- and p-phase shifts are taken into account. So the number of interfering electron waves is equal to eight: two of which are the s-type waves and the remaining six waves are of the p-type with different m values. The calculation of the scattering amplitudes in closed form (rather than in the form of S-matrix expansion) is reduced to solving a system of eight inhomogeneous algebraic equations. The differential and total cross sections of electron scattering by fixed-in-space molecules and randomly oriented ones have been calculated as well. We conclude by discussing the special features of the S-matrix method for the case of arbitrary non-spherical potentials. Contribution to the Topical Issue "Low energy positron and electron interactions", edited by James Sullivan, Ron White, Michael Bromley, Ilya Fabrikant, and David Cassidy.

Nonlinear modeling of crystal system transition of black phosphorus using continuum-DFT model.

PubMed

Setoodeh, A R; Farahmand, H

2018-01-24

In this paper, the nonlinear behavior of black phosphorus crystals is investigated in tandem with dispersion-corrected density functional theory (DFT-D) analysis under uniaxial loadings. From the identified anisotropic behavior of black phosphorus due to its morphological anisotropy, a hyperelastic anisotropic (HA) model named continuum-DFT is established to predict the nonlinear behavior of the material. In this respect, uniaxial Cauchy stresses are employed on both the DFT-D and HA models along the zig-zag and armchair directions. Simultaneously, the transition of the crystal system is recognized at about 4.5 GPa of the applied uniaxial tensile stress along the zig-zag direction on the DFT-D simulation in the nonlinear region. In order to develop the nonlinear continuum model, unknown constants are surveyed with the optimized least square technique. In this regard, the continuum model is obtained to reproduce the Cauchy stress-stretch and density of strain-stretch results of the DFT-D simulation. Consequently, the modified HA model is introduced to characterize the nonlinear behavior of black phosphorus along the zig-zag direction. More importantly, the specific transition of the crystal system is successfully predicted in the new modified continuum-DFT model. The results reveal that the multiscale continuum-DFT model is well defined to replicate the nonlinear behavior of black phosphorus along the zig-zag and armchair directions.

Coupling discrete and continuum concentration particle models for multiscale and hybrid molecular-continuum simulations

DOE PAGES

Petsev, Nikolai Dimitrov; Leal, L. Gary; Shell, M. Scott

2017-12-21

Hybrid molecular-continuum simulation techniques afford a number of advantages for problems in the rapidly burgeoning area of nanoscale engineering and technology, though they are typically quite complex to implement and limited to single-component fluid systems. We describe an approach for modeling multicomponent hydrodynamic problems spanning multiple length scales when using particle-based descriptions for both the finely-resolved (e.g. molecular dynamics) and coarse-grained (e.g. continuum) subregions within an overall simulation domain. This technique is based on the multiscale methodology previously developed for mesoscale binary fluids [N. D. Petsev, L. G. Leal, and M. S. Shell, J. Chem. Phys. 144, 84115 (2016)], simulatedmore » using a particle-based continuum method known as smoothed dissipative particle dynamics (SDPD). An important application of this approach is the ability to perform coupled molecular dynamics (MD) and continuum modeling of molecularly miscible binary mixtures. In order to validate this technique, we investigate multicomponent hybrid MD-continuum simulations at equilibrium, as well as non-equilibrium cases featuring concentration gradients.« less

Coupling discrete and continuum concentration particle models for multiscale and hybrid molecular-continuum simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Petsev, Nikolai Dimitrov; Leal, L. Gary; Shell, M. Scott

Hybrid molecular-continuum simulation techniques afford a number of advantages for problems in the rapidly burgeoning area of nanoscale engineering and technology, though they are typically quite complex to implement and limited to single-component fluid systems. We describe an approach for modeling multicomponent hydrodynamic problems spanning multiple length scales when using particle-based descriptions for both the finely-resolved (e.g. molecular dynamics) and coarse-grained (e.g. continuum) subregions within an overall simulation domain. This technique is based on the multiscale methodology previously developed for mesoscale binary fluids [N. D. Petsev, L. G. Leal, and M. S. Shell, J. Chem. Phys. 144, 84115 (2016)], simulatedmore » using a particle-based continuum method known as smoothed dissipative particle dynamics (SDPD). An important application of this approach is the ability to perform coupled molecular dynamics (MD) and continuum modeling of molecularly miscible binary mixtures. In order to validate this technique, we investigate multicomponent hybrid MD-continuum simulations at equilibrium, as well as non-equilibrium cases featuring concentration gradients.« less

On the origin of the water vapor continuum absorption within rotational and fundamental vibrational bands

NASA Astrophysics Data System (ADS)

Serov, E. A.; Odintsova, T. A.; Tretyakov, M. Yu.; Semenov, V. E.

2017-05-01

Analysis of the continuum absorption in water vapor at room temperature within the purely rotational and fundamental ro-vibrational bands shows that a significant part (up to a half) of the observed absorption cannot be explained within the framework of the existing concepts of the continuum. Neither of the two most prominent mechanisms of continuum originating, namely, the far wings of monomer lines and the dimers, cannot reproduce the currently available experimental data adequately. We propose a new approach to developing a physically based model of the continuum. It is demonstrated that water dimers and wings of monomer lines may contribute equally to the continuum within the bands, and their contribution should be taken into account in the continuum model. We propose a physical mechanism giving missing justification for the super-Lorentzian behavior of the intermediate line wing. The qualitative validation of the proposed approach is given on the basis of a simple empirical model. The obtained results are directly indicative of the necessity to reconsider the existing line wing theory and can guide this consideration.

A multiscale microstructural approach to ductile-phase toughened tungsten for plasma-facing materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nguyen, Ba Nghiep; Henager, Jr., Charles H.; Overman, Nicole R.

Increasing fracture toughness and modifying the ductile-brittle transition temperature of a tungsten-alloy relative to pure tungsten has been shown to be feasible by ductile-phase toughening (DPT) of tungsten for future plasma-facing materials for fusion energy. In DPT, a ductile phase is included in a brittle tungsten matrix to increase the overall work of fracture for the material. This research models the deformation behavior of DPT tungsten materials, such as tungsten-copper composites, using a multiscale modeling approach that involves a microstructural dual-phase (copper-tungsten) region of interest where the constituent phases are finely discretized and are described by a continuum damage mechanicsmore » model. Large deformation, damage, and fracture are allowed to occur and are modeled in a region that is connected to adjacent homogenized elastic regions to form a macroscopic structure, such as a test specimen. The present paper illustrates this multiscale modeling approach to analyze unnotched and single-edge notched (SENB) tungsten-copper composite specimens subjected to three-point bending. The predicted load-displacement responses and crack propagation patterns are compared to the corresponding experimental results to validate the model. Furthermore, such models may help design future DPT composite configurations for fusion materials, including volume fractions of ductile phase and microstructural optimization.« less

A multiscale microstructural approach to ductile-phase toughened tungsten for plasma-facing materials

DOE PAGES

Nguyen, Ba Nghiep; Henager, Jr., Charles H.; Overman, Nicole R.; ...

2018-05-23

Increasing fracture toughness and modifying the ductile-brittle transition temperature of a tungsten-alloy relative to pure tungsten has been shown to be feasible by ductile-phase toughening (DPT) of tungsten for future plasma-facing materials for fusion energy. In DPT, a ductile phase is included in a brittle tungsten matrix to increase the overall work of fracture for the material. This research models the deformation behavior of DPT tungsten materials, such as tungsten-copper composites, using a multiscale modeling approach that involves a microstructural dual-phase (copper-tungsten) region of interest where the constituent phases are finely discretized and are described by a continuum damage mechanicsmore » model. Large deformation, damage, and fracture are allowed to occur and are modeled in a region that is connected to adjacent homogenized elastic regions to form a macroscopic structure, such as a test specimen. The present paper illustrates this multiscale modeling approach to analyze unnotched and single-edge notched (SENB) tungsten-copper composite specimens subjected to three-point bending. The predicted load-displacement responses and crack propagation patterns are compared to the corresponding experimental results to validate the model. Furthermore, such models may help design future DPT composite configurations for fusion materials, including volume fractions of ductile phase and microstructural optimization.« less

Dispersion of folded phonons in {Si}/{Si xGe1- x} superlattices

NASA Astrophysics Data System (ADS)

Brugger, H.; Reiner, H.; Abstreiter, G.; Jorke, H.; Herzog, H. J.; Kasper, E.

Zone folding effects on acoustic phonons in {Si}/{Si xGe1- x} strained layer superlattices are studied by Raman spectroscopy. A quantitative explanation of the measured frequencies is given in terms of the elastic continuum theory. The scattering wavevector q s is varied by use of different laser lines to probe directly the phonon dispersion curve in the superlattices. For large period samples q s can be shifted through the new Brillouin zone boundary. We report on observation of a finite doublet splitting corresponding to the first zone-edge gap.

A continuum theory for multicomponent chromatography modeling.

PubMed

Pfister, David; Morbidelli, Massimo; Nicoud, Roger-Marc

2016-05-13

A continuum theory is proposed for modeling multicomponent chromatographic systems under linear conditions. The model is based on the description of complex mixtures, possibly involving tens or hundreds of solutes, by a continuum. The present approach is shown to be very efficient when dealing with a large number of similar components presenting close elution behaviors and whose individual analytical characterization is impossible. Moreover, approximating complex mixtures by continuous distributions of solutes reduces the required number of model parameters to the few ones specific to the characterization of the selected continuous distributions. Therefore, in the frame of the continuum theory, the simulation of large multicomponent systems gets simplified and the computational effectiveness of the chromatographic model is thus dramatically improved. Copyright © 2016 Elsevier B.V. All rights reserved.

Computing an upper bound on contact stress with surrogate duality

NASA Astrophysics Data System (ADS)

Xuan, Zhaocheng; Papadopoulos, Panayiotis

2016-07-01

We present a method for computing an upper bound on the contact stress of elastic bodies. The continuum model of elastic bodies with contact is first modeled as a constrained optimization problem by using finite elements. An explicit formulation of the total contact force, a fraction function with the numerator as a linear function and the denominator as a quadratic convex function, is derived with only the normalized nodal contact forces as the constrained variables in a standard simplex. Then two bounds are obtained for the sum of the nodal contact forces. The first is an explicit formulation of matrices of the finite element model, derived by maximizing the fraction function under the constraint that the sum of the normalized nodal contact forces is one. The second bound is solved by first maximizing the fraction function subject to the standard simplex and then using Dinkelbach's algorithm for fractional programming to find the maximum—since the fraction function is pseudo concave in a neighborhood of the solution. These two bounds are solved with the problem dimensions being only the number of contact nodes or node pairs, which are much smaller than the dimension for the original problem, namely, the number of degrees of freedom. Next, a scheme for constructing an upper bound on the contact stress is proposed that uses the bounds on the sum of the nodal contact forces obtained on a fine finite element mesh and the nodal contact forces obtained on a coarse finite element mesh, which are problems that can be solved at a lower computational cost. Finally, the proposed method is verified through some examples concerning both frictionless and frictional contact to demonstrate the method's feasibility, efficiency, and robustness.

A viscoelastic damage rheology and rate- and state-dependent friction

NASA Astrophysics Data System (ADS)

Lyakhovsky, Vladimir; Ben-Zion, Yehuda; Agnon, Amotz

2005-04-01

We analyse the relations between a viscoelastic damage rheology model and rate- and state-dependent (RS) friction. Both frameworks describe brittle deformation, although the former models localization zones in a deforming volume while the latter is associated with sliding on existing surfaces. The viscoelastic damage model accounts for evolving elastic properties and inelastic strain. The evolving elastic properties are related quantitatively to a damage state variable representing the local density of microcracks. Positive and negative changes of the damage variable lead, respectively, to degradation and recovery of the material in response to loading. A model configuration having an existing narrow zone with localized damage produces for appropriate loading and temperature-pressure conditions an overall cyclic stick-slip motion compatible with a frictional response. Each deformation cycle (limit cycle) can be divided into healing and weakening periods associated with decreasing and increasing damage, respectively. The direct effect of the RS friction and the magnitude of the frictional parameter a are related to material strengthening with increasing rate of loading. The strength and residence time of asperities (model elements) in the weakening stage depend on the rates of damage evolution and accumulation of irreversible strain. The evolutionary effect of the RS friction and overall change in the friction parameters (a-b) are controlled by the duration of the healing period and asperity (element) strengthening during this stage. For a model with spatially variable properties, the damage rheology reproduces the logarithmic dependency of the steady-state friction coefficient on the sliding velocity and the normal stress. The transition from a velocity strengthening regime to a velocity weakening one can be obtained by varying the rate of inelastic strain accumulation and keeping the other damage rheology parameters fixed. The developments unify previous damage rheology results on deformation localization leading to formation of new fault zones with detailed experimental results on frictional sliding. The results provide a route for extending the formulation of RS friction into a non-linear continuum mechanics framework.

Brittle fracture in viscoelastic materials as a pattern-formation process

NASA Astrophysics Data System (ADS)

Fleck, M.; Pilipenko, D.; Spatschek, R.; Brener, E. A.

2011-04-01

A continuum model of crack propagation in brittle viscoelastic materials is presented and discussed. Thereby, the phenomenon of fracture is understood as an elastically induced nonequilibrium interfacial pattern formation process. In this spirit, a full description of a propagating crack provides the determination of the entire time dependent shape of the crack surface, which is assumed to be extended over a finite and self-consistently selected length scale. The mechanism of crack propagation, that is, the motion of the crack surface, is then determined through linear nonequilibrium transport equations. Here we consider two different mechanisms, a first-order phase transformation and surface diffusion. We give scaling arguments showing that steady-state solutions with a self-consistently selected propagation velocity and crack shape can exist provided that elastodynamic or viscoelastic effects are taken into account, whereas static elasticity alone is not sufficient. In this respect, inertial effects as well as viscous damping are identified to be sufficient crack tip selection mechanisms. Exploring the arising description of brittle fracture numerically, we study steady-state crack propagation in the viscoelastic and inertia limit as well as in an intermediate regime, where both effects are important. The arising free boundary problems are solved by phase field methods and a sharp interface approach using a multipole expansion technique. Different types of loading, mode I, mode III fracture, as well as mixtures of them, are discussed.

Effect of solid distribution on elastic properties of open-cell cellular solids using numerical and experimental methods.

PubMed

Zargarian, A; Esfahanian, M; Kadkhodapour, J; Ziaei-Rad, S

2014-09-01

Effect of solid distribution between edges and vertices of three-dimensional cellular solid with an open-cell structure was investigated both numerically and experimentally. Finite element analysis (FEA) with continuum elements and appropriate periodic boundary condition was employed to calculate the elastic properties of cellular solids using tetrakaidecahedral (Kelvin) unit cell. Relative densities between 0.01 and 0.1 and various values of solid fractions were considered. In order to validate the numerical model, three scaffolds with the relative density of 0.08, but different amounts of solid in vertices, were fabricated via 3-D printing technique. Good agreement was observed between numerical simulation and experimental results. Results of numerical simulation showed that, at low relative densities (<0.03), Young׳s modulus increased by shifting materials away from edges to vertices at first and then decreased after reaching a critical point. However, for the high values of relative density, Young׳s modulus increased monotonically. Mechanisms of such a behavior were discussed in detail. Results also indicated that Poisson׳s ratio decreased by increasing relative density and solid fraction in vertices. By fitting a curve to the data obtained from the numerical simulation and considering the relative density and solid fraction in vertices, empirical relations were derived for Young׳s modulus and Poisson׳s ratio. Copyright © 2014 Elsevier Ltd. All rights reserved.

Molecular basis of endosomal-membrane association for the dengue virus envelope protein

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rogers, David M.; Kent, Michael S.; Rempe, Susan B.

