Elastic metamaterial beam with remotely tunable stiffness

NASA Astrophysics Data System (ADS)

Qian, Wei; Yu, Zhengyue; Wang, Xiaole; Lai, Yun; Yellen, Benjamin B.

2016-02-01

We demonstrate a dynamically tunable elastic metamaterial, which employs remote magnetic force to adjust its vibration absorption properties. The 1D metamaterial is constructed from a flat aluminum beam milled with a linear array of cylindrical holes. The beam is backed by a thin elastic membrane, on which thin disk-shaped permanent magnets are mounted. When excited by a shaker, the beam motion is tracked by a Laser Doppler Vibrometer, which conducts point by point scanning of the vibrating element. Elastic waves are unable to propagate through the beam when the driving frequency excites the first elastic bending mode in the unit cell. At these frequencies, the effective mass density of the unit cell becomes negative, which induces an exponentially decaying evanescent wave. Due to the non-linear elastic properties of the membrane, the effective stiffness of the unit cell can be tuned with an external magnetic force from nearby solenoids. Measurements of the linear and cubic static stiffness terms of the membrane are in excellent agreement with experimental measurements of the bandgap shift as a function of the applied force. In this implementation, bandgap shifts by as much as 40% can be achieved with ˜30 mN of applied magnetic force. This structure has potential for extension in 2D and 3D, providing a general approach for building dynamically tunable elastic metamaterials for applications in lensing and guiding elastic waves.

Solving the Problem of Bending of Multiply Connected Plates with Elastic Inclusions

NASA Astrophysics Data System (ADS)

Kaloerov, S. A.; Koshkin, A. A.

2017-11-01

This paper describes a method for determining the strain state of a thin anisotropic plate with elastic arbitrarily arranged elliptical inclusions. Complex potentials are used to reduce the problem to determining functions of generalized complex variables, which, in turn, comes down to an overdetermined system of linear algebraic equations, solved by singular expansions. This paper presents the results of numerical calculations that helped establish the influence of rigidity of elastic inclusions, distances between inclusions, and their geometric characteristics on the bending moments occurring in the plate. It is found that the specific properties of distribution of moments near the apexes of linear elastic inclusions, characterized by moment intensity coefficients, occur only in the case of sufficiently rigid and elastic inclusions.

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.

How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity

PubMed Central

2017-01-01

The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales. PMID:29225507

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Two Propositions on the Application of Point Elasticities to Finite Price Changes.

ERIC Educational Resources Information Center

Daskin, Alan J.

1992-01-01

Considers counterintuitive propositions about using point elasticities to estimate quantity changes in response to price changes. Suggests that elasticity increases with price along a linear demand curve, but falling quantity demand offsets it. Argues that point elasticity with finite percentage change in price only approximates percentage change…

Variational Theory of Motion of Curved, Twisted and Extensible Elastic Rods

DTIC Science & Technology

1993-01-18

nonlinear theory such as questions of existence of solutions and global behavior have been carried out by Antman (1976). His basic work entitled "The...Aerosp. Ens. Q017/018 16 REFERENCES Antman , S.S., "Ordinary Differential Equations of Non-Linear ElastIcity 1: Foundatious of the Theories of Non-Linearly...Elutic rods and Shells," A.R.M.A. 61 (1976), 307-351. Antman , S.S., "The Theory of Rods", Handbuch der Physik, Vol. Vla/2, Springer-Verlq, Berlin

Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

NASA Astrophysics Data System (ADS)

Geng, Jun; Shen, Zhongwei; Song, Liang

2017-06-01

This paper is concerned with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uniform optimal regularity estimates for solutions of Neumann problems in a bounded Lipschitz domain with L 2 boundary data. The proof relies on a boundary Korn inequality for solutions of systems of linear elasticity and uses a large-scale Rellich estimate obtained in Shen (Anal PDE, arXiv:1505.00694v2).

Extending double modulation: combinatorial rules for identifying the modulations necessary for determining elasticities in metabolic pathways.

PubMed

Giersch, C; Cornish-Bowden, A

1996-10-07

The double modulation method for determining the elasticities of pathway enzymes, originally devised by Kacser & Burns (Biochem. Soc. Trans. 7, 1149-1160, 1979), is extended to pathways of complex topological structure, including branching and feedback loops. An explicit system of linear equations for the unknown elasticities is derived. The constraints imposed on this linear system imply that modulations of more than one enzyme are not necessarily independent. Simple combinatorial rules are described for identifying without using any algebra the set of independent modulations that allow the determination of the elasticities of any enzyme. By repeated application, the minimum numbers of modulations required to determine the elasticities of all enzymes of a given pathway can be determined. The procedure is illustrated with numerous examples.

Summer Research Program (1992). Summer Faculty Research Program (SFRP) Reports. Volume 2. Armstrong Laboratory

DTIC Science & Technology

1992-12-01

desirable. In this study, the proposed model consists of a thick-walled, highly deformable elastic tube in which the blood flow is described by linearized ...presented a mechanical model consisting of linearized Navier-Stokes and finite elasticity equations to predict blood pooling under acceleration stress... linear multielement model of the cardiovascular system which can calculate blood pressures and flows at any point in the cardio- vascular system. It

Dynamics of an elastic sphere containing a thin creeping region and immersed in an acoustic region for similar viscous-elastic and acoustic time- and length-scales

NASA Astrophysics Data System (ADS)

Gat, Amir; Friedman, Yonathan

2017-11-01

The characteristic time of low-Reynolds number fluid-structure interaction scales linearly with the ratio of fluid viscosity to solid Young's modulus. For sufficiently large values of Young's modulus, both time- and length-scales of the viscous-elastic dynamics may be similar to acoustic time- and length-scales. However, the requirement of dominant viscous effects limits the validity of such regimes to micro-configurations. We here study the dynamics of an acoustic plane wave impinging on the surface of a layered sphere, immersed within an inviscid fluid, and composed of an inner elastic sphere, a creeping fluid layer and an external elastic shell. We focus on configurations with similar viscous-elastic and acoustic time- and length-scales, where the viscous-elastic speed of interaction between the creeping layer and the elastic regions is similar to the speed of sound. By expanding the linearized spherical Reynolds equation into the relevant spectral series solution for the hyperbolic elastic regions, a global stiffness matrix of the layered elastic sphere was obtained. This work relates viscous-elastic dynamics to acoustic scattering and may pave the way to the design of novel meta-materials with unique acoustic properties. ISF 818/13.

Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

NASA Astrophysics Data System (ADS)

Nadkarni, Neel; Daraio, Chiara; Kochmann, Dennis M.

2014-08-01

We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.

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

Linear analysis using secants for materials with temperature dependent nonlinear elastic modulus and thermal expansion properties

NASA Astrophysics Data System (ADS)

Pepi, John W.

2017-08-01

Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.

Small vibrations of a linearly elastic body surrounded by heavy, incompressible, non-Newtonian fluids with free surfaces

NASA Astrophysics Data System (ADS)

Licht, Christian; Tran Thu Ha

2005-02-01

We consider the small transient motions of a coupled system constituted by a linearly elastic body and two heavy, incompressible, non-Newtonian fluids.Through a formulation in terms of non-linear evolution equations in Hilbert spaces of possible states with finite mechanical energy, we obtain existence and uniqueness results and study the influence of gravity. To cite this article: C. Licht, Tran Thu Ha, C. R. Mecanique 333 (2005).

Analysis and control of hourglass instabilities in underintegrated linear and nonlinear elasticity

NASA Technical Reports Server (NTRS)

Jacquotte, Olivier P.; Oden, J. Tinsley

1994-01-01

Methods are described to identify and correct a bad finite element approximation of the governing operator obtained when under-integration is used in numerical code for several model problems: the Poisson problem, the linear elasticity problem, and for problems in the nonlinear theory of elasticity. For each of these problems, the reason for the occurrence of instabilities is given, a way to control or eliminate them is presented, and theorems of existence, uniqueness, and convergence for the given methods are established. Finally, numerical results are included which illustrate the theory.

Generation of wavy structure on lipid membrane by peripheral proteins: a linear elastic analysis.

PubMed

Mahata, Paritosh; Das, Sovan Lal

2017-05-01

We carry out a linear elastic analysis to study wavy structure generation on lipid membrane by peripheral membrane proteins. We model the lipid membrane as linearly elastic and anisotropic material. The hydrophobic insertion by proteins into the lipid membrane has been idealized as penetration of rigid rod-like inclusions into the membrane and the electrostatic interaction between protein and membrane has been modeled by a distributed surface traction acting on the membrane surface. With the proposed model we study curvature generation by several binding domains of peripheral membrane proteins containing BAR domains and amphipathic alpha-helices. It is observed that electrostatic interaction is essential for curvature generation by the BAR domains. © 2017 Federation of European Biochemical Societies.

Temperature dependence of elastic and strength properties of T300/5208 graphite-epoxy

NASA Technical Reports Server (NTRS)

Milkovich, S. M.; Herakovich, C. T.

1984-01-01

Experimental results are presented for the elastic and strength properties of T300/5208 graphite-epoxy at room temperature, 116K (-250 F), and 394K (+250 F). Results are presented for unidirectional 0, 90, and 45 degree laminates, and + or - 30, + or - 45, and + or - 60 degree angle-ply laminates. The stress-strain behavior of the 0 and 90 degree laminates is essentially linear for all three temperatures and that the stress-strain behavior of all other laminates is linear at 116K. A second-order curve provides the best fit for the temperature is linear at 116K. A second-order curve provides the best fit for the temperature dependence of the elastic modulus of all laminates and for the principal shear modulus. Poisson's ratio appears to vary linearly with temperature. all moduli decrease with increasing temperature except for E (sub 1) which exhibits a small increase. The strength temperature dependence is also quadratic for all laminates except the 0 degree - laminate which exhibits linear temperature dependence. In many cases the temperature dependence of properties is nearly linear.

Stability Analysis of an Encapsulated Microbubble against Gas Diffusion

PubMed Central

Katiyar, Amit; Sarkar, Kausik

2009-01-01

Linear stability analysis is performed for a mathematical model of diffusion of gases from an encapsulated microbubble. It is an Epstein-Plesset model modified to account for encapsulation elasticity and finite gas permeability. Although, bubbles, containing gases other than air is considered, the final stable bubble, if any, contains only air, and stability is achieved only when the surrounding medium is saturated or oversaturated with air. In absence of encapsulation elasticity, only a neutral stability is achieved for zero surface tension, the other solution being unstable. For an elastic encapsulation, different equilibrium solutions are obtained depending on the saturation level and whether the surface tension is smaller or higher than the elasticity. For an elastic encapsulation, elasticity can stabilize the bubble. However, imposing a non-negativity condition on the effective surface tension (consisting of reference surface tension and the elastic stress) leads to an equilibrium radius which is only neutrally stable. If the encapsulation can support net compressive stress, it achieves actual stability. The linear stability results are consistent with our recent numerical findings. Physical mechanisms for the stability or instability of various equilibriums are provided. PMID:20005522

A model for compression-weakening materials and the elastic fields due to contractile cells

NASA Astrophysics Data System (ADS)

Rosakis, Phoebus; Notbohm, Jacob; Ravichandran, Guruswami

2015-12-01

We construct a homogeneous, nonlinear elastic constitutive law that models aspects of the mechanical behavior of inhomogeneous fibrin networks. Fibers in such networks buckle when in compression. We model this as a loss of stiffness in compression in the stress-strain relations of the homogeneous constitutive model. Problems that model a contracting biological cell in a finite matrix are solved. It is found that matrix displacements and stresses induced by cell contraction decay slower (with distance from the cell) in a compression weakening material than linear elasticity would predict. This points toward a mechanism for long-range cell mechanosensing. In contrast, an expanding cell would induce displacements that decay faster than in a linear elastic matrix.