Dengue virus is coated by an icosahedral shell of 90 envelope protein dimers that convert to trimers at low pH and promote fusion of its membrane with the membrane of the host endosome. We provide the first estimates for the free energy barrier and minimum for two key steps in this process: host membrane bending and protein–membrane binding. Both are studied using complementary membrane elastic, continuum electrostatics and all-atom molecular dynamics simulations. The predicted host membrane bending required to form an initial fusion stalk presents a 22–30 kcal/mol free energy barrier according to a constrained membrane elastic model. Combined continuummore » and molecular dynamics results predict a 15 kcal/mol free energy decrease on binding of each trimer of dengue envelope protein to a membrane with 30% anionic phosphatidylglycerol lipid. The bending cost depends on the preferred curvature of the lipids composing the host membrane leaflets, while the free energy gained for protein binding depends on the surface charge density of the host membrane. The fusion loop of the envelope protein inserts exactly at the level of the interface between the membrane's hydrophobic and head-group regions. As a result, the methods used in this work provide a means for further characterization of the structures and free energies of protein-assisted membrane fusion.« less

Molecular basis of endosomal-membrane association for the dengue virus envelope protein

DOE PAGES

Rogers, David M.; Kent, Michael S.; Rempe, Susan B.

2015-01-02

Dengue virus is coated by an icosahedral shell of 90 envelope protein dimers that convert to trimers at low pH and promote fusion of its membrane with the membrane of the host endosome. We provide the first estimates for the free energy barrier and minimum for two key steps in this process: host membrane bending and protein–membrane binding. Both are studied using complementary membrane elastic, continuum electrostatics and all-atom molecular dynamics simulations. The predicted host membrane bending required to form an initial fusion stalk presents a 22–30 kcal/mol free energy barrier according to a constrained membrane elastic model. Combined continuummore » and molecular dynamics results predict a 15 kcal/mol free energy decrease on binding of each trimer of dengue envelope protein to a membrane with 30% anionic phosphatidylglycerol lipid. The bending cost depends on the preferred curvature of the lipids composing the host membrane leaflets, while the free energy gained for protein binding depends on the surface charge density of the host membrane. The fusion loop of the envelope protein inserts exactly at the level of the interface between the membrane's hydrophobic and head-group regions. As a result, the methods used in this work provide a means for further characterization of the structures and free energies of protein-assisted membrane fusion.« less

Linking scales in sea ice mechanics

PubMed Central

Weiss, Jérôme; Dansereau, Véronique

2017-01-01

Mechanics plays a key role in the evolution of the sea ice cover through its control on drift, on momentum and thermal energy exchanges between the polar oceans and the atmosphere along cracks and faults, and on ice thickness distribution through opening and ridging processes. At the local scale, a significant variability of the mechanical strength is associated with the microstructural heterogeneity of saline ice, however characterized by a small correlation length, below the ice thickness scale. Conversely, the sea ice mechanical fields (velocity, strain and stress) are characterized by long-ranged (more than 1000 km) and long-lasting (approx. few months) correlations. The associated space and time scaling laws are the signature of the brittle character of sea ice mechanics, with deformation resulting from a multi-scale accumulation of episodic fracturing and faulting events. To translate the short-range-correlated disorder on strength into long-range-correlated mechanical fields, several key ingredients are identified: long-ranged elastic interactions, slow driving conditions, a slow viscous-like relaxation of elastic stresses and a restoring/healing mechanism. These ingredients constrained the development of a new continuum mechanics modelling framework for the sea ice cover, called Maxwell–elasto-brittle. Idealized simulations without advection demonstrate that this rheological framework reproduces the main characteristics of sea ice mechanics, including anisotropy, spatial localization and intermittency, as well as the associated scaling laws. This article is part of the themed issue ‘Microdynamics of ice’. PMID:28025300

Linking scales in sea ice mechanics

NASA Astrophysics Data System (ADS)

Weiss, Jérôme; Dansereau, Véronique

2017-02-01

Mechanics plays a key role in the evolution of the sea ice cover through its control on drift, on momentum and thermal energy exchanges between the polar oceans and the atmosphere along cracks and faults, and on ice thickness distribution through opening and ridging processes. At the local scale, a significant variability of the mechanical strength is associated with the microstructural heterogeneity of saline ice, however characterized by a small correlation length, below the ice thickness scale. Conversely, the sea ice mechanical fields (velocity, strain and stress) are characterized by long-ranged (more than 1000 km) and long-lasting (approx. few months) correlations. The associated space and time scaling laws are the signature of the brittle character of sea ice mechanics, with deformation resulting from a multi-scale accumulation of episodic fracturing and faulting events. To translate the short-range-correlated disorder on strength into long-range-correlated mechanical fields, several key ingredients are identified: long-ranged elastic interactions, slow driving conditions, a slow viscous-like relaxation of elastic stresses and a restoring/healing mechanism. These ingredients constrained the development of a new continuum mechanics modelling framework for the sea ice cover, called Maxwell-elasto-brittle. Idealized simulations without advection demonstrate that this rheological framework reproduces the main characteristics of sea ice mechanics, including anisotropy, spatial localization and intermittency, as well as the associated scaling laws. This article is part of the themed issue 'Microdynamics of ice'.

A CONTINUUM HARD-SPHERE MODEL OF PROTEIN ADSORPTION

PubMed Central

Finch, Craig; Clarke, Thomas; Hickman, James J.

2012-01-01

Protein adsorption plays a significant role in biological phenomena such as cell-surface interactions and the coagulation of blood. Two-dimensional random sequential adsorption (RSA) models are widely used to model the adsorption of proteins on solid surfaces. Continuum equations have been developed so that the results of RSA simulations can be used to predict the kinetics of adsorption. Recently, Brownian dynamics simulations have become popular for modeling protein adsorption. In this work a continuum model was developed to allow the results from a Brownian dynamics simulation to be used as the boundary condition in a computational fluid dynamics (CFD) simulation. Brownian dynamics simulations were used to model the diffusive transport of hard-sphere particles in a liquid and the adsorption of the particles onto a solid surface. The configuration of the adsorbed particles was analyzed to quantify the chemical potential near the surface, which was found to be a function of the distance from the surface and the fractional surface coverage. The near-surface chemical potential was used to derive a continuum model of adsorption that incorporates the results from the Brownian dynamics simulations. The equations of the continuum model were discretized and coupled to a CFD simulation of diffusive transport to the surface. The kinetics of adsorption predicted by the continuum model closely matched the results from the Brownian dynamics simulation. This new model allows the results from mesoscale simulations to be incorporated into micro- or macro-scale CFD transport simulations of protein adsorption in practical devices. PMID:23729843

Progress toward bridging from atomistic to continuum modeling to predict nuclear waste glass dissolution.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zapol, Peter; Bourg, Ian; Criscenti, Louise Jacqueline

2011-10-01

This report summarizes research performed for the Nuclear Energy Advanced Modeling and Simulation (NEAMS) Subcontinuum and Upscaling Task. The work conducted focused on developing a roadmap to include molecular scale, mechanistic information in continuum-scale models of nuclear waste glass dissolution. This information is derived from molecular-scale modeling efforts that are validated through comparison with experimental data. In addition to developing a master plan to incorporate a subcontinuum mechanistic understanding of glass dissolution into continuum models, methods were developed to generate constitutive dissolution rate expressions from quantum calculations, force field models were selected to generate multicomponent glass structures and gel layers,more » classical molecular modeling was used to study diffusion through nanopores analogous to those in the interfacial gel layer, and a micro-continuum model (K{mu}C) was developed to study coupled diffusion and reaction at the glass-gel-solution interface.« less

A dislocation density-based continuum model of the anisotropic shock response of single crystal α-cyclotrimethylene trinitramine

NASA Astrophysics Data System (ADS)

Luscher, D. J.; Addessio, F. L.; Cawkwell, M. J.; Ramos, K. J.

2017-01-01

We have developed a model for the finite deformation thermomechanical response of α-cyclotrimethylene trinitramine (RDX). Our model accounts for nonlinear thermoelastic lattice deformation through a free energy-based equation of state developed by Cawkwell et al. (2016) in combination with temperature and pressure dependent elastic constants, as well as dislocation-mediated plastic slip on a set of slip systems motivated by experimental observation. The kinetics of crystal plasticity are modeled using the Orowan equation relating slip rate to dislocation density and the dislocation velocity developed by Austin and McDowell (2011), which naturally accounts for transition from thermally activated to dislocation drag limited regimes. Evolution of dislocation density is specified in terms of local ordinary differential equations reflecting dislocation-dislocation interactions. This paper presents details of the theory and parameterization of the model, followed by discussion of simulations of flyer plate impact experiments. Impact conditions explored within this combined simulation and experimental effort span shock pressures ranging from 1 to 3 GPa for four crystallographic orientations and multiple specimen thicknesses. Simulation results generated using this model are shown to be in strong agreement with velocimetry measurements from the corresponding plate impact experiments. Finally, simulation results are used to motivate conclusions about the nature of dislocation-mediated plasticity in RDX.

Analysis of an optimization-based atomistic-to-continuum coupling method for point defects

DOE PAGES

Olson, Derek; Shapeev, Alexander V.; Bochev, Pavel B.; ...

2015-11-16

Here, we formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Application of a potential-based atomistic model near the defect core enables accurate simulation of the defect. Away from the core, where site energies become nearly independent of the lattice position, the method switches to a more efficient continuum model. The two models are merged by minimizing the mismatch of their states on an overlap region, subject to the atomistic and continuum force balance equations acting independently in their domains. We prove that the optimization problem is well-posed and establish error estimates.

Continuum model of tensile fracture of metal melts and its application to a problem of high-current electron irradiation of metals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mayer, Alexander E., E-mail: mayer@csu.ru, E-mail: mayer.al.evg@gmail.com; Mayer, Polina N.

2015-07-21

A continuum model of the metal melt fracture is formulated on the basis of the continuum mechanics and theory of metastable liquid. A character of temperature and strain rate dependences of the tensile strength that is predicted by the continuum model is verified, and parameters of the model are fitted with the use of the results of the molecular dynamics simulations for ultra-high strain rates (≥1–10/ns). A comparison with experimental data from literature is also presented for Al and Ni melts. Using the continuum model, the dynamic tensile strength of initially uniform melts of Al, Cu, Ni, Fe, Ti, andmore » Pb within a wide range of strain rates (from 1–10/ms to 100/ns) and temperatures (from melting temperature up to 70–80% of critical temperature) is calculated. The model is applied to numerical investigation of a problem of the high-current electron irradiation of Al, Cu, and Fe targets.« less

Modeling stock price dynamics by continuum percolation system and relevant complex systems analysis

NASA Astrophysics Data System (ADS)

Xiao, Di; Wang, Jun

2012-10-01

The continuum percolation system is developed to model a random stock price process in this work. Recent empirical research has demonstrated various statistical features of stock price changes, the financial model aiming at understanding price fluctuations needs to define a mechanism for the formation of the price, in an attempt to reproduce and explain this set of empirical facts. The continuum percolation model is usually referred to as a random coverage process or a Boolean model, the local interaction or influence among traders is constructed by the continuum percolation, and a cluster of continuum percolation is applied to define the cluster of traders sharing the same opinion about the market. We investigate and analyze the statistical behaviors of normalized returns of the price model by some analysis methods, including power-law tail distribution analysis, chaotic behavior analysis and Zipf analysis. Moreover, we consider the daily returns of Shanghai Stock Exchange Composite Index from January 1997 to July 2011, and the comparisons of return behaviors between the actual data and the simulation data are exhibited.

Numerical simulation of freshwater/seawater interaction in a dual-permeability karst system with conduits: the development of discrete-continuum VDFST-CFP model

NASA Astrophysics Data System (ADS)

Xu, Zexuan; Hu, Bill

2016-04-01

Dual-permeability karst aquifers of porous media and conduit networks with significant different hydrological characteristics are widely distributed in the world. Discrete-continuum numerical models, such as MODFLOW-CFP and CFPv2, have been verified as appropriate approaches to simulate groundwater flow and solute transport in numerical modeling of karst hydrogeology. On the other hand, seawater intrusion associated with fresh groundwater resources contamination has been observed and investigated in numbers of coastal aquifers, especially under conditions of sea level rise. Density-dependent numerical models including SEAWAT are able to quantitatively evaluate the seawater/freshwater interaction processes. A numerical model of variable-density flow and solute transport - conduit flow process (VDFST-CFP) is developed to provide a better description of seawater intrusion and submarine groundwater discharge in a coastal karst aquifer with conduits. The coupling discrete-continuum VDFST-CFP model applies Darcy-Weisbach equation to simulate non-laminar groundwater flow in the conduit system in which is conceptualized and discretized as pipes, while Darcy equation is still used in continuum porous media. Density-dependent groundwater flow and solute transport equations with appropriate density terms in both conduit and porous media systems are derived and numerically solved using standard finite difference method with an implicit iteration procedure. Synthetic horizontal and vertical benchmarks are created to validate the newly developed VDFST-CFP model by comparing with other numerical models such as variable density SEAWAT, couplings of constant density groundwater flow and solute transport MODFLOW/MT3DMS and discrete-continuum CFPv2/UMT3D models. VDFST-CFP model improves the simulation of density dependent seawater/freshwater mixing processes and exchanges between conduit and matrix. Continuum numerical models greatly overestimated the flow rate under turbulent flow condition but discrete-continuum models provide more accurate results. Parameters sensitivities analysis indicates that conduit diameter and friction factor, matrix hydraulic conductivity and porosity are important parameters that significantly affect variable-density flow and solute transport simulation. The pros and cons of model assumptions, conceptual simplifications and numerical techniques in VDFST-CFP are discussed. In general, the development of VDFST-CFP model is an innovation in numerical modeling methodology and could be applied to quantitatively evaluate the seawater/freshwater interaction in coastal karst aquifers. Keywords: Discrete-continuum numerical model; Variable density flow and transport; Coastal karst aquifer; Non-laminar flow

Three-dimensional stress field around a membrane protein: atomistic and coarse-grained simulation analysis of gramicidin A.

PubMed

Yoo, Jejoong; Cui, Qiang

2013-01-08

Using both atomistic and coarse-grained (CG) models, we compute the three-dimensional stress field around a gramicidin A (gA) dimer in lipid bilayers that feature different degrees of negative hydrophobic mismatch. The general trends in the computed stress field are similar at the atomistic and CG levels, supporting the use of the CG model for analyzing the mechanical features of protein/lipid/water interfaces. The calculations reveal that the stress field near the protein-lipid interface exhibits a layered structure with both significant repulsive and attractive regions, with the magnitude of the stress reaching 1000 bar in certain regions. Analysis of density profiles and stress field distributions helps highlight the Trp residues at the protein/membrane/water interface as mechanical anchors, suggesting that similar analysis is useful for identifying tension sensors in other membrane proteins, especially membrane proteins involved in mechanosensation. This work fosters a connection between microscopic and continuum mechanics models for proteins in complex environments and makes it possible to test the validity of assumptions commonly made in continuum mechanics models for membrane mediated processes. For example, using the calculated stress field, we estimate the free energy of membrane deformation induced by the hydrophobic mismatch, and the results for regions beyond the annular lipids are in general consistent with relevant experimental data and previous theoretical estimates using elasticity theory. On the other hand, the assumptions of homogeneous material properties for the membrane and a bilayer thickness at the protein/lipid interface being independent of lipid type (e.g., tail length) appear to be oversimplified, highlighting the importance of annular lipids of membrane proteins. Finally, the stress field analysis makes it clear that the effect of even rather severe hydrophobic mismatch propagates to only about two to three lipid layers, thus putting a limit on the range of cooperativity between membrane proteins in crowded cellular membranes. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Multiscale simulations of PS-SiO2 nanocomposites: from melt to glassy state.