Modeling Elastic Wave Propagation from an Underground Chemical Explosion Using Higher Order Finite Difference Approximation: Theory, Validation and Application to SPE

NASA Astrophysics Data System (ADS)

Hirakawa, E. T.; Ezzedine, S. M.; Petersson, A.; Sjogreen, B.; Vorobiev, O.; Pitarka, A.; Antoun, T.; Walter, W. R.

2016-12-01

Motions from underground explosions are governed by non-linear hydrodynamic response of material. However, the numerical calculation of this non-linear constitutive behavior is computationally intensive in contrast to the elastic and acoustic linear wave propagation solvers. Here, we develop a hybrid modeling approach with one-way hydrodynamic-to-elastic coupling in three dimensions in order to propagate explosion generated ground motions from the non-linear near-source region to the far-field. Near source motions are computed using GEODYN-L, a Lagrangian hydrodynamics code for high-energy loading of earth materials. Motions on a dense grid of points sampled on two nested shells located beyond the non-linear damaged zone are saved, and then passed to SW4, an anelastic anisotropic fourth order finite difference code for seismic wave modeling. Our coupling strategy is based on the decomposition and uniqueness theorems where motions are introduced into SW4 as a boundary source and continue to propagate as elastic waves at a much lower computational cost than by using GEODYN-L to cover the entire near- and the far-field domain. The accuracy of the numerical calculations and the coupling strategy is demonstrated in cases with a purely elastic medium as well as non-linear medium. Our hybrid modeling approach is applied to SPE-4' and SPE-5 which are the most recent underground chemical explosions conducted at the Nevada National Security Site (NNSS) where the Source Physics Experiments (SPE) are performed. Our strategy by design is capable of incorporating complex non-linear effects near the source as well as volumetric and topographic material heterogeneity along the propagation path to receiver, and provides new prospects for modeling and understanding explosion generated seismic waveforms. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-698608.

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

QUANTITATIVE NON-DESTRUCTIVE EVALUATION (QNDE) OF THE ELASTIC MODULI OF POROUS TIAL ALLOYS

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

Yeheskel, O.

2008-02-28

The elastic moduli of {gamma}-TiA1 were studied in porous samples consolidated by various techniques e.g. cold isostatic pressing (CIP), pressure-less sintering, or hot isostatic pressing (HIP). Porosity linearly affects the dynamic elastic moduli of samples. The results indicate that the sound wave velocities and the elastic moduli affected by the processing route and depend not only on the attained density but also on the consolidation temperature. In this paper we show that there is linear correlation between the shear and the longitudinal sound velocities in porous TiA1. This opens the way to use a single sound velocity as a toolmore » for quantitative non-destructive evaluation (QNDE) of porous TiA1 alloys. Here we demonstrate the applicability of an equation derived from the elastic theory and used previously for porous cubic metals.« less

Instability of fiber-reinforced viscoelastic composite plates to in-plane compressive loads

NASA Technical Reports Server (NTRS)

Chandiramani, N. K.; Librescu, L.

1990-01-01

This study analyzes the stability behavior of unidirectional fiber-reinforced composite plates with viscoelastic material behavior subject to in-plane biaxial compressive edge loads. To predict the effective time-dependent material properties, elastic fibers embedded in a linearly viscoelastic matrix are examined. The micromechanical relations developed for a transversely isotropic medium are discussed along with the correspondence principle of linear viscoelasticity. It is concluded that the stability boundary obtained for a viscoelastic plate is lower (more critical) than its elastic counterpart, and the transverse shear deformation effects are more pronounced in viscoelastic plates than in their elastic counterparts.

Couple stress theory of curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-01-01

New models for plane curved rods based on linear couple stress theory of elasticity have been developed.2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and rotation along with body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby, all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of elasticity, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients have been obtained. Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear couple stress theory of elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scales when taking into account couple stress and rotation effects.

Improved Indentation Test for Measuring Nonlinear Elasticity

NASA Technical Reports Server (NTRS)

Eldridge, Jeffrey I.

2004-01-01

A cylindrical-punch indentation technique has been developed as a means of measuring the nonlinear elastic responses of materials -- more specifically, for measuring the moduli of elasticity of materials in cases in which these moduli vary with applied loads. This technique offers no advantage for characterizing materials that exhibit purely linear elastic responses (constant moduli of elasticity, independent of applied loads). However, the technique offers a significant advantage for characterizing such important materials as plasma-sprayed thermal-barrier coatings, which, in cyclic loading, exhibit nonlinear elasticity with hysteresis related to compaction and sliding within their microstructures.

Mechanical behaviour of the human atria.

PubMed

Bellini, Chiara; Di Martino, Elena S; Federico, Salvatore

2013-07-01

This work was aimed at providing a local mechanical characterisation of tissues from the healthy human atria. Thirty-two tissue specimens were harvested from nine adult subjects whose death was not directly related to cardiovascular diseases. Tissues were kept in Tyrode's solution and tested using a planar biaxial device. Results showed that tissues from healthy human atria undergo large deformations under in-plane distributed tensions roughly corresponding to an in vivo pressure of 15 mmHg. The material was modelled as hyperelastic and a Fung-type elastic strain energy potential was chosen. This class of potentials is based on a function of a quadratic form in the components of the Green-Lagrange strain tensor, and it has been previously proved that the fourth-order tensor of this quadratic form is proportional to the linear elasticity tensor of the linearised theory. This has three important consequences: (i) the coefficients in Fung-type potentials have a precise physical meaning; (ii) whenever a microstructural description for the linear elasticity tensor is available, this is automatically inherited by the Fung-type potential; (iii) because of the presence of the linear elasticity tensor in the definition of a Fung-type potential, each of the three normal stresses is coupled with all three normal strains.We propose to include information on the microstructure of the atrium by writing the linear elasticity tensor as the volumetric-fraction-weighed sum of the linear elasticity tensors of the three constituents of the tissue: the ground matrix, the main fibre family and the secondary fibre family. To the best of our knowledge, this is the first time that a Fung-type potential is given a precise structural meaning, based on the directions and the material properties of the fibres. Because of the coupling between normal strains and normal stresses, this structurally-based Fung-type potential allows for discriminating among all testing protocols in planar biaxial stretch.

A Galerkin approximation for linear elastic shallow shells

NASA Astrophysics Data System (ADS)

Figueiredo, I. N.; Trabucho, L.

1992-03-01

This work is a generalization to shallow shell models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lamé costants.

ZIP2DL: An Elastic-Plastic, Large-Rotation Finite-Element Stress Analysis and Crack-Growth Simulation Program

NASA Technical Reports Server (NTRS)

Deng, Xiaomin; Newman, James C., Jr.

1997-01-01

ZIP2DL is a two-dimensional, elastic-plastic finte element program for stress analysis and crack growth simulations, developed for the NASA Langley Research Center. It has many of the salient features of the ZIP2D program. For example, ZIP2DL contains five material models (linearly elastic, elastic-perfectly plastic, power-law hardening, linear hardening, and multi-linear hardening models), and it can simulate mixed-mode crack growth for prescribed crack growth paths under plane stress, plane strain and mixed state of stress conditions. Further, as an extension of ZIP2D, it also includes a number of new capabilities. The large-deformation kinematics in ZIP2DL will allow it to handle elastic problems with large strains and large rotations, and elastic-plastic problems with small strains and large rotations. Loading conditions in terms of surface traction, concentrated load, and nodal displacement can be applied with a default linear time dependence or they can be programmed according to a user-defined time dependence through a user subroutine. The restart capability of ZIP2DL will make it possible to stop the execution of the program at any time, analyze the results and/or modify execution options and resume and continue the execution of the program. This report includes three sectons: a theoretical manual section, a user manual section, and an example manual secton. In the theoretical secton, the mathematics behind the various aspects of the program are concisely outlined. In the user manual section, a line-by-line explanation of the input data is given. In the example manual secton, three types of examples are presented to demonstrate the accuracy and illustrate the use of this program.

Stiffness optimization of non-linear elastic structures

DOE PAGES

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

2017-11-13

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

A new Hysteretic Nonlinear Energy Sink (HNES)

NASA Astrophysics Data System (ADS)

Tsiatas, George C.; Charalampakis, Aristotelis E.

2018-07-01

The behavior of a new Hysteretic Nonlinear Energy Sink (HNES) coupled to a linear primary oscillator is investigated in shock mitigation. Apart from a small mass and a nonlinear elastic spring of the Duffing oscillator, the HNES is also comprised of a purely hysteretic and a linear elastic spring of potentially negative stiffness, connected in parallel. The Bouc-Wen model is used to describe the force produced by both the purely hysteretic and linear elastic springs. Coupling the primary oscillator with the HNES, three nonlinear equations of motion are derived in terms of the two displacements and the dimensionless hysteretic variable, which are integrated numerically using the analog equation method. The performance of the HNES is examined by quantifying the percentage of the initially induced energy in the primary system that is passively transferred and dissipated by the HNES. Remarkable results are achieved for a wide range of initial input energies. The great performance of the HNES is mostly evidenced when the linear spring stiffness takes on negative values.

Developing ultrasensitive pressure sensor based on graphene nanoribbon: Molecular dynamics simulation

NASA Astrophysics Data System (ADS)

Kwon, Oh Kuen; Lee, Jun Ha; Kim, Ki-Sub; Kang, Jeong Won

2013-01-01

We propose schematics for an ultra-sensitive pressure sensor based on graphene-nanoribbon (GNR) and investigate its electromechanical properties using classical molecular dynamics simulations and piezo-electricity theory. Since the top plate applied to the actual pressure is large whereas the contact area on the GNR is very small, both the sensitivity and the sensing range can be adjusted by controlling the aspect ratio between the top plate and the contact point areas. Our calculation shows that the electrical conductivity of GNRs can be tuned by the applied pressure and the electric conductance of the deflected GNR linearly increases with increasing applied pressure for the linear elastic region in low pressure below the cut-off point. In the curves for both the deflection and potential energy, the linear elastic regime in low pressure was explicitly separated with the non-linear elastic regime in high pressure. The proposed GNR-based nanoelectromechanical devices have great potential for application as electromechanical memory, relay or switching devices.

Stiffness optimization of non-linear elastic structures

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

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

Muscle shear elastic modulus is linearly related to muscle torque over the entire range of isometric contraction intensity.