PubMed

Mathioudakis, I G; Vogiatzis, G G; Tzoumanekas, C; Theodorou, D N

2016-09-28

The interaction energetics, molecular packing, entanglement network properties, segmental dynamics, and elastic constants of atactic polystyrene-amorphous silica nanocomposites in the molten and the glassy state are studied via molecular simulations using two interconnected levels of representation: (a) a coarse-grained one, wherein each polystyrene repeat unit is mapped onto a single "superatom" and the silica nanoparticle is viewed as a solid sphere. Equilibration at all length scales at this level is achieved via connectivity-altering Monte Carlo simulations. (b) A united-atom (UA) level, wherein the polymer chains are represented in terms of a united-atom forcefield and the silica nanoparticle is represented in terms of a simplified, fully atomistic model. Initial configurations for UA molecular dynamics (MD) simulations are obtained by reverse mapping well-equilibrated coarse-grained configurations. By analysing microcanonical UA MD trajectories, the polymer density profile is studied and the polymer is found to exhibit layering in the vicinity of the nanoparticle surface. An estimate of the enthalpy of mixing between polymer and nanoparticles, derived from the UA simulations, compares favourably against available experimental values. The dynamical behaviour of polystyrene (in neat and filled melt systems) is characterized in terms of bond orientation and dihedral angle time autocorrelation functions. At low concentration in the molten polymer matrix, silica nanoparticles are found to cause a slight deceleration of the segmental dynamics close to their surface compared to the bulk polymer. Well-equilibrated coarse-grained long-chain configurations are reduced to entanglement networks via topological analysis with the CReTA algorithm, yielding a slightly lower density of entanglements in the filled than in the neat systems. UA melt configurations are glassified by MD cooling. The elastic moduli of the resulting glassy nanocomposites are computed through an analysis of strain fluctuations in the undeformed state and through explicit mechanical deformation by MD, showing a stiffening of the polymer in the presence of nanoparticles. UA simulation results for the elastic constants are compared to continuum micromechanical calculations invoked in homogenization models of the overall mechanical behaviour of heterogeneous materials. They can be interpreted in terms of the presence of an "interphase" of approximate thickness 2 nm around the nanoparticles, with elastic constants intermediate between those of the filler and the matrix.

Translational research: understanding the continuum from bench to bedside.

PubMed

Drolet, Brian C; Lorenzi, Nancy M

2011-01-01

The process of translating basic scientific discoveries to clinical applications, and ultimately to public health improvements, has emerged as an important, but difficult, objective in biomedical research. The process is best described as a "translation continuum" because various resources and actions are involved in this progression of knowledge, which advances discoveries from the bench to the bedside. The current model of this continuum focuses primarily on translational research, which is merely one component of the overall translation process. This approach is ineffective. A revised model to address the entire continuum would provide a methodology to identify and describe all translational activities (eg, implementation, adoption translational research, etc) as well their place within the continuum. This manuscript reviews and synthesizes the literature to provide an overview of the current terminology and model for translation. A modification of the existing model is proposed to create a framework called the Biomedical Research Translation Continuum, which defines the translation process and describes the progression of knowledge from laboratory to health gains. This framework clarifies translation for readers who have not followed the evolving and complicated models currently described. Authors and researchers may use the continuum to understand and describe their research better as well as the translational activities within a conceptual framework. Additionally, the framework may increase the advancement of knowledge by refining discussions of translation and allowing more precise identification of barriers to progress. Copyright © 2011 Mosby, Inc. All rights reserved.

Atomistic to Continuum Multiscale and Multiphysics Simulation of NiTi Shape Memory Alloy

NASA Astrophysics Data System (ADS)

Gur, Sourav

Shape memory alloys (SMAs) are materials that show reversible, thermo-elastic, diffusionless, displacive (solid to solid) phase transformation, due to the application of temperature and/ or stress (/strain). Among different SMAs, NiTi is a popular one. NiTi shows reversible phase transformation, the shape memory effect (SME), where irreversible deformations are recovered upon heating, and superelasticity (SE), where large strains imposed at high enough temperatures are fully recovered. Phase transformation process in NiTi SMA is a very complex process that involves the competition between developed internal strain and phonon dispersion instability. In NiTi SMA, phase transformation occurs over a wide range of temperature and/ or stress (strain) which involves, evolution of different crystalline phases (cubic austenite i.e. B2, different monoclinic variant of martensite i.e. B19', and orthorhombic B19 or BCO structures). Further, it is observed from experimental and computational studies that the evolution kinetics and growth rate of different phases in NiTi SMA vary significantly over a wide spectrum of spatio-temporal scales, especially with length scales. At nano-meter length scale, phase transformation temperatures, critical transformation stress (or strain) and phase fraction evolution change significantly with sample or simulation cell size and grain size. Even, below a critical length scale, the phase transformation process stops. All these aspects make NiTi SMA very interesting to the science and engineering research community and in this context, the present focuses on the following aspects. At first this study address the stability, evolution and growth kinetics of different phases (B2 and variants of B19'), at different length scales, starting from the atomic level and ending at the continuum macroscopic level. The effects of simulation cell size, grain size, and presence of free surface and grain boundary on the phase transformation process (transformation temperature, phase fraction evolution kinetics due to temperature) are also demonstrated herein. Next, to couple and transfer the statistical information of length scale dependent phase transformation process, multiscale/ multiphysics methods are used. Here, the computational difficulty from the fact that the representative governing equations (i.e. different sub-methods such as molecular dynamics simulations, phase field simulations and continuum level constitutive/ material models) are only valid or can be implemented over a range of spatiotemporal scales. Therefore, in the present study, a wavelet based multiscale coupling method is used, where simulation results (phase fraction evolution kinetics) from different sub-methods are linked via concurrent multiscale coupling fashion. Finally, these multiscale/ multiphysics simulation results are used to develop/ modify the macro/ continuum scale thermo-mechanical constitutive relations for NiTi SMA. Finally, the improved material model is used to model new devices, such as thermal diodes and smart dampers.

A Comparison of Coarse-Grained and Continuum Models for Membrane Bending in Lipid Bilayer Fusion Pores

PubMed Central

Yoo, Jejoong; Jackson, Meyer B.; Cui, Qiang

2013-01-01

To establish the validity of continuum mechanics models quantitatively for the analysis of membrane remodeling processes, we compare the shape and energies of the membrane fusion pore predicted by coarse-grained (MARTINI) and continuum mechanics models. The results at these distinct levels of resolution give surprisingly consistent descriptions for the shape of the fusion pore, and the deviation between the continuum and coarse-grained models becomes notable only when the radius of curvature approaches the thickness of a monolayer. Although slow relaxation beyond microseconds is observed in different perturbative simulations, the key structural features (e.g., dimension and shape of the fusion pore near the pore center) are consistent among independent simulations. These observations provide solid support for the use of coarse-grained and continuum models in the analysis of membrane remodeling. The combined coarse-grained and continuum analysis confirms the recent prediction of continuum models that the fusion pore is a metastable structure and that its optimal shape is neither toroidal nor catenoidal. Moreover, our results help reveal a new, to our knowledge, bowing feature in which the bilayers close to the pore axis separate more from one another than those at greater distances from the pore axis; bowing helps reduce the curvature and therefore stabilizes the fusion pore structure. The spread of the bilayer deformations over distances of hundreds of nanometers and the substantial reduction in energy of fusion pore formation provided by this spread indicate that membrane fusion can be enhanced by allowing a larger area of membrane to participate and be deformed. PMID:23442963

Stochastic Ground Water Flow Simulation with a Fracture Zone Continuum Model

USGS Publications Warehouse

Langevin, C.D.

2003-01-01

A method is presented for incorporating the hydraulic effects of vertical fracture zones into two-dimensional cell-based continuum models of ground water flow and particle tracking. High hydraulic conductivity features are used in the model to represent fracture zones. For fracture zones that are not coincident with model rows or columns, an adjustment is required for the hydraulic conductivity value entered into the model cells to compensate for the longer flowpath through the model grid. A similar adjustment is also required for simulated travel times through model cells. A travel time error of less than 8% can occur for particles moving through fractures with certain orientations. The fracture zone continuum model uses stochastically generated fracture zone networks and Monte Carlo analysis to quantify uncertainties with simulated advective travel times. An approach is also presented for converting an equivalent continuum model into a fracture zone continuum model by establishing the contribution of matrix block transmissivity to the bulk transmissivity of the aquifer. The methods are used for a case study in west-central Florida to quantify advective travel times from a potential wetland rehydration site to a municipal supply wellfield. Uncertainties in advective travel times are assumed to result from the presence of vertical fracture zones, commonly observed on aerial photographs as photolineaments.

Electrical and Electron-Phonon Interactions in Graphene-Based Nanostructures and Aptamer-Based Electrical Sensors

NASA Astrophysics Data System (ADS)

Qian, Jun

This research work contains two main parts: the theoretical study of confined phonon modes and electron states in confined graphene nanostructures; the experimental part including two topics about fabricating a graphene-FET aptamer-sensor for cocaine detection and the study of the electronic transport properties of dsDNA. In the theory part, we study the confined optical phonon modes in graphene nanoribbons (GNR) and rectangular graphene quantum dots (RGQD) by the elastic continuum model. The carrier states are studied by effective mass approximation. The phonon bottleneck effect is expected in general for RGQDs. The scattering rates are calculated for specific RGQDs with carefully chosen dimensions to fulfill the momentum and energy conservation conditions. In the experimental part, we have developed a combined technique of semiconductor processes and molecular biological protocols to fabricate a signal-off graphene-FET aptamer-sensor for cocaine. In addition, DNA transport properties were studied by STM on GNP-dsDNA-Au conjugates in atmospheric condition. The dsDNA-complexes exhibit as a slightly n-type semiconductor by simulated with a Landauer-type model. A geometrical model is proposed to explain the distinct I-V spectra.

Nonlocal postbuckling analysis of graphene sheets with initial imperfection based on first order shear deformation theory

NASA Astrophysics Data System (ADS)

Soleimani, Ahmad; Naei, Mohammad Hasan; Mashhadi, Mahmoud Mosavi

In this paper, the first order shear deformation theory (FSDT) is used to investigate the postbuckling behavior of orthotropic single-layered graphene sheet (SLGS) under in-plane loadings. Nonlocal elasticity theory and von-Karman nonlinear model in combination with the isogeometric analysis (IGA) have been applied to study the postbuckling characteristics of SLGSs. In contrast to the classical model, the nonlocal continuum model developed in this work considers the size-effects on the postbuckling characteristics of SLGSs. FSDT takes into account effects of shear deformations through-the-thickness of plate. Geometric imperfection which is defined as a very small transverse displacement of the mid-plane is applied on undeformed nanoplate to create initial deviation in graphene sheet from being perfectly flat. Nonlinear governing equations of motion for SLGS are derived from the principle of virtual work and a variational formulation. At the end, the results are presented as the postbuckling equilibrium paths of SLGS. The influence of various parameters such as edge length, nonlocal parameter, compression ratio, boundary conditions and aspect ratio on the postbuckling path is investigated. The results of this work show the high accuracy of nonlocal FSDT-based analysis for postbuckling behavior of graphene sheets.

Ranges of Applicability for the Continuum-beam Model in the Constitutive Analysis of Carbon Nanotubes: Nanotubes or Nano-beams?

NASA Technical Reports Server (NTRS)

Harik, Vasyl Michael; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

Ranges of validity for the continuum-beam model, the length-scale effects and continuum assumptions are analyzed in the framework of scaling analysis of NT structure. Two coupled criteria for the applicability of the continuum model are presented. Scaling analysis of NT buckling and geometric parameters (e.g., diameter and length) is carried out to determine the key non-dimensional parameters that control the buckling strains and modes of NT buckling. A model applicability map, which represents two classes of NTs, is constructed in the space of non-dimensional parameters. In an analogy with continuum mechanics, a mechanical law of geometric similitude is presented for two classes of beam-like NTs having different geometries. Expressions for the critical buckling loads and strains are tailored for the distinct groups of NTs and compared with the data provided by the molecular dynamics simulations. Implications for molecular dynamics simulations and the NT-based scanning probes are discussed.

Incompressible inelasticity as an essential ingredient for the validity of the kinematic decomposition F =FeFi

NASA Astrophysics Data System (ADS)

Reina, Celia; Conti, Sergio

2017-10-01

The multiplicative decomposition of the total deformation F =FeFi between an elastic (Fe) and an inelastic component (Fi) is standard in the modeling of many irreversible processes such as plasticity, growth, thermoelasticity, viscoelasticty or phase transformations. The heuristic argument for such kinematic assumption is based on the chain rule for the compatible scenario (CurlFi = 0) where the individual deformation tensors are gradients of deformation mappings, i.e. F = D φ = D (φe ∘φi) = (Dφe) ∘φi (Dφi) =FeFi . Yet, the conditions for its validity in the general incompatible case (CurlFi ≠ 0) has so far remained uncertain. We show in this paper that detFi = 1 and CurlFi bounded are necessary and sufficient conditions for the validity of F =FeFi for a wide range of inelastic processes. In particular, in the context of crystal plasticity, we demonstrate via rigorous homogenization from discrete dislocations to the continuum level in two dimensions, that the volume preserving property of the mechanistics of dislocation glide, combined with a finite dislocation density, is sufficient to deliver F =FeFp at the continuum scale. We then generalize this result to general two-dimensional inelastic processes that may be described at a lower dimensional scale via a multiplicative decomposition while exhibiting a finite density of incompatibilities. The necessity of the conditions detFi = 1 and CurlFi bounded for such systems is demonstrated via suitable counterexamples.

Conformation and dynamics of polymer chains on dirty surfaces: A discrete-to-continuum approach

NASA Astrophysics Data System (ADS)

Foo, Grace M.; Pandey, R. B.

1998-07-01

A discrete-to-continuum (DC) simulation approach is introduced to study the statics and dynamics of polymer chains in two dimensions with quenched barriers, a dirty surface. In our DC hybrid approach, the large-scale relaxation of polymer chains on a discrete disordered lattice is followed by off-lattice simulation using a bead-spring chain model with a finitely extensible nonlinear elastic (FENE) potential for covalent bonds and Lennard-Jones (LJ) potential for nonbonded interactions. Segregation/folding of chains, which occurs at low temperatures (T=0.2, 1.0) with LJ interaction, becomes more difficult as the concentration of barriers increases, due to a screening effect of the barriers. In contrast to the chains' contraction at high temperature (i.e., T=5) and their collapse in athermal systems, chains are elongated on increasing the barrier concentration—a barrier-induced stretching. Variations of the root-mean-square (rms) displacements of the center of mass (Rcm) of the chains and their center node (Rcn) with time (t) show power-law behaviors (Rcm˜tν1, Rcn˜tν2) with nonuniversal exponents in the range ν1≃0.40-0.05 and ν2≃0.30-0.05, respectively, depending on temperature and barrier concentration. The radius of gyration (Rg) and the average bond length () expand on increasing the barrier concentration at low temperature and contract at high temperature, which is consistent with the variation of the width of the radial distribution function.

Shock-wave propagation and reflection in semicrystalline polyethylene: A molecular-level investigation

NASA Astrophysics Data System (ADS)

Elder, Robert M.; O'Connor, Thomas C.; Chantawansri, Tanya L.; Sliozberg, Yelena R.; Sirk, Timothy W.; Yeh, In-Chul; Robbins, Mark O.; Andzelm, Jan W.

2017-09-01

Semicrystalline polyethylene (PE) is attractive for a variety of mechanically demanding applications, where shock compression can occur. Although often highly crystalline, PE invariably contains nanoscale amorphous domains that influence shock propagation. Our objective in this work is to study the effects of such domains. To this end, we adopt a novel approach wherein we parametrize a simple continuum-level theory based on the shock impedance from molecular dynamics (MD) simulations. Using this theory, we predict how crystalline/amorphous interfaces attenuate shocks via energy reflection due to the impedance mismatch between the phases. The theory predicts that these interfaces attenuate weak shocks more effectively than strong shocks. We compare the theory to explicit nonequilibrium MD simulations of compressive shocks in semicrystalline PE containing nanometer-scale amorphous regions of varying size, where we analyze the pressure response and reflection of energy. The theory and simulations show good agreement for strong shocks (≥1.0 km /s ), but for weak shocks (<1.0 km /s ) the simulations show enhanced energy reflection relative to the continuum predictions. Furthermore, the simulations show an effect not captured by the continuum theory: the size of amorphous regions is important. The theory assumes a sharp (discontinuous) interface between two bulk phases and a sharp change in thermodynamic and hydrodynamic quantities at the shock front. However, the simulations show that when amorphous domains are narrow—with widths comparable to the shock front—reflection is reduced compared to the predictions. We identify several nanoscale mechanisms that reduce the impedance mismatch, and thus reduce reflection, at thin amorphous domains. First, the two-wave elastic-plastic structure of shocks in crystalline PE allows the faster-moving elastic precursor wave to compress small amorphous domains before the plastic wave arrives. Second, confinement between stiff, ordered crystalline domains increases the stiffness and chain ordering in small amorphous regions. Moreover, in terms of stiffness the interfaces are similar in width to the shock front, which may contribute to the underprediction of the theory for weak shocks, where the shock front is widest. We conclude by discussing the significance of these results, namely, how they can be applied to tune shock attenuation for particular applications.

Damage, Self-Healing, and Hysteresis in Spider Silks

PubMed Central

De Tommasi, D.; Puglisi, G.; Saccomandi, G.

2010-01-01

Abstract In this article, we propose a microstructure-based continuum model to describe the material behavior of spider silks. We suppose that the material is composed of a soft fraction with entropic elasticity and a hard, damageable fraction. The hard fraction models the presence of stiffer, crystal-rich, oriented regions and accounts for the effect of softening induced by the breaking of hydrogen bonds. To describe the observed presence of crystals with different size, composition, and orientation, this hard fraction is modeled as a distribution of materials with variable properties. The soft fraction describes the remaining regions of amorphous material and is here modeled as a wormlike chain. During stretching, we consider the effect of bond-breaking as a transition from the hard- to the soft-material phase. As we demonstrate, a crucial effect of bond-breaking that accompanies the softening of the material is an increase in contour length associated with chains unraveling. The model describes also the self-healing properties of the material by assuming partial bond reconnection upon unloading. Despite its simplicity, the proposed mechanical system reproduces the main experimental effects observed in cyclic loading of spider silks. Moreover, our approach is amenable to two- or three-dimensional extensions and may prove to be a useful tool in the field of microstructure optimization for bioinspired materials. PMID:20441758

Multi-scale Multi-mechanism Toughening of Hydrogels

NASA Astrophysics Data System (ADS)

Zhao, Xuanhe

Hydrogels are widely used as scaffolds for tissue engineering, vehicles for drug delivery, actuators for optics and fluidics, and model extracellular matrices for biological studies. The scope of hydrogel applications, however, is often severely limited by their mechanical properties. Inspired by the mechanics and hierarchical structures of tough biological tissues, we propose that a general principle for the design of tough hydrogels is to implement two mechanisms for dissipating mechanical energy and maintaining high elasticity in hydrogels. A particularly promising strategy for the design is to integrate multiple pairs of mechanisms across multiple length scales into a hydrogel. We develop a multiscale theoretical framework to quantitatively guide the design of tough hydrogels. On the network level, we have developed micro-physical models to characterize the evolution of polymer networks under deformation. On the continuum level, we have implemented constitutive laws formulated from the network-level models into a coupled cohesive-zone and Mullins-effect model to quantitatively predict crack propagation and fracture toughness of hydrogels. Guided by the design principle and quantitative model, we will demonstrate a set of new hydrogels, based on diverse types of polymers, yet can achieve extremely high toughness superior to their natural counterparts such as cartilages. The work was supported by NSF(No. CMMI- 1253495) and ONR (No. N00014-14-1-0528).

NiTi Alloy Negator Springs for Long-Stroke Constant-Force Shape Memory Actuators: Modeling, Simulation and Testing

NASA Astrophysics Data System (ADS)

Spaggiari, Andrea; Dragoni, Eugenio; Tuissi, Ausonio

2014-07-01

This work aims at the experimental characterization and modeling validation of shape memory alloy (SMA) Negator springs. According to the classic engineering books on springs, a Negator spring is a spiral spring made of strip of metal wound on the flat with an inherent curvature such that, in repose, each coil wraps tightly on its inner neighbor. The main feature of a Negator springs is the nearly constant force displacement behavior in the unwinding of the strip. Moreover the stroke is very long, theoretically infinite, as it depends only on the length of the initial strip. A Negator spring made in SMA is built and experimentally tested to demonstrate the feasibility of this actuator. The shape memory Negator spring behavior can be modeled with an analytical procedure, which is in good agreement with the experimental test and can be used for design purposes. In both cases, the material is modeled as elastic in austenitic range, while an exponential continuum law is used to describe the martensitic behavior. The experimental results confirms the applicability of this kind of geometry to the shape memory alloy actuators, and the analytical model is confirmed to be a powerful design tool to dimension and predict the spring behavior both in martensitic and austenitic range.

Glacier crevasses: Observations, models, and mass balance implications

NASA Astrophysics Data System (ADS)

Colgan, William; Rajaram, Harihar; Abdalati, Waleed; McCutchan, Cheryl; Mottram, Ruth; Moussavi, Mahsa S.; Grigsby, Shane

2016-03-01

We review the findings of approximately 60 years of in situ and remote sensing studies of glacier crevasses, as well as the three broad classes of numerical models now employed to simulate crevasse fracture. The relatively new insight that mixed-mode fracture in local stress equilibrium, rather than downstream advection alone, can introduce nontrivial curvature to crevasse geometry may merit the reinterpretation of some key historical observation studies. In the past three decades, there have been tremendous advances in the spatial resolution of satellite imagery, as well as fully automated algorithms capable of tracking crevasse displacements between repeat images. Despite considerable advances in developing fully transient three-dimensional ice flow models over the past two decades, both the zero stress and linear elastic fracture mechanics crevasse models have remained fundamentally unchanged over this time. In the past decade, however, multidimensional and transient formulations of the continuum damage mechanics approach to simulating ice fracture have emerged. The combination of employing damage mechanics to represent slow upstream deterioration of ice strength and fracture mechanics to represent rapid failure at downstream termini holds promise for implementation in large-scale ice sheet models. Finally, given the broad interest in the sea level rise implications of recent and future cryospheric change, we provide a synthesis of 10 mechanisms by which crevasses can influence glacier mass balance.

Thermal-mechanical-chemical responses of polymer-bonded explosives using a mesoscopic reactive model under impact loading.

PubMed

Wang, XinJie; Wu, YanQing; Huang, FengLei

2017-01-05

A mesoscopic framework is developed to quantify the thermal-mechanical-chemical responses of polymer-bonded explosive (PBX) samples under impact loading. A mesoscopic reactive model is developed for the cyclotetramethylenetetranitramine (HMX) crystal, which incorporates nonlinear elasticity, crystal plasticity, and temperature-dependent chemical reaction. The proposed model was implemented in the finite element code ABAQUS by the user subroutine VUMAT. A series of three-dimensional mesoscale models were constructed and calculated under low-strength impact loading scenarios from 100m/s to 600m/s where only the first wave transit is studied. Crystal anisotropy and microstructural heterogeneity are responsible for the nonuniform stress field and fluctuations of the stress wave front. At a critical impact velocity (≥300m/s), a chemical reaction is triggered because the temperature contributed by the volumetric and plastic works is sufficiently high. Physical quantities, including stress, temperature, and extent of reaction, are homogenized from those across the microstructure at the mesoscale to compare with macroscale measurements, which will advance the continuum-level models. The framework presented in this study has important implications in understanding hot spot ignition processes and improving predictive capabilities in energetic materials. Copyright © 2016 Elsevier B.V. All rights reserved.

A Micro-Mechanism-Based Continuum Corrosion Fatigue Damage Model for Steels

NASA Astrophysics Data System (ADS)

Sun, Bin; Li, Zhaoxia

2018-05-01

A micro-mechanism-based corrosion fatigue damage model is developed for studying the high-cycle corrosion fatigue of steel from multi-scale viewpoint. The developed physical corrosion fatigue damage model establishes micro-macro relationships between macroscopic continuum damage evolution and collective evolution behavior of microscopic pits and cracks, which can be used to describe the multi-scale corrosion fatigue process of steel. As a case study, the model is used to predict continuum damage evolution and number density of the corrosion pit and short crack of steel component in 5% NaCl water under constant stress amplitude at 20 kHz, and the numerical results are compared with experimental results. It shows that the model is effective and can be used to evaluate the continuum macroscopic corrosion fatigue damage and study microscopic corrosion fatigue mechanisms of steel.

A Micro-Mechanism-Based Continuum Corrosion Fatigue Damage Model for Steels

NASA Astrophysics Data System (ADS)

Sun, Bin; Li, Zhaoxia

2018-04-01

A micro-mechanism-based corrosion fatigue damage model is developed for studying the high-cycle corrosion fatigue of steel from multi-scale viewpoint. The developed physical corrosion fatigue damage model establishes micro-macro relationships between macroscopic continuum damage evolution and collective evolution behavior of microscopic pits and cracks, which can be used to describe the multi-scale corrosion fatigue process of steel. As a case study, the model is used to predict continuum damage evolution and number density of the corrosion pit and short crack of steel component in 5% NaCl water under constant stress amplitude at 20 kHz, and the numerical results are compared with experimental results. It shows that the model is effective and can be used to evaluate the continuum macroscopic corrosion fatigue damage and study microscopic corrosion fatigue mechanisms of steel.

Micropolar continuum modelling of bi-dimensional tetrachiral lattices

PubMed Central

Chen, Y.; Liu, X. N.; Hu, G. K.; Sun, Q. P.; Zheng, Q. S.

2014-01-01

The in-plane behaviour of tetrachiral lattices should be characterized by bi-dimensional orthotropic material owing to the existence of two orthogonal axes of rotational symmetry. Moreover, the constitutive model must also represent the chirality inherent in the lattices. To this end, a bi-dimensional orthotropic chiral micropolar model is developed based on the theory of irreducible orthogonal tensor decomposition. The obtained constitutive tensors display a hierarchy structure depending on the symmetry of the underlying microstructure. Eight additional material constants, in addition to five for the hemitropic case, are introduced to characterize the anisotropy under Z2 invariance. The developed continuum model is then applied to a tetrachiral lattice, and the material constants of the continuum model are analytically derived by a homogenization process. By comparing with numerical simulations for the discrete lattice, it is found that the proposed continuum model can correctly characterize the static and wave properties of the tetrachiral lattice. PMID:24808754

Dynamical discrete/continuum linear response shells theory of solvation: convergence test for NH4+ and OH- ions in water solution using DFT and DFTB methods.

PubMed

de Lima, Guilherme Ferreira; Duarte, Hélio Anderson; Pliego, Josefredo R

2010-12-09

A new dynamical discrete/continuum solvation model was tested for NH(4)(+) and OH(-) ions in water solvent. The method is similar to continuum solvation models in a sense that the linear response approximation is used. However, different from pure continuum models, explicit solvent molecules are included in the inner shell, which allows adequate treatment of specific solute-solvent interactions present in the first solvation shell, the main drawback of continuum models. Molecular dynamics calculations coupled with SCC-DFTB method are used to generate the configurations of the solute in a box with 64 water molecules, while the interaction energies are calculated at the DFT level. We have tested the convergence of the method using a variable number of explicit water molecules and it was found that even a small number of waters (as low as 14) are able to produce converged values. Our results also point out that the Born model, often used for long-range correction, is not reliable and our method should be applied for more accurate calculations.

Mathematics for understanding disease.

PubMed

Bies, R R; Gastonguay, M R; Schwartz, S L

2008-06-01

The application of mathematical models to reflect the organization and activity of biological systems can be viewed as a continuum of purpose. The far left of the continuum is solely the prediction of biological parameter values, wherein an understanding of the underlying biological processes is irrelevant to the purpose. At the far right of the continuum are mathematical models, the purposes of which are a precise understanding of those biological processes. No models in present use fall at either end of the continuum. Without question, however, the emphasis in regards to purpose has been on prediction, e.g., clinical trial simulation and empirical disease progression modeling. Clearly the model that ultimately incorporates a universal understanding of biological organization will also precisely predict biological events, giving the continuum the logical form of a tautology. Currently that goal lies at an immeasurable distance. Nonetheless, the motive here is to urge movement in the direction of that goal. The distance traveled toward understanding naturally depends upon the nature of the scientific question posed with respect to comprehending and/or predicting a particular disease process. A move toward mathematical models implies a move away from static empirical modeling and toward models that focus on systems biology, wherein modeling entails the systematic study of the complex pattern of organization inherent in biological systems.

Moving Contact Lines: Linking Molecular Dynamics and Continuum-Scale Modeling.

PubMed

Smith, Edward R; Theodorakis, Panagiotis E; Craster, Richard V; Matar, Omar K

2018-05-17

Despite decades of research, the modeling of moving contact lines has remained a formidable challenge in fluid dynamics whose resolution will impact numerous industrial, biological, and daily life applications. On the one hand, molecular dynamics (MD) simulation has the ability to provide unique insight into the microscopic details that determine the dynamic behavior of the contact line, which is not possible with either continuum-scale simulations or experiments. On the other hand, continuum-based models provide a link to the macroscopic description of the system. In this Feature Article, we explore the complex range of physical factors, including the presence of surfactants, which governs the contact line motion through MD simulations. We also discuss links between continuum- and molecular-scale modeling and highlight the opportunities for future developments in this area.

Solar radio continuum storms and a breathing magnetic field model

NASA Technical Reports Server (NTRS)

1975-01-01

Radio noise continuum emissions observed in metric and decametric wave frequencies are, in general, associated with actively varying sunspot groups accompanied by the S-component of microwave radio emissions. These continuum emission sources, often called type I storm sources, are often associated with type III burst storm activity from metric to hectometric wave frequencies. This storm activity is, therefore, closely connected with the development of these continuum emission sources. It is shown that the S-component emission in microwave frequencies generally precedes, by several days, the emission of these noise continuum storms of lower frequencies. In order for these storms to develop, the growth of sunspot groups into complex types is very important in addition to the increase of the average magnetic field intensity and area of these groups. After giving a review on the theory of these noise continuum storm emissions, a model is briefly considered to explain the relation of the emissions to the storms.

Ensuring congruency in multiscale modeling: towards linking agent based and continuum biomechanical models of arterial adaptation.

PubMed

Hayenga, Heather N; Thorne, Bryan C; Peirce, Shayn M; Humphrey, Jay D

2011-11-01

There is a need to develop multiscale models of vascular adaptations to understand tissue-level manifestations of cellular level mechanisms. Continuum-based biomechanical models are well suited for relating blood pressures and flows to stress-mediated changes in geometry and properties, but less so for describing underlying mechanobiological processes. Discrete stochastic agent-based models are well suited for representing biological processes at a cellular level, but not for describing tissue-level mechanical changes. We present here a conceptually new approach to facilitate the coupling of continuum and agent-based models. Because of ubiquitous limitations in both the tissue- and cell-level data from which one derives constitutive relations for continuum models and rule-sets for agent-based models, we suggest that model verification should enforce congruency across scales. That is, multiscale model parameters initially determined from data sets representing different scales should be refined, when possible, to ensure that common outputs are consistent. Potential advantages of this approach are illustrated by comparing simulated aortic responses to a sustained increase in blood pressure predicted by continuum and agent-based models both before and after instituting a genetic algorithm to refine 16 objectively bounded model parameters. We show that congruency-based parameter refinement not only yielded increased consistency across scales, it also yielded predictions that are closer to in vivo observations.

Models of collective cell spreading with variable cell aspect ratio: a motivation for degenerate diffusion models.

PubMed

Simpson, Matthew J; Baker, Ruth E; McCue, Scott W

2011-02-01

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multiscale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (PME). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the PME to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

Mirrored continuum and molecular scale simulations of the ignition of gamma phase RDX

NASA Astrophysics Data System (ADS)

Stewart, D. Scott; Chaudhuri, Santanu; Joshi, Kaushik; Lee, Kibaek

2017-01-01

We describe the ignition of an explosive crystal of gamma-phase RDX due to a thermal hot spot with reactive molecular dynamics (RMD), with first-principles trained, reactive force field based molecular potentials that represents an extremely complex reaction network. The RMD simulation is analyzed by sorting molecular product fragments into high and low molecular weight groups, to represent identifiable components that can be interpreted by a continuum model. A continuum model based on a Gibbs formulation has a single temperature and stress state for the mixture. The continuum simulation that mirrors the atomistic simulation allows us to study the atomistic simulation in the familiar physical chemistry framework and provides an essential, continuum/atomistic link.