PubMed

Ateş, Filiz; Hug, François; Bouillard, Killian; Jubeau, Marc; Frappart, Thomas; Couade, Mathieu; Bercoff, Jeremy; Nordez, Antoine

2015-08-01

Muscle shear elastic modulus is linearly related to muscle torque during low-level contractions (<60% of Maximal Voluntary Contraction, MVC). This measurement can therefore be used to estimate changes in individual muscle force. However, it is not known if this relationship remains valid for higher intensities. The aim of this study was to determine: (i) the relationship between muscle shear elastic modulus and muscle torque over the entire range of isometric contraction and (ii) the influence of the size of the region of interest (ROI) used to average the shear modulus value. Ten healthy males performed two incremental isometric little finger abductions. The joint torque produced by Abductor Digiti Minimi was considered as an index of muscle torque and elastic modulus. A high coefficient of determination (R(2)) (range: 0.86-0.98) indicated that the relationship between elastic modulus and torque can be accurately modeled by a linear regression over the entire range (0% to 100% of MVC). The changes in shear elastic modulus as a function of torque were highly repeatable. Lower R(2) values (0.89±0.13 for 1/16 of ROI) and significantly increased absolute errors were observed when the shear elastic modulus was averaged over smaller ROI, half, 1/4 and 1/16 of the full ROI) than the full ROI (mean size: 1.18±0.24cm(2)). It suggests that the ROI should be as large as possible for accurate measurement of muscle shear modulus. Copyright © 2015 Elsevier Ltd. All rights reserved.

Study of critical behavior in concrete during curing by application of dynamic linear and nonlinear means.

PubMed

Lacouture, Jean-Christoph; Johnson, Paul A; Cohen-Tenoudji, Frederic

2003-03-01

The monitoring of both linear and nonlinear elastic properties of a high performance concrete during curing is presented by application of compressional and shear waves. To follow the linear elastic behavior, both compressional and shear waves are used in wide band pulse echo mode. Through the value of the complex reflection coefficient between the cell material (Lucite) and the concrete within the cell, the elastic moduli are calculated. Simultaneously, the transmission of a continuous compressional sine wave at progressively increasing drive levels permits us to calculate the nonlinear properties by extracting the harmonics amplitudes of the signal. Information regarding the chemical evolution of the concrete based upon the reaction of hydration of cement is obtained by monitoring the temperature inside the sample. These different types of measurements are linked together to interpret the critical behavior.

Elastic and mechanical softening in boron-doped diamond

PubMed Central

Liu, Xiaobing; Chang, Yun-Yuan; Tkachev, Sergey N.; Bina, Craig R.; Jacobsen, Steven D.

2017-01-01

Alternative approaches to evaluating the hardness and elastic properties of materials exhibiting physical properties comparable to pure diamond have recently become necessary. The classic linear relationship between shear modulus (G) and Vickers hardness (HV), along with more recent non-linear formulations based on Pugh’s modulus extending into the superhard region (HV > 40 GPa) have guided synthesis and identification of novel superabrasives. These schemes rely on accurately quantifying HV of diamond-like materials approaching or potentially exceeding the hardness of the diamond indenter, leading to debate about methodology and the very definition of hardness. Elasticity measurements on such materials are equally challenging. Here we used a high-precision, GHz-ultrasonic interferometer in conjunction with a newly developed optical contact micrometer and 3D optical microscopy of indentations to evaluate elasticity-hardness relations in the ultrahard range (HV > 80 GPa) by examining single-crystal boron-doped diamond (BDD) with boron contents ranging from 50–3000 ppm. We observe a drastic elastic-mechanical softening in highly doped BDD relative to the trends observed for superhard materials, providing insight into elasticity-hardness relations for ultrahard materials. PMID:28233808

Creeping gaseous flows through elastic tube and annulus micro-configurations

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2016-11-01

Gaseous flows in elastic micro-configurations is relevant to biological systems (e.g. alveolar ducts in the lungs) as well as to applications such as gas actuated soft micro-robots. We here examine the effect of low-Mach-number compressibility on creeping gaseous axial flows through linearly elastic tube and annulus micro-configurations. For steady flows, the leading-order effects of elasticity on the pressure distribution and mass-flux are obtained. For transient flow in a tube with small deformations, elastic effects are shown to be negligible in leading order due to compressibility. We then examine transient flows in annular configurations where the deformation is significant compared with the gap between the inner and outer cylinders defining the annulus. Both compressibility and elasticity are obtained as dominant terms interacting with viscosity. For a sudden flux impulse, the governing non-linear leading order diffusion equation is initially approximated by a porous-medium-equation of order 2.5 for the pressure square. However, as the fluid expand and the pressure decreases, the governing equation degenerates to a porous-medium-equation of order 2 for the pressure.

Elastic and mechanical softening in boron-doped diamond

NASA Astrophysics Data System (ADS)

Liu, Xiaobing; Chang, Yun-Yuan; Tkachev, Sergey N.; Bina, Craig R.; Jacobsen, Steven D.

2017-02-01

Alternative approaches to evaluating the hardness and elastic properties of materials exhibiting physical properties comparable to pure diamond have recently become necessary. The classic linear relationship between shear modulus (G) and Vickers hardness (HV), along with more recent non-linear formulations based on Pugh’s modulus extending into the superhard region (HV > 40 GPa) have guided synthesis and identification of novel superabrasives. These schemes rely on accurately quantifying HV of diamond-like materials approaching or potentially exceeding the hardness of the diamond indenter, leading to debate about methodology and the very definition of hardness. Elasticity measurements on such materials are equally challenging. Here we used a high-precision, GHz-ultrasonic interferometer in conjunction with a newly developed optical contact micrometer and 3D optical microscopy of indentations to evaluate elasticity-hardness relations in the ultrahard range (HV > 80 GPa) by examining single-crystal boron-doped diamond (BDD) with boron contents ranging from 50-3000 ppm. We observe a drastic elastic-mechanical softening in highly doped BDD relative to the trends observed for superhard materials, providing insight into elasticity-hardness relations for ultrahard materials.

Elastic band prediction equations for combined free-weight and elastic band bench presses and squats.

PubMed

Shoepe, Todd C; Ramirez, David A; Almstedt, Hawley C

2010-01-01

Elastic bands added to traditional free-weight techniques have become a part of suggested training routines in recent years. Because of the variable loading patterns of elastic bands (i.e., greater stretch produces greater resistance), it is necessary to quantify the exact loading patterns of bands to identify the volume and intensity of training. The purpose of this study was to determine the length vs. tension properties of multiple sizes of a set of commonly used elastic bands to quantify the resistance that would be applied to free-weight plus elastic bench presses (BP) and squats (SQ). Five elastic bands of varying thickness were affixed to an overhead support beam. Dumbbells of varying weights were progressively added to the free end while the linear deformation was recorded with each subsequent weight increment. The resistance was plotted as a factor of linear deformation, and best-fit nonlinear logarithmic regression equations were then matched to the data. For both the BP and SQ loading conditions and all band thicknesses tested, R values were greater than 0.9623. These data suggest that differences in load exist as a result of the thickness of the elastic band, attachment technique, and type of exercise being performed. Facilities should adopt their own form of loading quantification to match their unique set of circumstances when acquiring, researching, and implementing elastic band and free-weight exercises into the training programs.

A Conforming Multigrid Method for the Pure Traction Problem of Linear Elasticity: Mixed Formulation

NASA Technical Reports Server (NTRS)

Lee, Chang-Ock

1996-01-01

A multigrid method using conforming P-1 finite element is developed for the two-dimensional pure traction boundary value problem of linear elasticity. The convergence is uniform even as the material becomes nearly incompressible. A heuristic argument for acceleration of the multigrid method is discussed as well. Numerical results with and without this acceleration as well as performance estimates on a parallel computer are included.

The Shock and Vibration Digest. Volume 16, Number 11

DTIC Science & Technology

1984-11-01

wave [19], a secular equation for Rayleigh waves on ing, seismic risk, and related problems are discussed. the surface of an anisotropic half-space...waves in an !so- tive equation of an elastic-plastic rack medium was....... tropic linear elastic half-space with plane material used; the coefficient...pair of semi-linear hyperbolic partial differential -- " Conditions under which the equations of motion equations governing slow variations in amplitude

Stability of elastic bending and torsion of uniform cantilever rotor blades in hover with variable structural coupling

NASA Technical Reports Server (NTRS)

Hodges, D. H., Roberta.

1976-01-01

The stability of elastic flap bending, lead-lag bending, and torsion of uniform, untwisted, cantilever rotor blades without chordwise offsets between the elastic, mass, tension, and areodynamic center axes is investigated for the hovering flight condition. The equations of motion are obtained by simplifying the general, nonlinear, partial differential equations of motion of an elastic rotating cantilever blade. The equations are adapted for a linearized stability analysis in the hovering flight condition by prescribing aerodynamic forces, applying Galerkin's method, and linearizing the resulting ordinary differential equations about the equilibrium operating condition. The aerodynamic forces are obtained from strip theory based on a quasi-steady approximation of two-dimensional unsteady airfoil theory. Six coupled mode shapes, calculated from free vibration about the equilibrium operating condition, are used in the linearized stability analysis. The study emphasizes the effects of two types of structural coupling that strongly influence the stability of hingeless rotor blades. The first structural coupling is the linear coupling between flap and lead-lag bending of the rotor blade. The second structural coupling is a nonlinear coupling between flap bending, lead-lag bending, and torsion deflections. Results are obtained for a wide variety of hingeless rotor configurations and operating conditions in order to provide a reasonably complete picture of hingeless rotor blade stability characteristics.

Achieving large linear elasticity and high strength in bulk nanocompsite via synergistic effect

DOE PAGES

Hao, Shijie; Cui, Lishan; Guo, Fangmin; ...

2015-03-09

Elastic strain in bulk metallic materials is usually limited to only a fraction of 1%. Developing bulk metallic materials showing large linear elasticity and high strength has proven to be difficult. Here, based on the synergistic effect between nanowires and orientated martensite NiTi shape memory alloy, we developed an in-situ Nb nanowires-orientated martensitic NiTi matrix composite showing an ultra-large linear elastic strain of 4% and an ultrahigh yield strength of 1.8 GPa. This material also has a high mechanical energy storage efficiency of 96% and a high energy storage density of 36 J/cm 3 that is almost one order ofmore » larger than that of spring steel. It is demonstrated that the synergistic effect allows the exceptional mechanical properties of nanowires to be harvested at macro scale and the mechanical properties of matrix to be greatly improved, resulting in these superior properties. This research provides new avenues for developing advanced composites with superior properties by using effective synergistic effect between components.« less

Approximate non-linear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-03-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-waves scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform (GRT). After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic non-linear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P-wave and S-wave information.