Reply to "Comment on 'Hydrodynamics of fractal continuum flow' and 'Map of fluid flow in fractal porous medium into fractal continuum flow'".

PubMed

Balankin, Alexander S; Elizarraraz, Benjamin Espinoza

2013-11-01

The aim of this Reply is to elucidate the difference between the fractal continuum models used in the preceding Comment and the models of fractal continuum flow which were put forward in our previous articles [Phys. Rev. E 85, 025302(R) (2012); 85, 056314 (2012)]. In this way, some drawbacks of the former models are highlighted. Specifically, inconsistencies in the definitions of the fractal derivative, the Jacobian of transformation, the displacement vector, and angular momentum are revealed. The proper forms of the Reynolds' transport theorem and angular momentum principle for the fractal continuum are reaffirmed in a more illustrative manner. Consequently, we emphasize that in the absence of any internal angular momentum, body couples, and couple stresses, the Cauchy stress tensor in the fractal continuum should be symmetric. Furthermore, we stress that the approach based on the Cartesian product measured and used in the preceding Comment cannot be employed to study the path-connected fractals, such as a flow in a fractally permeable medium. Thus, all statements of our previous works remain unchallenged.

Time-Resolved Properties and Global Trends in dMe Flares from Simultaneous Photometry and Spectra

NASA Astrophysics Data System (ADS)

Kowalski, Adam F.

We present a homogeneous survey of near-ultraviolet (NUV) /optical line and continuum emission during twenty M dwarf flares with simultaneous, high cadence photometry and spectra. These data were obtained to study the white-light continuum components to the blue and red of the Balmer jump to break the degeneracy with fitting emission mechanisms to broadband colors and to provide constraints for radiative-hydrodynamic flare models that seek to reproduce the white-light flare emission. The main results from the continuum analysis are the following: 1) the detection of Balmer continuum (in emission) that is present during all flares, with a wide range of relative contribution to the continuum flux in the NUV; 2) a blue continuum at the peak of the photometry that is linear with wavelength from λ = 4000 - 4800Å, matched by the spectral shape of hot, blackbody emission with typical temperatures of 10 000 - 12 000 K; 3) a redder continuum apparent at wavelengths longer than Hβ; this continuum becomes relatively more important to the energy budget during the late gradual phase. The hot blackbody component and redder continuum component (which we call "the conundruum") have been detected in previous UBVR colorimetry studies of flares. With spectra, one can compare the properties and detailed timings of all three components. Using time-resolved spectra during the rise phase of three flares, we calculate the speed of an expanding flare region assuming a simple geometry; the speeds are found to be ~5- 10 km s-1 and 50 - 120 km s -1, which are strikingly consistent with the speeds at which two-ribbon flares develop on the Sun. The main results from the emission line analysis are 1) the presentation of the "time-decrement", a relation between the timescales of the Balmer series; 2) a Neupert-like relation between Ca \\pcy K and the blackbody continuum, and 3) the detection of absorption wings in the Hydrogen Balmer lines during times of peak continuum emission, indicative of hot-star spectra forming during the flare. A byproduct of this study is a new method for deriving absolute fluxes during M dwarf flare observations obtained from narrow-slit spectra or during variable weather conditions. This technique allows us to analyze the spectra and photometry independently of one another, in order to connect the spectral properties to the rise, peak, and decay phases of broadband light curve morphology. We classify the light curve morphology according to an "impulsiveness index" and find that the fast (impulsive) flares have less Balmer continuum at peak emission than the slow (gradual) flares. In the gradual phase, the energy budget of the flare spectrum during almost all flares has a larger contribution from the Hydrogen Balmer component than in the impulsive phase, suggesting that the heating and cooling processes evolve over the course of a flare. We find that, in general, the evolution of the hot blackbody is rapid, and that the blackbody temperature decreases to ~8000 K in the gradual phase. The Balmer continuum evolves more slowly than the blackbody ¨C similar to the higher order Balmer lines but faster than the lower order Balmer lines. The height of the Balmer jump increases during the gradual decay phase. We model the Balmer continuum emission using the RHD F11 model spectrum from Allred et al. (2006), but we discuss several important systematic uncertainties in relating the apparent amount of Balmer continuum to a given RHD beam model. Good fits to the shape of the RHD F11 model spectrum are not obtained at peak times, in contrast to the gradual phase. We model the blackbody component using model hot star atmospheres from Castelli & Kurucz (2004) in order to account for the effects of flux redistribution in the flare atmosphere. This modeling is motivated by observations during a secondary flare in the decay phase of a megaflare, when the newly formed flare spectrum resembled that of Vega with the Balmer continuum and lines in absorption. We model this continuum phenomenologically with the RH code using hot spots placed at high column mass in the M dwarf quiescent atmosphere; a superposition of hot spot models and the RHD model are used to explain the anti-correlation in the apparent amount of Balmer continuum in emission and the U-band light curve. We attempt to reproduce the blackbody component in self-consistent 1D radiative hydrodynamic flare models using the RADYN code. We simulate the flare using a solar-type nonthermal electron beam heating function with a total energy flux of 1012 ergs cm-2 s-1 (F12) for a duration of 5 seconds and a subsequent gradual phase. Although there is a larger amount of NUV backwarming at log mc/(1g cm-2)~0 than in the F11 model, the resulting flare continuum shape is similar to the F11 model spectrum with a larger Balmer jump and a much redder spectral shape than is seen in the observations. We do not find evidence of white-light emitting chromospheric condensations, in contrast to the previous F12 model of Livshits et al. (1981). We discuss future avenues for RHD modeling in order to produce a hot blackbody component, including the treatment of nonthermal protons in M dwarf flares.

A micro-macro constitutive model for finite-deformation viscoelasticity of elastomers with nonlinear viscosity

NASA Astrophysics Data System (ADS)

Zhou, Jianyou; Jiang, Liying; Khayat, Roger E.

2018-01-01

Elastomers are known to exhibit viscoelastic behavior under deformation, which is linked to the diffusion processes of the highly mobile and flexible polymer chains. Inspired by the theories of polymer dynamics, a micro-macro constitutive model is developed to study the viscoelastic behaviors and the relaxation process of elastomeric materials under large deformation, in which the material parameters all have a microscopic foundation or a microstructural justification. The proposed model incorporates the nonlinear material viscosity into the continuum finite-deformation viscoelasticity theories which represent the polymer networks of elastomers with an elastic ground network and a few viscous subnetworks. The developed modeling framework is capable of adopting most of strain energy density functions for hyperelastic materials and thermodynamics evolution laws of viscoelastic solids. The modeling capacity of the framework is outlined by comparing the simulation results with the experimental data of three commonly used elastomeric materials, namely, VHB4910, HNBR50 and carbon black (CB) filled elastomers. The comparison shows that the stress responses and some typical behaviors of filled and unfilled elastomers can be quantitatively predicted by the model with suitable strain energy density functions. Particularly, the strain-softening effect of elastomers could be explained by the deformation-dependent (nonlinear) viscosity of the polymer chains. The presented modeling framework is expected to be useful as a modeling platform for further study on the performance of different type of elastomeric materials.

THE BINARY BLACK HOLE MODEL FOR MRK 231 BITES THE DUST

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leighly, Karen M.; Terndrup, Donald M.; Gallagher, Sarah C.

2016-09-20

Mrk 231 is a nearby quasar with an unusually red near-UV-to-optical continuum, generally explained as heavy reddening by dust. Yan et al. proposed that Mrk 231 is a milliparsec black hole binary with little intrinsic reddening. We show that if the observed FUV continuum is intrinsic, as assumed by Yan et al., it fails by a factor of about 100 in powering the observed strength of the near-infrared emission lines and the thermal near and mid-infrared continuum. In contrast, the line and continuum strengths are typical for a reddened AGN spectral energy distribution (SED). We find that the He i*/Pmore » β ratio is sensitive to the SED for a one-zone model. If this sensitivity is maintained in general broadline region models, then this ratio may prove a useful diagnostic for heavily reddened quasars. Analysis of archival Hubble Space Telescope STIS and Faint Object Camera data revealed evidence that the far-UV continuum emission is resolved on size scales of ∼40 pc. The lack of broad absorption lines in the far-UV continuum might be explained if it were not coincident with the central engine. One possibility is that it is the central engine continuum reflected from the receding wind on the far side of the quasar.« less

Theory of rheology

NASA Technical Reports Server (NTRS)

Hutton, J. F.

1973-01-01

The structure of the modern theory of rheology is discussed to show the assumptions and limitations. Rheology is discussed as a branch of continuum mechanics to determine the relationships between stress, strain, and strain rate which will give a closer representation of lubricant properties than the Newtonian flow equation. Rheology is also investigated as a branch of chemical physics. Consideration is limited to those theories of nonpolymeric and polymeric fluids which can represent viscoelasticity in terms of identifiable and measureable molecular characteristics. The possibility that elastic liquids may rupture in shear and linear tension analogous to the failure of solids is proposed.

Hamiltonian approach to continuum dynamics

NASA Astrophysics Data System (ADS)

Isaev, A. A.; Kovalevskii, M. Yu.; Peletminskii, S. V.

1995-02-01

A study is made of the problem of obtaining the Poisson-bracket algebra of the dynamical variables of continuous media on the basis of specification of the kinematic part of the Lagrangian in terms of generalized coordinates and momenta. Within this algebra, subalgebras of variables corresponding to the description of elastic media, the hydrodynamics of ordinary liquids, and the dynamics of some phases of liquid crystals are identified. The differential conservation laws associated with the symmetries of the Hamiltonian of the system are studied. The dynamics of nematics is considered, and features of the dynamics of the cholesteric, smectic, and discotic phases are noted.

Sub transitional and supersonic travelling field response in nonlinear viscoelastic media

NASA Technical Reports Server (NTRS)

Padovan, Joe

1989-01-01

This paper considers the problem of traveling fields in nonlinearly elastic and viscoelastic media. By introducing the appropriate hierarchical partitioning, the governing equations of motion are shown to be a continuum analogy of Duffing's equation. Through the use of a constrained perturbation procedure, the response behavior is obtained in sub, transitional as well as supersonic ranges of disturbance speed. Due to the generality of the approach taken, the effects of damping can be handled. To quantify the effects of material nonlinearity, strain softening and hardening are considered. Such behavior is quantified in general example problems.

Multiscale volatility duration characteristics on financial multi-continuum percolation dynamics

NASA Astrophysics Data System (ADS)

Wang, Min; Wang, Jun

A random stock price model based on the multi-continuum percolation system is developed to investigate the nonlinear dynamics of stock price volatility duration, in an attempt to explain various statistical facts found in financial data, and have a deeper understanding of mechanisms in the financial market. The continuum percolation system is usually referred to be a random coverage process or a Boolean model, it is a member of a class of statistical physics systems. In this paper, the multi-continuum percolation (with different values of radius) is employed to model and reproduce the dispersal of information among the investors. To testify the rationality of the proposed model, the nonlinear analyses of return volatility duration series are preformed by multifractal detrending moving average analysis and Zipf analysis. The comparison empirical results indicate the similar nonlinear behaviors for the proposed model and the actual Chinese stock market.

Unified description of ^{6}Li structure and deuterium-^{4}He dynamics with chiral two- and three-nucleon forces.

PubMed

Hupin, Guillaume; Quaglioni, Sofia; Navrátil, Petr

2015-05-29

We provide a unified ab initio description of the ^{6}Li ground state and elastic scattering of deuterium (d) on ^{4}He (α) using two- and three-nucleon forces from chiral effective field theory. We analyze the influence of the three-nucleon force and reveal the role of continuum degrees of freedom in shaping the low-lying spectrum of ^{6}Li. The calculation reproduces the empirical binding energy of ^{6}Li, yielding an asymptotic D- to S-state ratio of the ^{6}Li wave function in the d+α configuration of -0.027, in agreement with a determination from ^{6}Li-^{4}He elastic scattering, but overestimates the excitation energy of the 3^{+} state by 350 keV. The bulk of the computed differential cross section is in good agreement with data. These results endorse the application of the present approach to the evaluation of the ^{2}H(α,γ)^{6}Li radiative capture, responsible for the big-bang nucleosynthesis of ^{6}Li.

Deformation of a flexible disk bonded to an elastic half space-application to the lung.

PubMed

Lai-Fook, S J; Hajji, M A; Wilson, T A

1980-08-01

An analysis is presented of the deformation of a homogeneous, isotropic, elastic half space subjected to a constant radial strain in a circular area on the boundary. Explicit analytic expressions for the normal and radial displacements and the shear stress on the boundary are used to interpret experiments performed on inflated pig lungs. The boundary strain was induced by inflating or deflating the lung after bonding a flexible disk to the lung surface. The prediction that the surface bulges outward for positive boundary strain and inward for negative strain was observed in the experiments. Poisson's ratio at two transpulmonary pressures was measured, by use of the normal displacement equation evaluated at the surface. A direct estimate of Poisson's ratio was possible because the normal displacement of the surface depended uniquely on the compressibility of the material. Qualitative comparisons between theory and experiment support the use of continuum analyses in evaluating the behavior of the lung parenchyma when subjected to small local distortions.

Improvements in continuum modeling for biomolecular systems

NASA Astrophysics Data System (ADS)

Yu, Qiao; Ben-Zhuo, Lu

2016-01-01

Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson- Boltzmann (PB)/Poisson-Nernst-Planck (PNP) equations has made great contributions towards simulation of these processes. However, the model has shortcomings in its commonly used form and cannot capture (or cannot accurately capture) some important physical properties of the biological systems. Considerable efforts have been made to improve the continuum model to account for discrete particle interactions and to make progress in numerical methods to provide accurate and efficient simulations. This review will summarize recent main improvements in continuum modeling for biomolecular systems, with focus on the size-modified models, the coupling of the classical density functional theory and the PNP equations, the coupling of polar and nonpolar interactions, and numerical progress. Project supported by the National Natural Science Foundation of China (Grant No. 91230106) and the Chinese Academy of Sciences Program for Cross & Cooperative Team of the Science & Technology Innovation.

Extension of the ratio method to low energy

DOE PAGES

Colomer, Frederic; Capel, Pierre; Nunes, F. M.; ...

2016-05-25

The ratio method has been proposed as a means to remove the reaction model dependence in the study of halo nuclei. Originally, it was developed for higher energies but given the potential interest in applying the method at lower energy, in this work we explore its validity at 20 MeV/nucleon. The ratio method takes the ratio of the breakup angular distribution and the summed angular distribution (which includes elastic, inelastic and breakup) and uses this observable to constrain the features of the original halo wave function. In this work we use the Continuum Discretized Coupled Channel method and the Coulomb-correctedmore » Dynamical Eikonal Approximation for the study. We study the reactions of 11Be on 12C, 40Ca and 208Pb at 20 MeV/nucleon. We compare the various theoretical descriptions and explore the dependence of our result on the core-target interaction. Lastly, our study demonstrates that the ratio method is valid at these lower beam energies.« less

Liquid droplets of cross-linked actin filaments

NASA Astrophysics Data System (ADS)

Weirich, Kimberly; Banerjee, Shiladitya; Dasbiswas, Kinjal; Vaikuntanathan, Suriyanarayan; Gardel, Margaret

Soft materials constructed from biomolecules self-assemble into a myriad of structures that work in concert to support cell physiology. One critical soft material is the actin cytoskeleton, a viscoelastic gel composed of cross-linked actin filaments. Although actin networks are primarily known for their elastic properties, which are crucial to regulating cell mechanics, the viscous behavior has been theorized to enable shape changes and flows. We experimentally demonstrate a fluid phase of cross-linked actin, where cross-linker condenses dilute short actin filaments into spindle-shaped droplets, or tactoids. Tactoids have shape dynamics consistent with a continuum model of liquid crystal droplets. The cross-linker, which acts as a long range attractive interaction, analogous to molecular cohesion, controls the tactoid shape and dynamics, which reports on the liquid's interfacial tension and viscosity. We investigate how the cross-linker properties and filament length influence the liquid properties. These results demonstrate a novel mechanism to control organization of the actin cytoskeleton and provide insight into design principles for complex, macromolecular liquid phases.

Interrelated structures of the transport shock and collisional relaxation layer in a multitemperature, multilevel ionized gas

NASA Technical Reports Server (NTRS)

Vinolo, A. R.; Clarke, J. H.

1973-01-01

The gas dynamic structures of the transport shock and the downstream collisional relaxation layer are evaluated for partially ionized monatomic gases. Elastic and inelastic collisional nonequilibrium effects are taken into consideration. In the microscopic model of the atom, three electronic levels are accounted for. By using an asymptotic technique, the shock morphology is found on a continuum flow basis. This procedure gives two distinct layers in which the nonequilibrium effects to be considered are different. A transport shock appears as the inner solution to an outer collisional relaxation layer. The results show four main interesting points: (1) on structuring the transport shock, ionization and excitation rates must be included in the formulation, since the flow is not frozen with respect to the population of the different electronic levels; (2) an electron temperature precursor appears at the beginning of the transport shock; (3) the collisional layer is rationally reduced to quadrature for special initial conditions, which (4) are obtained from new Rankine-Hugoniot relations for the inner shock.

Shape design sensitivity analysis and optimization of three dimensional elastic solids using geometric modeling and automatic regridding. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Yao, Tse-Min; Choi, Kyung K.

1987-01-01

An automatic regridding method and a three dimensional shape design parameterization technique were constructed and integrated into a unified theory of shape design sensitivity analysis. An algorithm was developed for general shape design sensitivity analysis of three dimensional eleastic solids. Numerical implementation of this shape design sensitivity analysis method was carried out using the finite element code ANSYS. The unified theory of shape design sensitivity analysis uses the material derivative of continuum mechanics with a design velocity field that represents shape change effects over the structural design. Automatic regridding methods were developed by generating a domain velocity field with boundary displacement method. Shape design parameterization for three dimensional surface design problems was illustrated using a Bezier surface with boundary perturbations that depend linearly on the perturbation of design parameters. A linearization method of optimization, LINRM, was used to obtain optimum shapes. Three examples from different engineering disciplines were investigated to demonstrate the accuracy and versatility of this shape design sensitivity analysis method.

Partonic structure of neutral pseudoscalars via two photon transition form factors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Raya, Khepani; Ding, Minghui; Bashir, Adnan

Here, the γγ* → η c,b transition form factors are computed using a continuum approach to the two valence-body bound-state problem in relativistic quantum field theory, and thereby unified with equivalent calculations of electromagnetic pion elastic and transition form factors. The resulting γγ* → η c form factor, G ηc(Q 2), is consistent with available data; significantly, at accessible momentum transfers, Q 2G ηc(Q 2) lies well below its conformal limit. These observations confirm that the leading-twist parton distribution amplitudes of heavy-heavy bound states are compressed relative to the conformal limit. A clear understanding of the distribution of valence quarksmore » within mesons thus emerges, a picture which connects Goldstone modes, built from the lightest quarks in nature, with systems containing the heaviest valence quarks that can now be studied experimentally, and highlights basic facts about manifestations of mass within the Standard Model.« less

Partonic structure of neutral pseudoscalars via two photon transition form factors

DOE PAGES

Raya, Khepani; Ding, Minghui; Bashir, Adnan; ...

2017-04-10

Here, the γγ* → η c,b transition form factors are computed using a continuum approach to the two valence-body bound-state problem in relativistic quantum field theory, and thereby unified with equivalent calculations of electromagnetic pion elastic and transition form factors. The resulting γγ* → η c form factor, G ηc(Q 2), is consistent with available data; significantly, at accessible momentum transfers, Q 2G ηc(Q 2) lies well below its conformal limit. These observations confirm that the leading-twist parton distribution amplitudes of heavy-heavy bound states are compressed relative to the conformal limit. A clear understanding of the distribution of valence quarksmore » within mesons thus emerges, a picture which connects Goldstone modes, built from the lightest quarks in nature, with systems containing the heaviest valence quarks that can now be studied experimentally, and highlights basic facts about manifestations of mass within the Standard Model.« less

Reverse depletion effects and the determination of ligand density on some spherical bioparticles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Chunxiang; Liu, Yanhui, E-mail: ionazati@itp.ac.cn; Fan, Yangtao

In cell environments crowded with macromolecules, the depletion effects act and assist in the assembly of a wide range of cellular structures, from the cytoskeleton to the chromatin loop, which are well accepted. But a recent quantum dot experiment indicated that the dimensions of the receptor–ligand complex have strong effects on the size-dependent exclusion of proteins in cell environments. In this article, a continuum elastic model is constructed to resolve the competition between the dimension of the receptor–ligand complex and depletion effects in the endocytosis of a spherical virus-like bioparticle. Our results show that the depletion effects do not alwaysmore » assist endocytosis of a spherical virus-like bioparticle; while the dimension of the ligand–receptor complex is larger than the size of a small bioparticle in cell environments, the depletion effects do not work and reverse effects appear. The ligand density covered on the virus can be identified quantitatively.« less

Recent Advances in the Method of Forces: Integrated Force Method of Structural Analysis

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.

1998-01-01

Stress that can be induced in an elastic continuum can be determined directly through the simultaneous application of the equilibrium equations and the compatibility conditions. In the literature, this direct stress formulation is referred to as the integrated force method. This method, which uses forces as the primary unknowns, complements the popular equilibrium-based stiffness method, which considers displacements as the unknowns. The integrated force method produces accurate stress, displacement, and frequency results even for modest finite element models. This version of the force method should be developed as an alternative to the stiffness method because the latter method, which has been researched for the past several decades, may have entered its developmental plateau. Stress plays a primary role in the development of aerospace and other products, and its analysis is difficult. Therefore, it is advisable to use both methods to calculate stress and eliminate errors through comparison. This paper examines the role of the integrated force method in analysis, animation and design.

Subcritical fracture propagation in rocks: An examination using the methods of fracture mechanics and non-destructive testing. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Swanson, P. L.

1984-01-01

An experimental investigation of tensile rock fracture is presented with an emphasis on characterizing time dependent crack growth using the methods of fracture mechanics. Subcritical fracture experiments were performed in moist air on glass and five different rock types at crack velocities using the double torsion technique. The experimental results suggest that subcritical fracture resistance in polycrystals is dominated by microstructural effects. Evidence for gross violations of the assumptions of linear elastic fracture mechanics and double torsion theory was found in the tests on rocks. In an effort to obtain a better understanding of the physical breakdown processes associated with rock fracture, a series of nondestructive evaluation tests were performed during subcritical fracture experiments on glass and granite. Comparison of the observed process zone shape with that expected on the basis of a critical normal principal tensile stress criterion shows that the zone is much more elongated in the crack propagation direction than predicted by the continuum based microcracking model alone.

Bronchial-arterial interdependence in isolated dog lung.

PubMed

Lai-Fook, S J; Kallok, M J

1982-04-01

The bronchus and artery, embedded in the lung parenchyma, were modeled as adjoining cylindrical tubes in an elastic continuum. Solutions using finite-element analysis of nonuniform stress and strain occurring from an initial uniform state were computed for a reduction in arterial pressure. Maximal nonuniform principal and shear stresses in the parenchyma, equal to 2.5 times the mean periarterial stresses, occurred in the region adjacent to the bronchial-arterial joint. Bronchial cross section became oval and elongated along the line passing through the centers of the tubes, whereas arterial cross section elongated at right angles to this line. These predicted changes in shape of bronchus and artery were verified by radiographic measurements in isolated lobes, held at constant transpulmonary pressures of 4 and 25 cmH2O while arterial pressure was varied. Results suggest that peribronchovascular interstitial fluid pressure may be nonuniform and that the bronchial-arterial joint may be the preferential site for emphysematous perivascular lesions, which may occur on lung hyperinflation.

Modified Continuum Mechanics Modeling on Size-Dependent Properties of Piezoelectric Nanomaterials: A Review

PubMed Central

Yan, Zhi; Jiang, Liying

2017-01-01

Piezoelectric nanomaterials (PNs) are attractive for applications including sensing, actuating, energy harvesting, among others in nano-electro-mechanical-systems (NEMS) because of their excellent electromechanical coupling, mechanical and physical properties. However, the properties of PNs do not coincide with their bulk counterparts and depend on the particular size. A large amount of efforts have been devoted to studying the size-dependent properties of PNs by using experimental characterization, atomistic simulation and continuum mechanics modeling with the consideration of the scale features of the nanomaterials. This paper reviews the recent progresses and achievements in the research on the continuum mechanics modeling of the size-dependent mechanical and physical properties of PNs. We start from the fundamentals of the modified continuum mechanics models for PNs, including the theories of surface piezoelectricity, flexoelectricity and non-local piezoelectricity, with the introduction of the modified piezoelectric beam and plate models particularly for nanostructured piezoelectric materials with certain configurations. Then, we give a review on the investigation of the size-dependent properties of PNs by using the modified continuum mechanics models, such as the electromechanical coupling, bending, vibration, buckling, wave propagation and dynamic characteristics. Finally, analytical modeling and analysis of nanoscale actuators and energy harvesters based on piezoelectric nanostructures are presented. PMID:28336861

Modified Continuum Mechanics Modeling on Size-Dependent Properties of Piezoelectric Nanomaterials: A Review.

PubMed

Yan, Zhi; Jiang, Liying

2017-01-26

Piezoelectric nanomaterials (PNs) are attractive for applications including sensing, actuating, energy harvesting, among others in nano-electro-mechanical-systems (NEMS) because of their excellent electromechanical coupling, mechanical and physical properties. However, the properties of PNs do not coincide with their bulk counterparts and depend on the particular size. A large amount of efforts have been devoted to studying the size-dependent properties of PNs by using experimental characterization, atomistic simulation and continuum mechanics modeling with the consideration of the scale features of the nanomaterials. This paper reviews the recent progresses and achievements in the research on the continuum mechanics modeling of the size-dependent mechanical and physical properties of PNs. We start from the fundamentals of the modified continuum mechanics models for PNs, including the theories of surface piezoelectricity, flexoelectricity and non-local piezoelectricity, with the introduction of the modified piezoelectric beam and plate models particularly for nanostructured piezoelectric materials with certain configurations. Then, we give a review on the investigation of the size-dependent properties of PNs by using the modified continuum mechanics models, such as the electromechanical coupling, bending, vibration, buckling, wave propagation and dynamic characteristics. Finally, analytical modeling and analysis of nanoscale actuators and energy harvesters based on piezoelectric nanostructures are presented.

Microcracking and Healing in Semibrittle Salt-Rock: Elastic and Plastic Behavior

NASA Astrophysics Data System (ADS)

Ding, J.; Chester, F. M.; Chester, J. S.; Shen, X.; Arson, C. F.

2017-12-01

Microcracking and healing during semibrittle deformation are important processes that affect physical properties such as elastic moduli and permeability. We study these processes through triaxial compression tests involving cyclic differential loading and isostatic-holds on synthetic salt-rock at room temperature and low confining pressure (Pc, 1 to 4 MPa). The salt samples are produced by uniaxial pressing of granular (300 µm dia.) halite to 75 MPa at 150˚C for 10^3 s, to create low-porosity ( 5%) aggregates of nearly equant, work-hardened grains. Alternating large- and small-load cycles are performed to track the evolution of plastic and elastic properties, respecitively, with progressive strain to 8% axial shortening. 24-hour holds are carried out at about 4% axial shortening followed by renewed cyclic loading to investigate healing. During large load cycles samples yield and exhibit distributed flow with dilatancy and small work hardening. Young's Modulus (YM) decreases and then tends to stabilize, while Poisson's Ratio (PR) increases at a reducing rate, with progressive strain. Microstructures at sequential stages show that opening-mode grain-boundary cracking, grain-boundary sliding, and some intracrystalline plasticity are the dominant deformation processes. Opening and shear occur preferentially on boundaries that are parallel and inclined to the shortening axis, respectively, leading to progressive redistribution of porosity. Opening-mode grain-boundary cracks increase in number and aperature with strain, and are linked by sliding grain-boundaries to form en echelon arrays. After a 24-hour hold, samples show yielding and flow behavior consistent with that prior to the hold, whereas YM and PR are reset to the same values documented at zero strain and subsequently evolve with additional strain similar to that documented at smaller strains prior to the hold. Open grain-boundary cracks are not closed or healed during the hold. Observations suggest that changes in elastic properties in the semibrittle salt-rock reflect weakening and healing of grain-boundaries undergoing sliding rather than progressive dilatancy or healing of opening-mode cracks. Findings are being used to inform and develop continuum damage mechanics models of semibrittle deformation in polycrystalline aggregates

Porous Media Approach for Modeling Closed Cell Foam

NASA Technical Reports Server (NTRS)

Ghosn, Louis J.; Sullivan, Roy M.

2006-01-01

In order to minimize boil off of the liquid oxygen and liquid hydrogen and to prevent the formation of ice on its exterior surface, the Space Shuttle External Tank (ET) is insulated using various low-density, closed-cell polymeric foams. Improved analysis methods for these foam materials are needed to predict the foam structural response and to help identify the foam fracture behavior in order to help minimize foam shedding occurrences. This presentation describes a continuum based approach to modeling the foam thermo-mechanical behavior that accounts for the cellular nature of the material and explicitly addresses the effect of the internal cell gas pressure. A porous media approach is implemented in a finite element frame work to model the mechanical behavior of the closed cell foam. The ABAQUS general purpose finite element program is used to simulate the continuum behavior of the foam. The soil mechanics element is implemented to account for the cell internal pressure and its effect on the stress and strain fields. The pressure variation inside the closed cells is calculated using the ideal gas laws. The soil mechanics element is compatible with an orthotropic materials model to capture the different behavior between the rise and in-plane directions of the foam. The porous media approach is applied to model the foam thermal strain and calculate the foam effective coefficient of thermal expansion. The calculated foam coefficients of thermal expansion were able to simulate the measured thermal strain during heat up from cryogenic temperature to room temperature in vacuum. The porous media approach was applied to an insulated substrate with one inch foam and compared to a simple elastic solution without pore pressure. The porous media approach is also applied to model the foam mechanical behavior during subscale laboratory experiments. In this test, a foam layer sprayed on a metal substrate is subjected to a temperature variation while the metal substrate is stretched to simulate the structural response of the tank during operation. The thermal expansion mismatch between the foam and the metal substrate and the thermal gradient in the foam layer causes high tensile stresses near the metal/foam interface that can lead to delamination.

Peridynamics with LAMMPS : a user guide.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehoucq, Richard B.; Silling, Stewart Andrew; Seleson, Pablo

Peridynamics is a nonlocal extension of classical continuum mechanics. The discrete peridynamic model has the same computational structure as a molecular dynamics model. This document provides a brief overview of the peridynamic model of a continuum, then discusses how the peridynamic model is discretized within LAMMPS. An example problem is also included.

Multiphasic modelling of bone-cement injection into vertebral cancellous bone.

PubMed

Bleiler, Christian; Wagner, Arndt; Stadelmann, Vincent A; Windolf, Markus; Köstler, Harald; Boger, Andreas; Gueorguiev-Rüegg, Boyko; Ehlers, Wolfgang; Röhrle, Oliver

2015-01-01

Percutaneous vertebroplasty represents a current procedure to effectively reinforce osteoporotic bone via the injection of bone cement. This contribution considers a continuum-mechanically based modelling approach and simulation techniques to predict the cement distributions within a vertebra during injection. To do so, experimental investigations, imaging data and image processing techniques are combined and exploited to extract necessary data from high-resolution μCT image data. The multiphasic model is based on the Theory of Porous Media, providing the theoretical basis to describe within one set of coupled equations the interaction of an elastically deformable solid skeleton, of liquid bone cement and the displacement of liquid bone marrow. The simulation results are validated against an experiment, in which bone cement was injected into a human vertebra under realistic conditions. The major advantage of this comprehensive modelling approach is the fact that one can not only predict the complex cement flow within an entire vertebra but is also capable of taking into account solid deformations in a fully coupled manner. The presented work is the first step towards the ultimate and future goal of extending this framework to a clinical tool allowing for pre-operative cement distribution predictions by means of numerical simulations. Copyright © 2015 John Wiley & Sons, Ltd.