Experiment study and FEM simulation on erythrocytes under linear stretching of optical micromanipulation

NASA Astrophysics Data System (ADS)

Liu, Ying; Song, Huadong; Zhu, Panpan; Lu, Hao; Tang, Qi

2017-08-01

The elasticity of erythrocytes is an important criterion to evaluate the quality of blood. This paper presents a novel research on erythrocytes' elasticity with the application of optical tweezers and the finite element method (FEM) during blood storage. In this work, the erythrocytes with different in vitro times were linearly stretched by trapping force using optical tweezers and the time dependent elasticity of erythrocytes was investigated. The experimental results indicate that the membrane shear moduli of erythrocytes increased with the increasing in vitro time, namely the elasticity was decreasing. Simultaneously, an erythrocyte shell model with two parameters (membrane thickness h and membrane shear modulus H) was built to simulate the linear stretching states of erythrocytes by the FEM, and the simulations conform to the results obtained in the experiment. The evolution process was found that the erythrocytes membrane thicknesses were decreasing. The analysis assumes that the partial proteins and lipid bilayer of erythrocyte membrane were decomposed during the in vitro preservation of blood, which results in thin thickness, weak bending resistance, and losing elasticity of erythrocyte membrane. This study implies that the FEM can be employed to investigate the inward mechanical property changes of erythrocyte in different environments, which also can be a guideline for studying the erythrocyte mechanical state suffered from different diseases.

Soft actuators and soft actuating devices

DOEpatents

Yang, Dian; Whitesides, George M.

2017-10-17

A soft buckling linear actuator is described, including: a plurality of substantially parallel bucklable, elastic structural components each having its longest dimension along a first axis; and a plurality of secondary structural components each disposed between and bridging two adjacent bucklable, elastic structural components; wherein every two adjacent bucklable, elastic structural components and the secondary structural components in-between define a layer comprising a plurality of cells each capable of being connected with a fluid inflation or deflation source; the secondary structural components from two adjacent layers are not aligned along a second axis perpendicular to the first axis; and the secondary structural components are configured not to buckle, the bucklable, elastic structural components are configured to buckle along the second axis to generate a linear force, upon the inflation or deflation of the cells. Methods of actuation using the same are also described.

Nonlocal theory of curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-09-01

New models for plane curved rods based on linear nonlocal theory of elasticity have been developed. The 2-D theory is developed from general 2-D equations of linear nonlocal elasticity using a special curvilinear system of coordinates related to the middle line of the rod along with special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including nonlocal constitutive relations have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of local elasticity, a system of differential equations in terms of displacements for Fourier coefficients has been obtained. First and second order approximations have been considered in detail. Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear nonlocal theory of elasticity which are considered in a special curvilinear system of coordinates related to the middle line of the rod. The obtained equations can be used to calculate stress-strain and to model thin walled structures in micro- and nanoscales when taking into account size dependent and nonlocal effects.

Ultrasonic Characterization of the Linear Elastic Properties of Myocardium and Other Anisotropic Soft Tissues

NASA Astrophysics Data System (ADS)

Hoffmeister, Brentley Keith

1995-01-01

This thesis seeks to contribute to a better understanding of the physics of interaction of ultrasonic waves with inhomogeneous and anisotropic media, one example of which is the human heart. The clinical success of echocardiography has generated a considerable interest in the development of ultrasonic techniques to measure the elastic properties of heart tissue. It is hypothesized that the elastic properties of myocardium are influenced by the interstitial content and organization of collagen. Collagen, which is the main component of tendon, interconnects the muscle cells of the heart to form locally unidirectional myofibers. This thesis therefore employs ultrasonic techniques to characterize the linear elastic properties of both heart and tendon. The linear elastic properties of tissues possessing a unidirectional arrangement of fibers may be described in terms of five independent elastic stiffness coefficients. Three of these coefficients were determined for formalin fixed specimens of bovine Achilles tendon and human myocardium by measuring the velocity of longitudinal mode ultrasonic pulses as a function of angle of propagation relative to the fiber axis of the tissue. The remaining two coefficients were determined by measuring the velocity of transverse mode ultrasonic waves through these tissues. To overcome technical difficulties associated with the extremely high attenuation of transverse mode waves at low megahertz frequencies, a novel measurement system was developed based on the sampled continuous wave technique. Results of these measurements were used to assess the influence of interstitial collagen, and to model the mechanical properties of heart wall.

A global assessment of climate-water quality relationships in large rivers: an elasticity perspective.

PubMed

Jiang, Jiping; Sharma, Ashish; Sivakumar, Bellie; Wang, Peng

2014-01-15

To uncover climate-water quality relationships in large rivers on a global scale, the present study investigates the climate elasticity of river water quality (CEWQ) using long-term monthly records observed at 14 large rivers. Temperature and precipitation elasticities of 12 water quality parameters, highlighted by N- and P-nutrients, are assessed. General observations on elasticity values show the usefulness of this approach to describe the magnitude of stream water quality responses to climate change, which improves that of simple statistical correlation. Sensitivity type, intensity and variability rank of CEWQ are reported and specific characteristics and mechanism of elasticity of nutrient parameters are also revealed. Among them, the performance of ammonia, total phosphorus-air temperature models, and nitrite, orthophosphorus-precipitation models are the best. Spatial and temporal assessment shows that precipitation elasticity is more variable in space than temperature elasticity and that seasonal variation is more evident for precipitation elasticity than for temperature elasticity. Moreover, both anthropogenic activities and environmental factors are found to impact CEWQ for select variables. The major relationships that can be inferred include: (1) human population has a strong linear correlation with temperature elasticity of turbidity and total phosphorus; and (2) latitude has a strong linear correlation with precipitation elasticity of turbidity and N nutrients. As this work improves our understanding of the relation between climate factors and surface water quality, it is potentially helpful for investigating the effect of climate change on water quality in large rivers, such as on the long-term change of nutrient concentrations. © 2013.

Nonlinear isochrones in murine left ventricular pressure-volume loops: how well does the time-varying elastance concept hold?

PubMed

Claessens, T E; Georgakopoulos, D; Afanasyeva, M; Vermeersch, S J; Millar, H D; Stergiopulos, N; Westerhof, N; Verdonck, P R; Segers, P

2006-04-01

The linear time-varying elastance theory is frequently used to describe the change in ventricular stiffness during the cardiac cycle. The concept assumes that all isochrones (i.e., curves that connect pressure-volume data occurring at the same time) are linear and have a common volume intercept. Of specific interest is the steepest isochrone, the end-systolic pressure-volume relationship (ESPVR), of which the slope serves as an index for cardiac contractile function. Pressure-volume measurements, achieved with a combined pressure-conductance catheter in the left ventricle of 13 open-chest anesthetized mice, showed a marked curvilinearity of the isochrones. We therefore analyzed the shape of the isochrones by using six regression algorithms (two linear, two quadratic, and two logarithmic, each with a fixed or time-varying intercept) and discussed the consequences for the elastance concept. Our main observations were 1) the volume intercept varies considerably with time; 2) isochrones are equally well described by using quadratic or logarithmic regression; 3) linear regression with a fixed intercept shows poor correlation (R(2) < 0.75) during isovolumic relaxation and early filling; and 4) logarithmic regression is superior in estimating the fixed volume intercept of the ESPVR. In conclusion, the linear time-varying elastance fails to provide a sufficiently robust model to account for changes in pressure and volume during the cardiac cycle in the mouse ventricle. A new framework accounting for the nonlinear shape of the isochrones needs to be developed.

Dynamical theory of stability for elastic rods with nonlinear curvature and twist

NASA Technical Reports Server (NTRS)

Wauer, J.

1977-01-01

Considering non-linear terms in the curvature as well as in the twist, the governing boundary value problem for lateral bending of elastic, transverse loaded rods is formulated by means of Hamilton's principle. Using the method of small vibrations, the associated linearized equations of stability are derived, which complete the currently accepted relations. The example of the simplest lateral bending problem illustrates the improved effect of the proposed equations.

Using an elastic magnifier to increase power output and performance of heart-beat harvesters

NASA Astrophysics Data System (ADS)

Galbier, Antonio C.; Karami, M. Amin

2017-09-01

Embedded piezoelectric energy harvesting (PEH) systems in medical pacemakers have been a growing and innovative research area. The goal of these systems, at present, is to remove the pacemaker battery, which makes up 60%-80% of the unit, and replace it with a sustainable power source. This requires that energy harvesting systems provide sufficient power, 1-3 μW, for operating a pacemaker. The goal of this work is to develop, test, and simulate cantilevered energy harvesters with a linear elastic magnifier (LEM). This research hopes to provide insight into the interaction between pacemaker energy harvesters and the heart. By introducing the elastic magnifier into linear and nonlinear systems oscillations of the tip are encouraged into high energy orbits and large tip deflections. A continuous nonlinear model is presented for the bistable piezoelectric energy harvesting (BPEH) system and a one-degree-of-freedom linear mass-spring-damper model is presented for the elastic magnifier. The elastic magnifier will not consider the damping negligible, unlike most models. A physical model was created for the bistable structure and formed to an elastic magnifier. A hydrogel was designed for the experimental model for the LEM. Experimental results show that the BPEH coupled with a LEM (BPEH + LEM) produces more power at certain input frequencies and operates a larger bandwidth than a PEH, BPEH, and a standard piezoelectric energy harvester with the elastic magnifier (PEH + LEM). Numerical simulations are consistent with these results. It was observed that the system enters high-energy and high orbit oscillations and that, ultimately, BPEH systems implemented in medical pacemakers can, if designed properly, have enhanced performance if positioned over the heart.

Blocky inversion of multichannel elastic impedance for elastic parameters

NASA Astrophysics Data System (ADS)

Mozayan, Davoud Karami; Gholami, Ali; Siahkoohi, Hamid Reza

2018-04-01

Petrophysical description of reservoirs requires proper knowledge of elastic parameters like P- and S-wave velocities (Vp and Vs) and density (ρ), which can be retrieved from pre-stack seismic data using the concept of elastic impedance (EI). We propose an inversion algorithm which recovers elastic parameters from pre-stack seismic data in two sequential steps. In the first step, using the multichannel blind seismic inversion method (exploited recently for recovering acoustic impedance from post-stack seismic data), high-resolution blocky EI models are obtained directly from partial angle-stacks. Using an efficient total-variation (TV) regularization, each angle-stack is inverted independently in a multichannel form without prior knowledge of the corresponding wavelet. The second step involves inversion of the resulting EI models for elastic parameters. Mathematically, under some assumptions, the EI's are linearly described by the elastic parameters in the logarithm domain. Thus a linear weighted least squares inversion is employed to perform this step. Accuracy of the concept of elastic impedance in predicting reflection coefficients at low and high angles of incidence is compared with that of exact Zoeppritz elastic impedance and the role of low frequency content in the problem is discussed. The performance of the proposed inversion method is tested using synthetic 2D data sets obtained from the Marmousi model and also 2D field data sets. The results confirm the efficiency and accuracy of the proposed method for inversion of pre-stack seismic data.

A Lagrangian meshfree method applied to linear and nonlinear elasticity.

PubMed

Walker, Wade A

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.