Development an efficient calibrated nonlocal plate model for nonlinear axial instability of zirconia nanosheets using molecular dynamics simulation.

PubMed

Sahmani, S; Fattahi, A M

2017-08-01

New ceramic materials containing nanoscaled crystalline phases create a main object of scientific interest due to their attractive advantages such as biocompatibility. Zirconia as a transparent glass ceramic is one of the most useful binary oxides in a wide range of applications. In the present study, a new size-dependent plate model is constructed to predict the nonlinear axial instability characteristics of zirconia nanosheets under axial compressive load. To accomplish this end, the nonlocal continuum elasticity of Eringen is incorporated to a refined exponential shear deformation plate theory. A perturbation-based solving process is put to use to derive explicit expressions for nonlocal equilibrium paths of axial-loaded nanosheets. After that, some molecular dynamics (MD) simulations are performed for axial instability response of square zirconia nanosheets with different side lengths, the results of which are matched with those of the developed nonlocal plate model to capture the proper value of nonlocal parameter. It is demonstrated that the calibrated nonlocal plate model with nonlocal parameter equal to 0.37nm has a very good capability to predict the axial instability characteristics of zirconia nanosheets, the accuracy of which is comparable with that of MD simulation. Copyright © 2017 Elsevier Inc. All rights reserved.

Coupled Multi-physics analysis of Caprock Integrity and Fault Reactivation during CO2 Sequestration*

NASA Astrophysics Data System (ADS)

Newell, P.; Martinez, M. J.; Bishop, J.

2012-12-01

Structural/stratigraphic trapping beneath a low-permeable caprock layer is the primary trapping mechanism for long-term subsurface sequestration of CO2. Pre-existing fracture networks, injection induced fractures, and faults are of concern for possible CO2 leakage both during and after injection. In this work we model the effects of both caprock jointing and a fault on the caprock sealing integrity during various injection scenarios. The modeling effort uses a three-dimensional finite-element based coupled multiphase flow and geomechanics simulator. The joints within the caprock are idealized as equally spaced and parallel. Both the mechanical and flow behavior of the joint network are treated within an effective continuum formulation. The mechanical behavior of the joint network is linear elastic in shear and nonlinear elastic in the normal direction. The flow behavior of the joint network is treated using the classical cubic-law relating flow rate and aperture. The flow behavior is then upscaled to obtain an effective permeability. The fault is modeled as a finite-thickness layer with multiple joint sets. The joint sets within the fault region are modeled following the same mechanical and flow formulation as the joints within the caprock. Various injection schedules as well as fault and caprock jointing configurations within a proto-typical sequestration site have been investigated. The resulting leakage rates through the caprock and fault are compared to those assuming intact material. The predicted leakage rates are a strong nonlinear function of the injection rate. *This material is based upon work supported as part of the Center for Frontiers of Subsurface Energy Security, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001114. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energys National Nuclear Security Administration under Contract DE-AC04-94AL85000.

The History of the Planar Elastica: Insights into Mechanics and Scientific Method

NASA Astrophysics Data System (ADS)

Goss, Victor Geoffrey Alan

2009-08-01

Euler’s formula for the buckling of an elastic column is widely used in engineering design. However, only a handful of engineers will be familiar with Euler’s classic paper De Curvis Elasticis in which the formula is derived. In addition to the Euler Buckling Formula, De Curvis Elasticis classifies all the bent configurations of elastic rod—a landmark in the development of a rational theory of continuum mechanics. As a historical case study, Euler’s work on elastic rods offers an insight into some important concepts which underlie mechanics. It sheds light on the search for unifying principles of mechanics and the role of analysis. The connection between results obtained from theory and those obtained from experiments on rods, highlights two different approaches to scientific discovery, which can be traced back to Bacon, Descartes and Galileo. The bent rod also has an analogy in dynamics, with a pendulum, which highlights the crucial distinctions between initial value and boundary value problems and between linear and nonlinear differential equations. In addition to benefiting from the overview which a historical study provides, the particular problem of the elastica offers students of science and engineering a clear elucidation of the connection between mathematics and real-world engineering, issues which still have relevance today.

Production cross sections for Lee-Wick massive electromagnetic bosons and for spin-zero and spin-one W bosons at high energies.

NASA Technical Reports Server (NTRS)

Linsker, R.

1972-01-01

Production cross sections for three types of hypothetical particles are calculated in the presented paper. Several (Z, Z') cases were studied corresponding to elastic scattering off protons and neutrons (either free or embedded within a Fermi sea), coherent scattering off a nucleus, and inelastic scattering off a proton (in which case Z' denotes a nucleon resonance or hadronic system in the continuum). Detailed structure-function data are used to improve the accuracy of the inelastic scattering calculation. Results of calculations are given for beam energies between 50 and 10,000 GeV, and masses between 5 and 40 GeV for the massive Lee-Wick spin-1 boson. Cross sections were computed for resonant and semiweak processes. The production cross section of spin-zero weak intermediate bosons was found to be at least one order of magnitude smaller than for spin-1 weak bosons in nearly all regions of interest. The production cross section of spin-zero weak intermediate bosons for inelastic scattering off protons compares with that for elastic scattering in the regions of interest. In the case of massive spin-1 bosons and spin-1 weak intermediates, the main contribution to total production cross section off protons is elastic.

Outdoor Program Models: Placing Cooperative Adventure and Adventure Education Models on the Continuum.

ERIC Educational Resources Information Center

Guthrie, Steven P.

In two articles on outdoor programming models, Watters distinguished four models on a continuum ranging from the common adventure model, with minimal organizational structure and leadership control, to the guide service model, in which leaders are autocratic and trips are highly structured. Club programs and instructional programs were in between,…

Simulation and theory of spontaneous TAE frequency sweeping

NASA Astrophysics Data System (ADS)

Wang, Ge; Berk, H. L.

2012-09-01

A simulation model, based on the linear tip model of Rosenbluth, Berk and Van Dam (RBV), is developed to study frequency sweeping of toroidal Alfvén eigenmodes (TAEs). The time response of the background wave in the RBV model is given by a Volterra integral equation. This model captures the properties of TAE waves both in the gap and in the continuum. The simulation shows that phase space structures form spontaneously at frequencies close to the linearly predicted frequency, due to resonant particle-wave interactions and background dissipation. The frequency sweeping signals are found to chirp towards the upper and lower continua. However, the chirping signals penetrate only the lower continuum, whereupon the frequency chirps and mode amplitude increases in synchronism to produce an explosive solution. An adiabatic theory describing the evolution of a chirping signal is developed which replicates the chirping dynamics of the simulation in the lower continuum. This theory predicts that a decaying chirping signal will terminate at the upper continuum though in the numerical simulation the hole disintegrates before the upper continuum is reached.

Spin waves, vortices, fermions, and duality in the Ising and Baxter models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ogilvie, M.C.

1981-10-15

Field-theoretic methods are applied to a number of two-dimensional lattice models with Abelian symmetry groups. It is shown, using a vortex+spin-wave decomposition, that the Z/sub p/-Villain models are related to a class of continuum field theories with analogous duality properties. Fermion operators for these field theories are discussed. In the case of the Ising model, the vortices and spin-waves conspire to produce a free, massive Majorana field theory in the continuum limit. The continuum limit of the Baxter model is also studied, and the recent results of Kadanoff and Brown are rederived and extended.

Multiscale Modeling of Carbon Nanotube-Epoxy Nanocomposites

NASA Astrophysics Data System (ADS)

Fasanella, Nicholas A.

Epoxy-composites are widely used in the aerospace industry. In order to improve upon stiffness and thermal conductivity; carbon nanotube additives to epoxies are being explored. This dissertation presents multiscale modeling techniques to study the engineering properties of single walled carbon nanotube (SWNT)-epoxy nanocomposites, consisting of pristine and covalently functionalized systems. Using Molecular Dynamics (MD), thermomechanical properties were calculated for a representative polymer unit cell. Finite Element (FE) and orientation distribution function (ODF) based methods were used in a multiscale framework to obtain macroscale properties. An epoxy network was built using the dendrimer growth approach. The epoxy model was verified by matching the experimental glass transition temperature, density, and dilatation. MD, via the constant valence force field (CVFF), was used to explore the mechanical and dilatometric effects of adding pristine and functionalized SWNTs to epoxy. Full stiffness matrices and linear coefficient of thermal expansion vectors were obtained. The Green-Kubo method was used to investigate the thermal conductivity as a function of temperature for the various nanocomposites. Inefficient phonon transport at the ends of nanotubes is an important factor in the thermal conductivity of the nanocomposites, and for this reason discontinuous nanotubes were modeled in addition to long nanotubes. To obtain continuum-scale elastic properties from the MD data, multiscale modeling was considered to give better control over the volume fraction of nanotubes, and investigate the effects of nanotube alignment. Two methods were considered; an FE based method, and an ODF based method. The FE method probabilistically assigned elastic properties of elements from the MD lattice results based on the desired volume fraction and alignment of the nanotubes. For the ODF method, a distribution function was generated based on the desired amount of nanotube alignment; and the stiffness matrix was calculated. A rule of mixture approach was implemented in the ODF model to vary the SWNT volume fraction. Both the ODF and FE models are compared and contrasted. ODF analysis is significantly faster for nanocomposites and is a novel contribution in this thesis. Multiscale modeling allows for the effects of nanofillers in epoxy systems to be characterized without having to run costly experiments.

Modeling of Continuum Manipulators Using Pythagorean Hodograph Curves.

PubMed

Singh, Inderjeet; Amara, Yacine; Melingui, Achille; Mani Pathak, Pushparaj; Merzouki, Rochdi

2018-05-10

Research on continuum manipulators is increasingly developing in the context of bionic robotics because of their many advantages over conventional rigid manipulators. Due to their soft structure, they have inherent flexibility, which makes it a huge challenge to control them with high performances. Before elaborating a control strategy of such robots, it is essential to reconstruct first the behavior of the robot through development of an approximate behavioral model. This can be kinematic or dynamic depending on the conditions of operation of the robot itself. Kinematically, two types of modeling methods exist to describe the robot behavior; quantitative methods describe a model-based method, and qualitative methods describe a learning-based method. In kinematic modeling of continuum manipulator, the assumption of constant curvature is often considered to simplify the model formulation. In this work, a quantitative modeling method is proposed, based on the Pythagorean hodograph (PH) curves. The aim is to obtain a three-dimensional reconstruction of the shape of the continuum manipulator with variable curvature, allowing the calculation of its inverse kinematic model (IKM). It is noticed that the performances of the PH-based kinematic modeling of continuum manipulators are considerable regarding position accuracy, shape reconstruction, and time/cost of the model calculation, than other kinematic modeling methods, for two cases: free load manipulation and variable load manipulation. This modeling method is applied to the compact bionic handling assistant (CBHA) manipulator for validation. The results are compared with other IKMs developed in case of CBHA manipulator.

On the physically based modeling of surface tension and moving contact lines with dynamic contact angles on the continuum scale

NASA Astrophysics Data System (ADS)

Huber, M.; Keller, F.; Säckel, W.; Hirschler, M.; Kunz, P.; Hassanizadeh, S. M.; Nieken, U.

2016-04-01

The description of wetting phenomena is a challenging problem on every considerable length-scale. The behavior of interfaces and contact lines on the continuum scale is caused by intermolecular interactions like the Van der Waals forces. Therefore, to describe surface tension and the resulting dynamics of interfaces and contact lines on the continuum scale, appropriate formulations must be developed. While the Continuum Surface Force (CSF) model is well-engineered for the description of interfaces, there is still a lack of treatment of contact lines, which are defined by the intersection of an ending fluid interface and a solid boundary surface. In our approach we use a balance equation for the contact line and extend the Navier-Stokes equations in analogy to the extension of a two-phase interface in the CSF model. Since this model depicts a physically motivated approach on the continuum scale, no fitting parameters are introduced and the deterministic description leads to a dynamical evolution of the system. As verification of our theory, we show a Smoothed Particle Hydrodynamics (SPH) model and simulate the evolution of droplet shapes and their corresponding contact angles.

Hydration and conformational equilibria of simple hydrophobic and amphiphilic solutes.

PubMed Central

Ashbaugh, H S; Kaler, E W; Paulaitis, M E

1998-01-01

We consider whether the continuum model of hydration optimized to reproduce vacuum-to-water transfer free energies simultaneously describes the hydration free energy contributions to conformational equilibria of the same solutes in water. To this end, transfer and conformational free energies of idealized hydrophobic and amphiphilic solutes in water are calculated from explicit water simulations and compared to continuum model predictions. As benchmark hydrophobic solutes, we examine the hydration of linear alkanes from methane through hexane. Amphiphilic solutes were created by adding a charge of +/-1e to a terminal methyl group of butane. We find that phenomenological continuum parameters fit to transfer free energies are significantly different from those fit to conformational free energies of our model solutes. This difference is attributed to continuum model parameters that depend on solute conformation in water, and leads to effective values for the free energy/surface area coefficient and Born radii that best describe conformational equilibrium. In light of these results, we believe that continuum models of hydration optimized to fit transfer free energies do not accurately capture the balance between hydrophobic and electrostatic contributions that determines the solute conformational state in aqueous solution. PMID:9675177

Constitutive Theory Developed for Monolithic Ceramic Materials

NASA Technical Reports Server (NTRS)

Janosik, Lesley A.

1998-01-01

With the increasing use of advanced ceramic materials in high-temperature structural applications such as advanced heat engine components, the need arises to accurately predict thermomechanical behavior that is inherently time-dependent and that is hereditary in the sense that the current behavior depends not only on current conditions but also on the material's thermomechanical history. Most current analytical life prediction methods for both subcritical crack growth and creep models use elastic stress fields to predict the time-dependent reliability response of components subjected to elevated service temperatures. Inelastic response at high temperatures has been well documented in the materials science literature for these material systems, but this issue has been ignored by the engineering design community. From a design engineer's perspective, it is imperative to emphasize that accurate predictions of time-dependent reliability demand accurate stress field information. Ceramic materials exhibit different time-dependent behavior in tension and compression. Thus, inelastic deformation models for ceramics must be constructed in a fashion that admits both sensitivity to hydrostatic stress and differing behavior in tension and compression. A number of constitutive theories for materials that exhibit sensitivity to the hydrostatic component of stress have been proposed that characterize deformation using time-independent classical plasticity as a foundation. However, none of these theories allow different behavior in tension and compression. In addition, these theories are somewhat lacking in that they are unable to capture the creep, relaxation, and rate-sensitive phenomena exhibited by ceramic materials at high temperatures. The objective of this effort at the NASA Lewis Research Center has been to formulate a macroscopic continuum theory that captures these time-dependent phenomena. Specifically, the effort has focused on inelastic deformation behavior associated with these service conditions by developing a multiaxial viscoplastic constitutive model that accounts for time-dependent hereditary material deformation (such as creep and stress relaxation) in monolithic structural ceramics. Using continuum principles of engineering mechanics, we derived the complete viscoplastic theory from a scalar dissipative potential function.

Effect of nonlinearity in hybrid kinetic Monte Carlo-continuum models.

PubMed

Balter, Ariel; Lin, Guang; Tartakovsky, Alexandre M

2012-01-01

Recently there has been interest in developing efficient ways to model heterogeneous surface reactions with hybrid computational models that couple a kinetic Monte Carlo (KMC) model for a surface to a finite-difference model for bulk diffusion in a continuous domain. We consider two representative problems that validate a hybrid method and show that this method captures the combined effects of nonlinearity and stochasticity. We first validate a simple deposition-dissolution model with a linear rate showing that the KMC-continuum hybrid agrees with both a fully deterministic model and its analytical solution. We then study a deposition-dissolution model including competitive adsorption, which leads to a nonlinear rate, and show that in this case the KMC-continuum hybrid and fully deterministic simulations do not agree. However, we are able to identify the difference as a natural result of the stochasticity coming from the KMC surface process. Because KMC captures inherent fluctuations, we consider it to be more realistic than a purely deterministic model. Therefore, we consider the KMC-continuum hybrid to be more representative of a real system.

Effect of Nonlinearity in Hybrid Kinetic Monte Carlo-Continuum Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balter, Ariel I.; Lin, Guang; Tartakovsky, Alexandre M.

2012-04-23

Recently there has been interest in developing efficient ways to model heterogeneous surface reactions with hybrid computational models that couple a KMC model for a surface to a finite difference model for bulk diffusion in a continuous domain. We consider two representative problems that validate a hybrid method and also show that this method captures the combined effects of nonlinearity and stochasticity. We first validate a simple deposition/dissolution model with a linear rate showing that the KMC-continuum hybrid agrees with both a fully deterministic model and its analytical solution. We then study a deposition/dissolution model including competitive adsorption, which leadsmore » to a nonlinear rate, and show that, in this case, the KMC-continuum hybrid and fully deterministic simulations do not agree. However, we are able to identify the difference as a natural result of the stochasticity coming from the KMC surface process. Because KMC captures inherent fluctuations, we consider it to be more realistic than a purely deterministic model. Therefore, we consider the KMC-continuum hybrid to be more representative of a real system.« less

Passing waves from atomistic to continuum

NASA Astrophysics Data System (ADS)

Chen, Xiang; Diaz, Adrian; Xiong, Liming; McDowell, David L.; Chen, Youping

2018-02-01

Progress in the development of coupled atomistic-continuum methods for simulations of critical dynamic material behavior has been hampered by a spurious wave reflection problem at the atomistic-continuum interface. This problem is mainly caused by the difference in material descriptions between the atomistic and continuum models, which results in a mismatch in phonon dispersion relations. In this work, we introduce a new method based on atomistic dynamics of lattice coupled with a concurrent atomistic-continuum method to enable a full phonon representation in the continuum description. This permits the passage of short-wavelength, high-frequency phonon waves from the atomistic to continuum regions. The benchmark examples presented in this work demonstrate that the new scheme enables the passage of all allowable phonons through the atomistic-continuum interface; it also preserves the wave coherency and energy conservation after phonons transport across multiple atomistic-continuum interfaces. This work is the first step towards developing a concurrent atomistic-continuum simulation tool for non-equilibrium phonon-mediated thermal transport in materials with microstructural complexity.

Explicitly Representing the Solvation Shell in Continuum Solvent Calculations

PubMed Central

Svendsen, Hallvard F.; Merz, Kenneth M.

2009-01-01

A method is presented to explicitly represent the first solvation shell in continuum solvation calculations. Initial solvation shell geometries were generated with classical molecular dynamics simulations. Clusters consisting of solute and 5 solvent molecules were fully relaxed in quantum mechanical calculations. The free energy of solvation of the solute was calculated from the free energy of formation of the cluster and the solvation free energy of the cluster calculated with continuum solvation models. The method has been implemented with two continuum solvation models, a Poisson-Boltzmann model and the IEF-PCM model. Calculations were carried out for a set of 60 ionic species. Implemented with the Poisson-Boltzmann model the method gave an unsigned average error of 2.1 kcal/mol and a RMSD of 2.6 kcal/mol for anions, for cations the unsigned average error was 2.8 kcal/mol and the RMSD 3.9 kcal/mol. Similar results were obtained with the IEF-PCM model. PMID:19425558

Toward more accurate basal boundary conditions: a new 2-D model of distributed and channelised subglacial drainage

NASA Astrophysics Data System (ADS)

Werder, M. A.; Hewitt, I. J.; Schoof, C.; Flowers, G. E.

2012-04-01

Basal boundary conditions are one of the least constrained components of today's ice sheet models. To get at these one needs to know the distributed basal water pressure. We present a new glacier drainage system model to contribute to this missing piece of the puzzle. This two dimensional mathematical/numerical model combines distributed and channelised drainage at the ice-bed interface coupled to a water storage component. Notably the model determines the location of the channels as part of the solution. This is achieved by allowing channels (modelled as R-channels) to form on any of the edges of the unstructured triangular grid used to discretise the model. The distributed system is represented by a water sheet which is a continuum description of a linked-cavity system and exchanges water with the channels along their length. Water storage is parameterised as a function of the subglacial water pressure, which can be interpreted as storage in an englacial aquifer or due to elastic processes. The parabolic equation that determines the water pressure is solved using finite elements, the time evolution of the water sheet thickness and channel diameter are governed by local differential equations that are integrated using explicit methods. To explore the model's properties, we apply it to synthetic ice sheet catchments with areas up to 3000km2. We present steady state drainage system configurations and evaluate their channel-network properties (fractal dimensions, channel spacing). We find that an arborescent channel network forms whose density depends on the water sheet conductivity relative to water input. As a further experiment, we force the model with a seasonally and diurnally varying melt water input to investigate how the modelled drainage system evolves on these time scales: a channelised system grows up glacier as meltwater is delivered to the bed in spring and collapses in autumn. Water pressure is highest just before the formation of channels and then drops. Conversely, the diurnal variations in discharge affect the drainage system morphology only slightly. Instead they lead to large water pressure variations which lag meltwater input and coincide with changes in the volume of stored water. By incorporating an evolving R-channel network within a continuum model of distributed water drainage and storage, this 2-D model succeeds in qualitatively reproducing many of the observed and postulated features of the glacier drainage system.

Radiative lifetimes of zincblende CdSe/CdS quantum dots

DOE PAGES

Gong, Ke; Martin, James E.; Shea-Rohwer, Lauren E.; ...

2015-01-02

Recent synthetic advances have made available very monodisperse zincblende CdSe/CdS quantum dots having near-unity photoluminescence quantum yields. Because of the absence of nonradiative decay pathways, accurate values of the radiative lifetimes can be obtained from time-resolved PL measurements. Radiative lifetimes can also be obtained from the Einstein relations, using the static absorption spectra and the relative thermal populations in the angular momentum sublevels. We found that one of the inputs into these calculations is the shell thickness, and it is useful to be able to determine shell thickness from spectroscopic measurements. We use an empirically corrected effective mass model tomore » produce a “map” of exciton wavelength as a function of core size and shell thickness. These calculations use an elastic continuum model and the known lattice and elastic constants to include the effect of lattice strain on the band gap energy. The map is in agreement with the known CdSe sizing curve and with the shell thicknesses of zincblende core/shell particles obtained from TEM images. Furthermore, if selenium–sulfur diffusion is included and lattice strain is omitted from the calculation then the resulting map is appropriate for wurtzite CdSe/CdS quantum dots synthesized at high temperatures, and this map is very similar to one previously reported (J. Am. Chem. Soc. 2009, 131, 14299). Radiative lifetimes determined from time-resolved measurements are compared to values obtained from the Einstein relations, and found to be in excellent agreement. For a specific core size (2.64 nm diameter, in the present case), radiative lifetimes are found to decrease with increasing shell thickness. Thus, this is similar to the size dependence of one-component CdSe quantum dots and in contrast to the size dependence in type-II quantum dots.« less

Modeling seismic stimulation: Enhanced non-aqueous fluid extraction from saturated porous media under pore-pressure pulsing at low frequencies

NASA Astrophysics Data System (ADS)

Lo, Wei-Cheng; Sposito, Garrison; Huang, Yu-Han

2012-03-01

Seismic stimulation, the application of low-frequency stress-pulsing to the boundary of a porous medium containing water and a non-aqueous fluid to enhance the removal of the latter, shows great promise for both contaminated groundwater remediation and enhanced oil recovery, but theory to elucidate the underlying mechanisms lag significantly behind the progress achieved in experimental research. We address this conceptual lacuna by formulating a boundary-value problem to describe pore-pressure pulsing at seismic frequencies that is based on the continuum theory of poroelasticity for an elastic porous medium permeated by two immiscible fluids. An exact analytical solution is presented that is applied numerically using elasticity parameters and hydraulic data relevant to recent proof-of-principle laboratory experiments investigating the stimulation-induced mobilization of trichloroethene (TCE) in water flowing through a compressed sand core. The numerical results indicated that significant stimulation-induced increases of the TCE concentration in effluent can be expected from pore-pressure pulsing in the frequency range of 25-100 Hz, which is in good agreement with what was observed in the laboratory experiments. Sensitivity analysis of our numerical results revealed that the TCE concentration in the effluent increases with the porous medium framework compressibility and the pulsing pressure. Increasing compressibility also leads to an optimal stimulation response at lower frequencies, whereas changing the pulsing pressure does not affect the optimal stimulation frequency. Within the context of our model, the dominant physical cause for enhancement of non-aqueous fluid mobility by seismic stimulation is the dilatory motion of the porous medium in which the solid and fluid phases undergo opposite displacements, resulting in stress-induced changes of the pore volume.

Mirrored continuum and molecular scale simulations of the ignition of gamma phase RDX

NASA Astrophysics Data System (ADS)

Stewart, D. Scott; Chaudhuri, Santanu; Joshi, Kaushik; Lee, Kiabek

2015-06-01

We consider the ignition of a high-pressure gamma-phase of an explosive crystal of RDX which forms during overdriven shock initiation. Molecular dynamics (MD), with first-principles based or reactive force field based molecular potentials, provides a description of the chemistry as an extremely complex reaction network. The results of the molecular simulation is analyzed by sorting molecular product fragments into high and low molecular groups, to represent identifiable components that can be interpreted by a continuum model. A continuum model based on a Gibbs formulation, that has a single temperature and stress state for the mixture is used to represent the same RDX material and its chemistry. Each component in the continuum model has a corresponding Gibbs continuum potential, that are in turn inferred from molecular MD informed equation of state libraries such as CHEETAH, or are directly simulated by Monte Carlo MD simulations. Information about transport, kinetic rates and diffusion are derived from the MD simulation and the growth of a reactive hot spot in the RDX is studied with both simulations that mirror the other results to provide an essential, continuum/atomistic link. Supported by N000014-12-1-0555, subaward-36561937 (ONR).

Reducing Actuator Requirements in Continuum Robots Through Optimized Cable Routing.

PubMed

Case, Jennifer C; White, Edward L; SunSpiral, Vytas; Kramer-Bottiglio, Rebecca

2018-02-01

Continuum manipulators offer many advantages compared to their rigid-linked counterparts, such as increased degrees of freedom and workspace volume. Inspired by biological systems, such as elephant trunks and octopus tentacles, many continuum manipulators are made of multiple segments that allow large-scale deformations to be distributed throughout the body. Most continuum manipulators currently control each segment individually. For example, a planar cable-driven system is typically controlled by a pair of cables for each segment, which implies two actuators per segment. In this article, we demonstrate how highly coupled crossing cable configurations can reduce both actuator count and actuator torque requirements in a planar continuum manipulator, while maintaining workspace reachability and manipulability. We achieve highly coupled actuation by allowing cables to cross through the manipulator to create new cable configurations. We further derive an analytical model to predict the underactuated manipulator workspace and experimentally verify the model accuracy with a physical system. We use this model to compare crossing cable configurations to the traditional cable configuration using workspace performance metrics. Our work here focuses on a simplified planar robot, both in simulation and in hardware, with the goal of extending this to spiraling-cable configurations on full 3D continuum robots in future work.

Flow Interpretation Implications for Poro-Elastic Modeling

DTIC Science & Technology

2010-06-01

interpretation of acoustical inversions based on poro-elastic models . I. INTRODUCTION Poro-elastic models for acoustic propagation in sediments arose out of the...porous solid. ii. higher freqency range, J. Acoust . Soc. America, 28, 179– 191, 1956. [11] Bear, J., and Y. Bachmat (Eds.), Introduction to Modeling of...Flow interpretation implications for Poro-Elastic Modeling James K. Fulford Naval Research Laboratory Stennis Space Center Stennis Space Center

Linking scales in sea ice mechanics.

PubMed

Weiss, Jérôme; Dansereau, Véronique

2017-02-13

Mechanics plays a key role in the evolution of the sea ice cover through its control on drift, on momentum and thermal energy exchanges between the polar oceans and the atmosphere along cracks and faults, and on ice thickness distribution through opening and ridging processes. At the local scale, a significant variability of the mechanical strength is associated with the microstructural heterogeneity of saline ice, however characterized by a small correlation length, below the ice thickness scale. Conversely, the sea ice mechanical fields (velocity, strain and stress) are characterized by long-ranged (more than 1000 km) and long-lasting (approx. few months) correlations. The associated space and time scaling laws are the signature of the brittle character of sea ice mechanics, with deformation resulting from a multi-scale accumulation of episodic fracturing and faulting events. To translate the short-range-correlated disorder on strength into long-range-correlated mechanical fields, several key ingredients are identified: long-ranged elastic interactions, slow driving conditions, a slow viscous-like relaxation of elastic stresses and a restoring/healing mechanism. These ingredients constrained the development of a new continuum mechanics modelling framework for the sea ice cover, called Maxwell-elasto-brittle. Idealized simulations without advection demonstrate that this rheological framework reproduces the main characteristics of sea ice mechanics, including anisotropy, spatial localization and intermittency, as well as the associated scaling laws.This article is part of the themed issue 'Microdynamics of ice'. © 2016 The Author(s).

Micromechanics effects in creep of metal-matrix composites

NASA Astrophysics Data System (ADS)

Davis, L. C.; Allison, J. E.

1995-12-01

The creep of metal-matrix composites is analyzed by finite element techniques. An axisymmetric unit-cell model with spherical reinforcing particles is used. Parameters appropriate to TiC particles in a precipitation-hardened (2219) Al matrix are chosen. The effects of matrix plasticity and residual stresses on the creep of the composite are calculated. We confirm (1) that the steady-state rate is independent of the particle elastic moduli and the matrix elastic and plastic properties, (2) that the ratio of composite to matrix steady-state rates depends only on the volume fraction and geometry of the reinforcing phase, and (3) that this ratio can be determined from a calculation of the stress-strain relation for the geometrically identical composite (same phase volume and geometry) with rigid particles in the appropriate power-law hardening matrix. The values of steady-state creep are compared to experimental ones (Krajewski et al.). Continuum mechanics predictions give a larger reduction of the composite creep relative to the unreinforced material than measured, suggesting that the effective creep rate of the matrix is larger than in unreinforced precipitation-hardened Al due to changes in microstructure, dislocation density, or creep mechanism. Changes in matrix creep properties are also suggested by the comparison of calculated and measured creep strain rates in the primary creep regime, where significantly different time dependencies are found. It is found that creep calculations performed for a timeindependent matrix creep law can be transformed to obtain the creep for a time-dependent creep law.

Discrete and continuum modelling of soil cutting

NASA Astrophysics Data System (ADS)

Coetzee, C. J.

2014-12-01

Both continuum and discrete methods are used to investigate the soil cutting process. The Discrete Element Method ( dem) is used for the discrete modelling and the Material-Point Method ( mpm) is used for continuum modelling. M pmis a so-called particle method or meshless finite element method. Standard finite element methods have difficulty in modelling the entire cutting process due to large displacements and deformation of the mesh. The use of meshless methods overcomes this problem. M pm can model large deformations, frictional contact at the soil-tool interface, and dynamic effects (inertia forces). In granular materials the discreteness of the system is often important and rotational degrees of freedom are active, which might require enhanced theoretical approaches like polar continua. In polar continuum theories, the material points are considered to possess orientations. A material point has three degrees-of-freedom for rigid rotations, in addition to the three classic translational degrees-of-freedom. The Cosserat continuum is the most transparent and straightforward extension of the nonpolar (classic) continuum. Two-dimensional dem and mpm (polar and nonpolar) simulations of the cutting problem are compared to experiments. The drag force and flow patterns are compared using cohesionless corn grains as material. The corn macro (continuum) and micro ( dem) properties were obtained from shear and oedometer tests. Results show that the dilatancy angle plays a significant role in the flow of material but has less of an influence on the draft force. Nonpolar mpm is the most accurate in predicting blade forces, blade-soil interface stresses and the position and orientation of shear bands. Polar mpm fails in predicting the orientation of the shear band, but is less sensitive to mesh size and mesh orientation compared to nonpolar mpm. dem simulations show less material dilation than observed during experiments.