A Lagrangian meshfree method applied to linear and nonlinear elasticity

PubMed Central

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code. PMID:29045443

Variation of nanostructures, molecular interactions, and anisotropic elastic moduli of lignocellulosic cell walls with moisture

Treesearch

S. Youssefian; J. E. Jakes; N. Rahbar

2017-01-01

A combination of experimental, theoretical and numerical studies is used to investigate the variation of elastic moduli of lignocellulosic (bamboo) fiber cell walls with moisture content (MC). Our Nanoindentation results show that the longitudinal elastic modulus initially increased to a maximum value at about 3% MC and then decreased linearly with increasing MC. In...

A Review of the Proposed KIsi Offset-Secant Method for Size-Insensitive Linear-Elastic Fracture Toughness Evaluation

NASA Technical Reports Server (NTRS)

James, Mark; Wells, Doug; Allen, Phillip; Wallin, Kim

2017-01-01

Recently proposed modifications to ASTM E399 would provide a new size-insensitive approach to analyzing the force-displacement test record. The proposed size-insensitive linear-elastic fracture toughness, KIsi, targets a consistent 0.5mm crack extension for all specimen sizes by using an offset secant that is a function of the specimen ligament length. The KIsi evaluation also removes the Pmax/PQ criterion and increases the allowable specimen deformation. These latter two changes allow more plasticity at the crack tip, prompting the review undertaken in this work to ensure the validity of this new interpretation of the force-displacement curve. This paper provides a brief review of the proposed KIsi methodology and summarizes a finite element study into the effects of increased crack tip plasticity on the method given the allowance for additional specimen deformation. The study has two primary points of investigation: the effect of crack tip plasticity on compliance change in the force-displacement record and the continued validity of linear-elastic fracture mechanics to describe the crack front conditions. The analytical study illustrates that linear-elastic fracture mechanics assumptions remain valid at the increased deformation limit; however, the influence of plasticity on the compliance change in the test record is problematic. A proposed revision to the validity criteria for the KIsi test method is briefly discussed.

Deformations of a pre-stretched and lubricated finite elastic membrane driven by non-uniform external forcing

NASA Astrophysics Data System (ADS)

Boyko, Evgeniy; Gat, Amir; Bercovici, Moran

2017-11-01

We study viscous-elastic dynamics of a fluid confined between a rigid plate and a finite pre-stretched circular elastic membrane, pinned at its boundaries. The membrane is subjected to forces acting either directly on the membrane or through a pressure distribution in the fluid. Under the assumptions of strong pre-stretching and small deformations of the elastic sheet, and by applying the lubrication approximation for the flow, we derive the Green's function for the resulting linearized 4th order diffusion equation governing the deformation field in cylindrical coordinates. In addition, defining an asymptotic expansion with the ratio of the induced to prescribed tension serving as the small parameter, we reduce the coupled Reynolds and non-linear von-Karman equations to a set of three one-way coupled linear equations. The solutions to these equations provide insight onto the effects of induced tension, and enable simplified prediction of the correction for the deformation field. Funded by the European Research Council (ERC) under the European Union'sHorizon 2020 Research and Innovation Programme, Grant Agreement No. 678734 (MetamorphChip). E.B. is supported by the Adams Fellowship Program.

Estimation of the behavior factor of existing RC-MRF buildings

NASA Astrophysics Data System (ADS)

Vona, Marco; Mastroberti, Monica

2018-01-01

In recent years, several research groups have studied a new generation of analysis methods for seismic response assessment of existing buildings. Nevertheless, many important developments are still needed in order to define more reliable and effective assessment procedures. Moreover, regarding existing buildings, it should be highlighted that due to the low knowledge level, the linear elastic analysis is the only analysis method allowed. The same codes (such as NTC2008, EC8) consider the linear dynamic analysis with behavior factor as the reference method for the evaluation of seismic demand. This type of analysis is based on a linear-elastic structural model subject to a design spectrum, obtained by reducing the elastic spectrum through a behavior factor. The behavior factor (reduction factor or q factor in some codes) is used to reduce the elastic spectrum ordinate or the forces obtained from a linear analysis in order to take into account the non-linear structural capacities. The behavior factors should be defined based on several parameters that influence the seismic nonlinear capacity, such as mechanical materials characteristics, structural system, irregularity and design procedures. In practical applications, there is still an evident lack of detailed rules and accurate behavior factor values adequate for existing buildings. In this work, some investigations of the seismic capacity of the main existing RC-MRF building types have been carried out. In order to make a correct evaluation of the seismic force demand, actual behavior factor values coherent with force based seismic safety assessment procedure have been proposed and compared with the values reported in the Italian seismic code, NTC08.

A 1-D model of the nonlinear dynamics of the human lumbar intervertebral disc

NASA Astrophysics Data System (ADS)

Marini, Giacomo; Huber, Gerd; Püschel, Klaus; Ferguson, Stephen J.

2017-01-01

Lumped parameter models of the spine have been developed to investigate its response to whole body vibration. However, these models assume the behaviour of the intervertebral disc to be linear-elastic. Recently, the authors have reported on the nonlinear dynamic behaviour of the human lumbar intervertebral disc. This response was shown to be dependent on the applied preload and amplitude of the stimuli. However, the mechanical properties of a standard linear elastic model are not dependent on the current deformation state of the system. The aim of this study was therefore to develop a model that is able to describe the axial, nonlinear quasi-static response and to predict the nonlinear dynamic characteristics of the disc. The ability to adapt the model to an individual disc's response was a specific focus of the study, with model validation performed against prior experimental data. The influence of the numerical parameters used in the simulations was investigated. The developed model exhibited an axial quasi-static and dynamic response, which agreed well with the corresponding experiments. However, the model needs further improvement to capture additional peculiar characteristics of the system dynamics, such as the change of mean point of oscillation exhibited by the specimens when oscillating in the region of nonlinear resonance. Reference time steps were identified for specific integration scheme. The study has demonstrated that taking into account the nonlinear-elastic behaviour typical of the intervertebral disc results in a predicted system oscillation much closer to the physiological response than that provided by linear-elastic models. For dynamic analysis, the use of standard linear-elastic models should be avoided, or restricted to study cases where the amplitude of the stimuli is relatively small.

Linear elastic fracture mechanics primer

NASA Technical Reports Server (NTRS)

Wilson, Christopher D.

1992-01-01

This primer is intended to remove the blackbox perception of fracture mechanics computer software by structural engineers. The fundamental concepts of linear elastic fracture mechanics are presented with emphasis on the practical application of fracture mechanics to real problems. Numerous rules of thumb are provided. Recommended texts for additional reading, and a discussion of the significance of fracture mechanics in structural design are given. Griffith's criterion for crack extension, Irwin's elastic stress field near the crack tip, and the influence of small-scale plasticity are discussed. Common stress intensities factor solutions and methods for determining them are included. Fracture toughness and subcritical crack growth are discussed. The application of fracture mechanics to damage tolerance and fracture control is discussed. Several example problems and a practice set of problems are given.

Linear elastic properties derivation from microstructures representative of transport parameters.

PubMed

Hoang, Minh Tan; Bonnet, Guy; Tuan Luu, Hoang; Perrot, Camille

2014-06-01

It is shown that three-dimensional periodic unit cells (3D PUC) representative of transport parameters involved in the description of long wavelength acoustic wave propagation and dissipation through real foam samples may also be used as a standpoint to estimate their macroscopic linear elastic properties. Application of the model yields quantitative agreement between numerical homogenization results, available literature data, and experiments. Key contributions of this work include recognizing the importance of membranes and properties of the base material for the physics of elasticity. The results of this paper demonstrate that a 3D PUC may be used to understand and predict not only the sound absorbing properties of porous materials but also their transmission loss, which is critical for sound insulation problems.

Gaseous Viscous Peeling of Linearly Elastic Substrates

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2017-11-01

We study pressure-driven propagation of gas into a micron-scale gap between two linearly elastic substrates. Applying the lubrication approximation, the governing nonlinear evolution equation describes the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-number compressibility, characteristic to gaseous microflows. Several physical limits allow simplification of the evolution equation and enable solution by self-similarity. During the peeling process the flow-field transitions between the different limits and the respective approximate solutions. The sequence of limits occurring during the propagation dynamics can be related to the thickness of the prewetting layer of the configuration at rest, yielding an approximate description of the entire peeling dynamics. The results are validated by numerical solutions of the evolution equation. Israel Science Foundation 818/13.

The Dynamic Response and Vibration of Functionally Graded Carbon Nanotube-Reinforced Composite (FG-CNTRC) Truncated Conical Shells Resting on Elastic Foundations

PubMed Central

Nguyen Dinh, Duc; Nguyen, Pham Dinh

2017-01-01

Based on the classical shell theory, the linear dynamic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) truncated conical shells resting on elastic foundations subjected to dynamic loads is presented. The truncated conical shells are reinforced by single-walled carbon nanotubes (SWCNTs) that vary according to the linear functions of the shell thickness. The motion equations are solved by the Galerkin method and the fourth-order Runge–Kutta method. In numerical results, the influences of geometrical parameters, elastic foundations, natural frequency parameters, and nanotube volume fraction of FG-CNTRC truncated conical shells are investigated. The proposed results are validated by comparing them with those of other authors. PMID:29057821

Fe-Mg substitution in aluminate spinels: effects on elastic properties investigated by Brillouin scattering

NASA Astrophysics Data System (ADS)

Bruschini, Enrico; Speziale, Sergio; Bosi, Ferdinando; Andreozzi, Giovanni B.

2018-03-01

We investigated by a multi-analytical approach (Brillouin scattering, X-ray diffraction and electron microprobe) the dependence of the elastic properties on the chemical composition of six spinels in the series (Mg1-x ,Fe x )Al2O4 (0 ≤ x ≤ 0.5). With the exception of C 12, all the elastic moduli (C 11, C 44, K S0 and G) are insensitive to chemical composition for low iron concentration, while they decrease linearly for higher Fe2+ content. Only C 12 shows a continuous linear increase with increasing Fe2+ across the whole compositional range under investigation. The high cation disorder showed by the sample with x = 0.202 has little or no influence on the elastic parameters. The range 0.202 < x < 0.388 bounds the percolation threshold (p c) for nearest neighbor interaction of Fe in the cation sublattices of the spinel structure. Below x = 0.202, the iron atoms are diluted in the system and far from each other, and the elastic moduli are nearly constant. Above x = 0.388, Fe atoms form extended interconnected clusters and show a cooperative behavior thus affecting the single-crystal elastic moduli. The elastic anisotropy largely increases with the introduction of Fe2+ in substitution of magnesium in spinel. This behavior is different with respect to other spinels containing transition metals such as Mn2+ and Co2+.

Linear Elastic Waves - Series: Cambridge Texts in Applied Mathematics (No. 26)

NASA Astrophysics Data System (ADS)

Harris, John G.

2001-10-01

Wave propagation and scattering are among the most fundamental processes that we use to comprehend the world around us. While these processes are often very complex, one way to begin to understand them is to study wave propagation in the linear approximation. This is a book describing such propagation using, as a context, the equations of elasticity. Two unifying themes are used. The first is that an understanding of plane wave interactions is fundamental to understanding more complex wave interactions. The second is that waves are best understood in an asymptotic approximation where they are free of the complications of their excitation and are governed primarily by their propagation environments. The topics covered include reflection, refraction, the propagation of interfacial waves, integral representations, radiation and diffraction, and propagation in closed and open waveguides. Linear Elastic Waves is an advanced level textbook directed at applied mathematicians, seismologists, and engineers. Aimed at beginning graduate students Includes examples and exercises Has application in a wide range of disciplines

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

DOE PAGES

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...

2015-11-12

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

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

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

Spatio-Temporal Modelling of the Pre-Eruptive Strain Localization in a Volcanic Edifice Using a Maxwell-Elasto-Brittle Rheology

NASA Astrophysics Data System (ADS)

Dansereau, V.; Got, J. L.

2017-12-01

Before a volcanic eruption, the pressurization of the volcanic edifice by a magma reservoir induces earthquakes and damage in the edifice; damage lowers the strength of the edifice and decreases its elastic properties. Anelastic deformations cumulate and lead to rupture and eruption. These deformations translate into surface displacements, measurable via GPS or InSAR (e.g., Kilauea, southern flank, or Piton de la Fournaise, eastern flank).Attempts to represent these processes are usually based on a linear-elastic rheology. More recently, linear elastic-perfectly plastic or elastic-brittle damage approaches were used to explain the time evolution of the surface displacements in basaltic volcanoes before an eruption. However these models are non-linear elastic, and can not account for the anelastic deformation that occurs during the pre-eruptive process. Therefore, they can not be used to represent the complete eruptive cycle, comprising loading and unloading phases. Here we present a new rheological approach for modelling the eruptive cycle called Maxwell-Elasto-Brittle, which incorporates a viscous-like relaxation of the stresses in an elastic-brittle damage framework. This mechanism allows accounting for the anelastic deformations that cumulate and lead to rupture and eruption. The inclusion of healing processes in this model is another step towards a complete spatio-temporal representation of the eruptive cycle. Plane-strain Maxwell-EB modelling of the deformation of a magma reservoir and volcanic edifice will be presented. The model represents the propagation of damage towards the surface and the progressive localization of the deformation along faults under the pressurization of the magma reservoir. This model allows a complete spatio-temporal representation of the rupture process. We will also discuss how available seismicity records and time series of surface displacements could be used jointly to constrain the model.

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.

Polycrystalline gamma plutonium's elastic moduli versus temperature

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

Migliori, Albert; Betts, J; Trugman, A

2009-01-01

Resonant ultrasound spectroscopy was used to measure the elastic properties of pure polycrystalline {sup 239}Pu in the {gamma} phase. Shear and longitudinal elastic moduli were measured simultaneously and the bulk modulus was computed from them. A smooth, linear, and large decrease of all elastic moduli with increasing temperature was observed. They calculated the Poisson ratio and found that it increases from 0.242 at 519 K to 0.252 at 571 K. These measurements on extremely well characterized pure Pu are in agreement with other reported results where overlap occurs.

Toward efficient biomechanical-based deformable image registration of lungs for image-guided radiotherapy

NASA Astrophysics Data System (ADS)

Al-Mayah, Adil; Moseley, Joanne; Velec, Mike; Brock, Kristy

2011-08-01

Both accuracy and efficiency are critical for the implementation of biomechanical model-based deformable registration in clinical practice. The focus of this investigation is to evaluate the potential of improving the efficiency of the deformable image registration of the human lungs without loss of accuracy. Three-dimensional finite element models have been developed using image data of 14 lung cancer patients. Each model consists of two lungs, tumor and external body. Sliding of the lungs inside the chest cavity is modeled using a frictionless surface-based contact model. The effect of the type of element, finite deformation and elasticity on the accuracy and computing time is investigated. Linear and quadrilateral tetrahedral elements are used with linear and nonlinear geometric analysis. Two types of material properties are applied namely: elastic and hyperelastic. The accuracy of each of the four models is examined using a number of anatomical landmarks representing the vessels bifurcation points distributed across the lungs. The registration error is not significantly affected by the element type or linearity of analysis, with an average vector error of around 2.8 mm. The displacement differences between linear and nonlinear analysis methods are calculated for all lungs nodes and a maximum value of 3.6 mm is found in one of the nodes near the entrance of the bronchial tree into the lungs. The 95 percentile of displacement difference ranges between 0.4 and 0.8 mm. However, the time required for the analysis is reduced from 95 min in the quadratic elements nonlinear geometry model to 3.4 min in the linear element linear geometry model. Therefore using linear tetrahedral elements with linear elastic materials and linear geometry is preferable for modeling the breathing motion of lungs for image-guided radiotherapy applications.

High elastic modulus polymer electrolytes

DOEpatents

Balsara, Nitash Pervez; Singh, Mohit; Eitouni, Hany Basam; Gomez, Enrique Daniel

2013-10-22

A polymer that combines high ionic conductivity with the structural properties required for Li electrode stability is useful as a solid phase electrolyte for high energy density, high cycle life batteries that do not suffer from failures due to side reactions and dendrite growth on the Li electrodes, and other potential applications. The polymer electrolyte includes a linear block copolymer having a conductive linear polymer block with a molecular weight of at least 5000 Daltons, a structural linear polymer block with an elastic modulus in excess of 1.times.10.sup.7 Pa and an ionic conductivity of at least 1.times.10.sup.-5 Scm.sup.-1. The electrolyte is made under dry conditions to achieve the noted characteristics.

Dynamic acousto-elastic testing of concrete with a coda-wave probe: comparison with standard linear and nonlinear ultrasonic techniques.

PubMed

Shokouhi, Parisa; Rivière, Jacques; Lake, Colton R; Le Bas, Pierre-Yves; Ulrich, T J

2017-11-01

The use of nonlinear acoustic techniques in solids consists in measuring wave distortion arising from compliant features such as cracks, soft intergrain bonds and dislocations. As such, they provide very powerful nondestructive tools to monitor the onset of damage within materials. In particular, a recent technique called dynamic acousto-elasticity testing (DAET) gives unprecedented details on the nonlinear elastic response of materials (classical and non-classical nonlinear features including hysteresis, transient elastic softening and slow relaxation). Here, we provide a comprehensive set of linear and nonlinear acoustic responses on two prismatic concrete specimens; one intact and one pre-compressed to about 70% of its ultimate strength. The two linear techniques used are Ultrasonic Pulse Velocity (UPV) and Resonance Ultrasound Spectroscopy (RUS), while the nonlinear ones include DAET (fast and slow dynamics) as well as Nonlinear Resonance Ultrasound Spectroscopy (NRUS). In addition, the DAET results correspond to a configuration where the (incoherent) coda portion of the ultrasonic record is used to probe the samples, as opposed to a (coherent) first arrival wave in standard DAET tests. We find that the two visually identical specimens are indistinguishable based on parameters measured by linear techniques (UPV and RUS). On the contrary, the extracted nonlinear parameters from NRUS and DAET are consistent and orders of magnitude greater for the damaged specimen than those for the intact one. This compiled set of linear and nonlinear ultrasonic testing data including the most advanced technique (DAET) provides a benchmark comparison for their use in the field of material characterization. Copyright © 2017 Elsevier B.V. All rights reserved.

Classical and sequential limit analysis revisited

NASA Astrophysics Data System (ADS)

Leblond, Jean-Baptiste; Kondo, Djimédo; Morin, Léo; Remmal, Almahdi

2018-04-01

Classical limit analysis applies to ideal plastic materials, and within a linearized geometrical framework implying small displacements and strains. Sequential limit analysis was proposed as a heuristic extension to materials exhibiting strain hardening, and within a fully general geometrical framework involving large displacements and strains. The purpose of this paper is to study and clearly state the precise conditions permitting such an extension. This is done by comparing the evolution equations of the full elastic-plastic problem, the equations of classical limit analysis, and those of sequential limit analysis. The main conclusion is that, whereas classical limit analysis applies to materials exhibiting elasticity - in the absence of hardening and within a linearized geometrical framework -, sequential limit analysis, to be applicable, strictly prohibits the presence of elasticity - although it tolerates strain hardening and large displacements and strains. For a given mechanical situation, the relevance of sequential limit analysis therefore essentially depends upon the importance of the elastic-plastic coupling in the specific case considered.

Effects of aging on the architecture of the ileocecal junction in rats

PubMed Central

de Brito, Maria Cícera; Chopard, Renato Paulo; Cury, Diego Pulzatto; Watanabe, Ii Sei; Mendes, Cristina Eusébio; Castelucci, Patricia

2016-01-01

AIM: To evaluate the structural organization of the elastic and collagen fibers in the region of the ileocecal transition in 30 young and old male Wistar rats. METHODS: Histology, immunohistochemistry (IHC), transmission electron microscopy and scanning electron microscopy were employed in this study. The results demonstrated that there was a demarcation of the ileocecal region between the ileum and the cecum in both groups. RESULTS: The connective tissue fibers had different distribution patterns in the two groups. IHC revealed the presence of nitric oxide synthase, enteric neurons and smooth muscle fibers in the ileocecal junctions (ICJs) of both groups. Compared to the young group, the elderly group exhibited an increase in collagen type I fibers, a decrease in collagen type III fibers, a decreased linear density of oxytalan elastic fibers, and a greater linear density of elaunin and mature elastic fibers. CONCLUSION: The results revealed changes in the patterns of distribution of collagen and elastic fibers that may lead to a possible decrease in ICJ functionality. PMID:27602243

Functional forms and price elasticities in a discrete continuous choice model of the residential water demand

NASA Astrophysics Data System (ADS)

Vásquez Lavín, F. A.; Hernandez, J. I.; Ponce, R. D.; Orrego, S. A.

2017-07-01

During recent decades, water demand estimation has gained considerable attention from scholars. From an econometric perspective, the most used functional forms include log-log and linear specifications. Despite the advances in this field and the relevance for policymaking, little attention has been paid to the functional forms used in these estimations, and most authors have not provided justifications for their selection of functional forms. A discrete continuous choice model of the residential water demand is estimated using six functional forms (log-log, full-log, log-quadratic, semilog, linear, and Stone-Geary), and the expected consumption and price elasticity are evaluated. From a policy perspective, our results highlight the relevance of functional form selection for both the expected consumption and price elasticity.

Comparison of the DeWitt metric in general relativity with the fourth-rank constitutive tensors in electrodynamics and in elasticity theory

NASA Astrophysics Data System (ADS)

Hehl, Friedrich W.; Kiefer, Claus

2018-01-01

We perform a short comparison between the local and linear constitutive tensor χ ^{λ ν σ κ } in four-dimensional electrodynamics, the elasticity tensor c^{ijkl} in three-dimensional elasticity theory, and the DeWitt metric G^{abcd} in general relativity, with {a,b,\\ldots =1,2,3}. We find that the DeWitt metric has only six independent components.

An Experimental and Finite Element Investigation into the Nonlinear Material Behavior of Pin-Loaded Composite Laminates

DTIC Science & Technology

1991-01-01

their midsurface counterparts due to the nature of the pin deflection and resulting load transfer. Linear elastic coupon radial stresses also followed... midsurface counterparts. The effects of the nonlinear elastic material behavior were quite evident when viewing the [(0/90)3,01, coupon intralaminar...to the midsurface of the coupon. The nonlinear elastic intralaminar shear stress-strain assumption acted to increase through thickness stresses

Experimental and theoretical studies of spectral alteration in ultrasonic waves resulting from nonlinear elastic response in rock

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

Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr.

1993-11-01

Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime.

Series elastic actuation of an elbow rehabilitation exoskeleton with axis misalignment adaptation.

PubMed

Wu, Kuan-Yi; Su, Yin-Yu; Yu, Ying-Lung; Lin, Kuei-You; Lan, Chao-Chieh

2017-07-01

Powered exoskeletons can facilitate rehabilitation of patients with upper limb disabilities. Designs using rotary motors usually result in bulky exoskeletons to reduce the problem of moving inertia. This paper presents a new linearly actuated elbow exoskeleton that consists of a slider crank mechanism and a linear motor. The linear motor is placed beside the upper arm and closer to shoulder joint. Thus better inertia properties can be achieved while lightweight and compactness are maintained. A passive joint is introduced to compensate for the exoskeleton-elbow misalignment and intersubject size variation. A linear series elastic actuator (SEA) is proposed to obtain accurate force and impedance control at the exoskeleton-elbow interface. Bidirectional actuation between exoskeleton and forearm is verified, which is required for various rehabilitation processes. We expect this exoskeleton can provide a means of robot-aided elbow rehabilitation.

Perception of Elasticity in the Kinetic Illusory Object with Phase Differences in Inducer Motion

PubMed Central

Masuda, Tomohiro; Sato, Kazuki; Murakoshi, Takuma; Utsumi, Ken; Kimura, Atsushi; Shirai, Nobu; Kanazawa, So; Yamaguchi, Masami K.; Wada, Yuji

2013-01-01

Background It is known that subjective contours are perceived even when a figure involves motion. However, whether this includes the perception of rigidity or deformation of an illusory surface remains unknown. In particular, since most visual stimuli used in previous studies were generated in order to induce illusory rigid objects, the potential perception of material properties such as rigidity or elasticity in these illusory surfaces has not been examined. Here, we elucidate whether the magnitude of phase difference in oscillation influences the visual impressions of an object's elasticity (Experiment 1) and identify whether such elasticity perceptions are accompanied by the shape of the subjective contours, which can be assumed to be strongly correlated with the perception of rigidity (Experiment 2). Methodology/Principal Findings In Experiment 1, the phase differences in the oscillating motion of inducers were controlled to investigate whether they influenced the visual impression of an illusory object's elasticity. The results demonstrated that the impression of the elasticity of an illusory surface with subjective contours was systematically flipped with the degree of phase difference. In Experiment 2, we examined whether the subjective contours of a perceived object appeared linear or curved using multi-dimensional scaling analysis. The results indicated that the contours of a moving illusory object were perceived as more curved than linear in all phase-difference conditions. Conclusions/Significance These findings suggest that the phase difference in an object's motion is a significant factor in the material perception of motion-related elasticity. PMID:24205281

The Application of Simulation Method in Isothermal Elastic Natural Gas Pipeline

NASA Astrophysics Data System (ADS)

Xing, Chunlei; Guan, Shiming; Zhao, Yue; Cao, Jinggang; Chu, Yanji

2018-02-01

This Elastic pipeline mathematic model is of crucial importance in natural gas pipeline simulation because of its compliance with the practical industrial cases. The numerical model of elastic pipeline will bring non-linear complexity to the discretized equations. Hence the Newton-Raphson method cannot achieve fast convergence in this kind of problems. Therefore A new Newton Based method with Powell-Wolfe Condition to simulate the Isothermal elastic pipeline flow is presented. The results obtained by the new method aregiven based on the defined boundary conditions. It is shown that the method converges in all cases and reduces significant computational cost.

An analysis of hypercritical states in elastic and inelastic systems

NASA Astrophysics Data System (ADS)

Kowalczk, Maciej

The author raises a wide range of problems whose common characteristic is an analysis of hypercritical states in elastic and inelastic systems. the article consists of two basic parts. The first part primarily discusses problems of modelling hypercritical states, while the second analyzes numerical methods (so-called continuation methods) used to solve non-linear problems. The original approaches for modelling hypercritical states found in this article include the combination of plasticity theory and an energy condition for cracking, accounting for the variability and cyclical nature of the forms of fracture of a brittle material under a die, and the combination of plasticity theory and a simplified description of the phenomenon of localization along a discontinuity line. The author presents analytical solutions of three non-linear problems for systems made of elastic/brittle/plastic and elastic/ideally plastic materials. The author proceeds to discuss the analytical basics of continuation methods and analyzes the significance of the parameterization of non-linear problems, provides a method for selecting control parameters based on an analysis of the rank of a rectangular matrix of a uniform system of increment equations, and also provides a new method for selecting an equilibrium path originating from a bifurcation point. The author provides a general outline of continuation methods based on an analysis of the rank of a matrix of a corrective system of equations. The author supplements his theoretical solutions with numerical solutions of non-linear problems for rod systems and problems of the plastic disintegration of a notched rectangular plastic plate.

Elastic and viscoelastic mechanical properties of brain tissues on the implanting trajectory of sub-thalamic nucleus stimulation.

PubMed

Li, Yan; Deng, Jianxin; Zhou, Jun; Li, Xueen

2016-11-01

Corresponding to pre-puncture and post-puncture insertion, elastic and viscoelastic mechanical properties of brain tissues on the implanting trajectory of sub-thalamic nucleus stimulation are investigated, respectively. Elastic mechanical properties in pre-puncture are investigated through pre-puncture needle insertion experiments using whole porcine brains. A linear polynomial and a second order polynomial are fitted to the average insertion force in pre-puncture. The Young's modulus in pre-puncture is calculated from the slope of the two fittings. Viscoelastic mechanical properties of brain tissues in post-puncture insertion are investigated through indentation stress relaxation tests for six interested regions along a planned trajectory. A linear viscoelastic model with a Prony series approximation is fitted to the average load trace of each region using Boltzmann hereditary integral. Shear relaxation moduli of each region are calculated using the parameters of the Prony series approximation. The results show that, in pre-puncture insertion, needle force almost increases linearly with needle displacement. Both fitting lines can perfectly fit the average insertion force. The Young's moduli calculated from the slope of the two fittings are worthy of trust to model linearly or nonlinearly instantaneous elastic responses of brain tissues, respectively. In post-puncture insertion, both region and time significantly affect the viscoelastic behaviors. Six tested regions can be classified into three categories in stiffness. Shear relaxation moduli decay dramatically in short time scales but equilibrium is never truly achieved. The regional and temporal viscoelastic mechanical properties in post-puncture insertion are valuable for guiding probe insertion into each region on the implanting trajectory.

Elastic collisions of classical point particles on a finite frictionless linear track with perfectly reflecting endpoints

NASA Astrophysics Data System (ADS)

DeLuca, R.

2006-03-01

Repeated elastic collisions of point particles on a finite frictionless linear track with perfectly reflecting endpoints are considered. The problem is analysed by means of an elementary linear algebra approach. It is found that, starting with a state consisting of a projectile particle in motion at constant velocity and a target particle at rest in a fixed known position, the points at which collisions occur on track, when plotted versus progressive numerals, corresponding to the collisions themselves, show periodic patterns for a rather large choice of values of the initial position x(0) and on the mass ratio r. For certain values of these parameters, however, only regular behaviour over a large number of collisions is detected.

The elastic properties of woven polymeric fabric

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

Warren, W.E.

1989-01-01

The in-plane linear elastic constants of woven fabric are determined in terms of the specific fabric microstructure. The fabric is assumed to be a spatially periodic interlaced network of orthogonal yarns and the individual yarns are modeled as extensible elastica. These results indicate that a significant coupling of bending and stretching effects occurs during deformation. Results of this theoretical analysis compare favorable with measured in-plane elastic constants for Vincel yarn fabrics. 17 refs., 2 figs., 1 tab.

Calculation of skin-stiffener interface stresses in stiffened composite panels

NASA Technical Reports Server (NTRS)

Cohen, David; Hyer, Michael W.

1987-01-01

A method for computing the skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The finite-element analysis is standard, while the elasticity solution is based on an eigenvalue expansion of the stress functions. The eigenvalue expansion is assumed to be valid in the local flange termination region and is coupled with the finite-element analysis using collocation of stresses on the local region boundaries. Accuracy and convergence of the local elasticity solution are assessed using a geometrically linear analysis. Using this analysis procedure, the influence of geometric nonlinearities and stiffener parameters on the skin-stiffener interface stresses is evaluated.

A novel method for calculating the energy barriers for carbon diffusion in ferrite under heterogeneous stress

NASA Astrophysics Data System (ADS)

Tchitchekova, Deyana S.; Morthomas, Julien; Ribeiro, Fabienne; Ducher, Roland; Perez, Michel

2014-07-01

A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ˜3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress.

A novel method for calculating the energy barriers for carbon diffusion in ferrite under heterogeneous stress.

PubMed

Tchitchekova, Deyana S; Morthomas, Julien; Ribeiro, Fabienne; Ducher, Roland; Perez, Michel

2014-07-21

A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ∼3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress.

New non-linear model of groundwater recharge: Inclusion of memory, heterogeneity and visco-elasticity

NASA Astrophysics Data System (ADS)

Spannenberg, Jescica; Atangana, Abdon; Vermeulen, P. D.

2017-09-01

Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.

The non-linear response of a muscle in transverse compression: assessment of geometry influence using a finite element model.

PubMed

Gras, Laure-Lise; Mitton, David; Crevier-Denoix, Nathalie; Laporte, Sébastien

2012-01-01

Most recent finite element models that represent muscles are generic or subject-specific models that use complex, constitutive laws. Identification of the parameters of such complex, constitutive laws could be an important limit for subject-specific approaches. The aim of this study was to assess the possibility of modelling muscle behaviour in compression with a parametric model and a simple, constitutive law. A quasi-static compression test was performed on the muscles of dogs. A parametric finite element model was designed using a linear, elastic, constitutive law. A multi-variate analysis was performed to assess the effects of geometry on muscle response. An inverse method was used to define Young's modulus. The non-linear response of the muscles was obtained using a subject-specific geometry and a linear elastic law. Thus, a simple muscle model can be used to have a bio-faithful, biomechanical response.

Large poroelastic deformation of a soft material

NASA Astrophysics Data System (ADS)

MacMinn, Christopher W.; Dufresne, Eric R.; Wettlaufer, John S.

2014-11-01

Flow through a porous material will drive mechanical deformation when the fluid pressure becomes comparable to the stiffness of the solid skeleton. This has applications ranging from hydraulic fracture for recovery of shale gas, where fluid is injected at high pressure, to the mechanics of biological cells and tissues, where the solid skeleton is very soft. The traditional linear theory of poroelasticity captures this fluid-solid coupling by combining Darcy's law with linear elasticity. However, linear elasticity is only volume-conservative to first order in the strain, which can become problematic when damage, plasticity, or extreme softness lead to large deformations. Here, we compare the predictions of linear poroelasticity with those of a large-deformation framework in the context of two model problems. We show that errors in volume conservation are compounded and amplified by coupling with the fluid flow, and can become important even when the deformation is small. We also illustrate these results with a laboratory experiment.

Importance of elastic finite-size effects: Neutral defects in ionic compounds

DOE PAGES

Burr, P. A.; Cooper, M. W. D.

2017-09-15

Small system sizes are a well known source of error in DFT calculations, yet computational constraints frequently dictate the use of small supercells, often as small as 96 atoms in oxides and compound semiconductors. In ionic compounds, electrostatic finite size effects have been well characterised, but self-interaction of charge neutral defects is often discounted or assumed to follow an asymptotic behaviour and thus easily corrected with linear elastic theory. Here we show that elastic effect are also important in the description of defects in ionic compounds and can lead to qualitatively incorrect conclusions if inadequatly small supercells are used; moreover,more » the spurious self-interaction does not follow the behaviour predicted by linear elastic theory. Considering the exemplar cases of metal oxides with fluorite structure, we show that numerous previous studies, employing 96-atom supercells, misidentify the ground state structure of (charge neutral) Schottky defects. We show that the error is eliminated by employing larger cells (324, 768 and 1500 atoms), and careful analysis determines that elastic effects, not electrostatic, are responsible. The spurious self-interaction was also observed in non-oxide ionic compounds and irrespective of the computational method used, thereby resolving long standing discrepancies between DFT and force-field methods, previously attributed to the level of theory. The surprising magnitude of the elastic effects are a cautionary tale for defect calculations in ionic materials, particularly when employing computationally expensive methods (e.g. hybrid functionals) or when modelling large defect clusters. We propose two computationally practicable methods to test the magnitude of the elastic self-interaction in any ionic system. In commonly studies oxides, where electrostatic effects would be expected to be dominant, it is the elastic effects that dictate the need for larger supercells | greater than 96 atoms.« less

Importance of elastic finite-size effects: Neutral defects in ionic compounds

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

Burr, P. A.; Cooper, M. W. D.

Small system sizes are a well known source of error in DFT calculations, yet computational constraints frequently dictate the use of small supercells, often as small as 96 atoms in oxides and compound semiconductors. In ionic compounds, electrostatic finite size effects have been well characterised, but self-interaction of charge neutral defects is often discounted or assumed to follow an asymptotic behaviour and thus easily corrected with linear elastic theory. Here we show that elastic effect are also important in the description of defects in ionic compounds and can lead to qualitatively incorrect conclusions if inadequatly small supercells are used; moreover,more » the spurious self-interaction does not follow the behaviour predicted by linear elastic theory. Considering the exemplar cases of metal oxides with fluorite structure, we show that numerous previous studies, employing 96-atom supercells, misidentify the ground state structure of (charge neutral) Schottky defects. We show that the error is eliminated by employing larger cells (324, 768 and 1500 atoms), and careful analysis determines that elastic effects, not electrostatic, are responsible. The spurious self-interaction was also observed in non-oxide ionic compounds and irrespective of the computational method used, thereby resolving long standing discrepancies between DFT and force-field methods, previously attributed to the level of theory. The surprising magnitude of the elastic effects are a cautionary tale for defect calculations in ionic materials, particularly when employing computationally expensive methods (e.g. hybrid functionals) or when modelling large defect clusters. We propose two computationally practicable methods to test the magnitude of the elastic self-interaction in any ionic system. In commonly studies oxides, where electrostatic effects would be expected to be dominant, it is the elastic effects that dictate the need for larger supercells | greater than 96 atoms.« less

Importance of elastic finite-size effects: Neutral defects in ionic compounds

NASA Astrophysics Data System (ADS)

Burr, P. A.; Cooper, M. W. D.

2017-09-01

Small system sizes are a well-known source of error in density functional theory (DFT) calculations, yet computational constraints frequently dictate the use of small supercells, often as small as 96 atoms in oxides and compound semiconductors. In ionic compounds, electrostatic finite-size effects have been well characterized, but self-interaction of charge-neutral defects is often discounted or assumed to follow an asymptotic behavior and thus easily corrected with linear elastic theory. Here we show that elastic effects are also important in the description of defects in ionic compounds and can lead to qualitatively incorrect conclusions if inadequately small supercells are used; moreover, the spurious self-interaction does not follow the behavior predicted by linear elastic theory. Considering the exemplar cases of metal oxides with fluorite structure, we show that numerous previous studies, employing 96-atom supercells, misidentify the ground-state structure of (charge-neutral) Schottky defects. We show that the error is eliminated by employing larger cells (324, 768, and 1500 atoms), and careful analysis determines that elastic, not electrostatic, effects are responsible. The spurious self-interaction was also observed in nonoxide ionic compounds irrespective of the computational method used, thereby resolving long-standing discrepancies between DFT and force-field methods, previously attributed to the level of theory. The surprising magnitude of the elastic effects is a cautionary tale for defect calculations in ionic materials, particularly when employing computationally expensive methods (e.g., hybrid functionals) or when modeling large defect clusters. We propose two computationally practicable methods to test the magnitude of the elastic self-interaction in any ionic system. In commonly studied oxides, where electrostatic effects would be expected to be dominant, it is the elastic effects that dictate the need for larger supercells: greater than 96 atoms.

Fillet Weld Stress Using Finite Element Methods

NASA Technical Reports Server (NTRS)

Lehnhoff, T. F.; Green, G. W.

1985-01-01

Average elastic Von Mises equivalent stresses were calculated along the throat of a single lap fillet weld. The average elastic stresses were compared to initial yield and to plastic instability conditions to modify conventional design formulas is presented. The factor is a linear function of the thicknesses of the parent plates attached by the fillet weld.

Wave-front singularities for two-dimensional anisotropic elastic waves.

NASA Technical Reports Server (NTRS)

Payton, R. G.

1972-01-01

Wavefront singularities for the displacement functions, associated with the radiation of linear elastic waves from a point source embedded in a finitely strained two-dimensional elastic solid, are examined in detail. It is found that generally the singularities are of order d to the -1/2 power, where d measures distance away from the front. However, in certain exceptional cases singularities of order d to the -n power, where n = 1/4, 2/3, 3/4, may be encountered.

Finite Deformations and Internal Forces in Elastic-Plastic Crystals: Interpretations From Nonlinear Elasticity and Anharmonic Lattice Statics

DTIC Science & Technology

2009-09-01

Sec. 2, while the latter ase—which implicitly includes the effects of image forces of efects in neighboring volume elements—may be more practical rom...versetzungen und eigenspannungen,” Arch . Ration. Mech. Anal., 4, pp. 273–334. 25 Lee, E. H., 1969, “Elastic-Plastic Deformation at Finite Strains,” ASME J...Rev., 73, pp. 373–382. 27 Kroner, E., and Seeger, A., 1959, “Nicht-Lineare Elastizitatstheorie der Verset- zungen und Eigenspannungen,” Arch . Ration

Ab-initio study of electronic structure and elastic properties of ZrC

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

Mund, H. S., E-mail: hmoond@gmail.com; Ahuja, B. L.

2016-05-23

The electronic and elastic properties of ZrC have been investigated using the linear combination of atomic orbitals method within the framework of density functional theory. Different exchange-correlation functionals are taken into account within generalized gradient approximation. We have computed energy bands, density of states, elastic constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, lattice parameters and pressure derivative of the bulk modulus by calculating ground state energy of the rock salt structure type ZrC.

How tall can gelatin towers be? An introduction to elasticity and buckling

NASA Astrophysics Data System (ADS)

Taberlet, Nicolas; Ferrand, Jérémy; Camus, Élise; Lachaud, Léa; Plihon, Nicolas

2017-12-01

The stability of elastic towers is studied through simple hands-on experiments. Using gelatin-based stackable bricks, one can investigate the maximum height a simple structure can reach before collapsing. We show through experiments and by using the classical linear elastic theory that the main limitation to the height of such towers is the buckling of the elastic structures under their own weight. Moreover, the design and architecture of the towers can be optimized to greatly improve their resistance to self-buckling. To this aim, the maximum height of hollow and tapered towers is investigated. The experimental and theoretical developments presented in this paper can help students grasp the fundamental concepts in elasticity and mechanical stability.

Emergence of linear elasticity from the atomistic description of matter

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

Cakir, Abdullah, E-mail: acakir@ntu.edu.sg; Pica Ciamarra, Massimo; Dipartimento di Scienze Fisiche, CNR–SPIN, Università di Napoli Federico II, I-80126 Napoli

2016-08-07

We investigate the emergence of the continuum elastic limit from the atomistic description of matter at zero temperature considering how locally defined elastic quantities depend on the coarse graining length scale. Results obtained numerically investigating different model systems are rationalized in a unifying picture according to which the continuum elastic limit emerges through a process determined by two system properties, the degree of disorder, and a length scale associated to the transverse low-frequency vibrational modes. The degree of disorder controls the emergence of long-range local shear stress and shear strain correlations, while the length scale influences the amplitude of themore » fluctuations of the local elastic constants close to the jamming transition.« less

Micromechanical analysis on anisotropy of structured magneto-rheological elastomer

NASA Astrophysics Data System (ADS)

Li, R.; Zhang, Z.; Chen, S. W.; Wang, X. J.

2015-07-01

This paper investigates the equivalent elastic modulus of structured magneto-rheological elastomer (MRE) in the absence of magnetic field. We assume that both matrix and ferromagnetic particles are linear elastic materials, and ferromagnetic particles are embedded in matrix with layer-like structure. The structured composite could be divided into matrix layer and reinforced layer, in which the reinforced layer is composed of matrix and the homogenously distributed ferromagnetic particles in matrix. The equivalent elastic modulus of reinforced layer is analysed by the Mori-Tanaka method. Finite Element Method (FEM) is also carried out to illustrate the relationship between the elastic modulus and the volume fraction of ferromagnetic particles. The results show that the anisotropy of elastic modulus becomes noticeable, as the volume fraction of particles increases.

Envelope of coda waves for a double couple source due to non-linear elasticity

NASA Astrophysics Data System (ADS)

Calisto, Ignacia; Bataille, Klaus

2014-10-01

Non-linear elasticity has recently been considered as a source of scattering, therefore contributing to the coda of seismic waves, in particular for the case of explosive sources. This idea is analysed further here, theoretically solving the expression for the envelope of coda waves generated by a point moment tensor in order to compare with earthquake data. For weak non-linearities, one can consider each point of the non-linear medium as a source of scattering within a homogeneous and linear medium, for which Green's functions can be used to compute the total displacement of scattered waves. These sources of scattering have specific radiation patterns depending on the incident and scattered P or S waves, respectively. In this approach, the coda envelope depends on three scalar parameters related to the specific non-linearity of the medium; however these parameters only change the scale of the coda envelope. The shape of the coda envelope is sensitive to both the source time function and the intrinsic attenuation. We compare simulations using this model with data from earthquakes in Taiwan, with a good fit.

Elastic and Photoelastic Properties of M(NO3)2, MO (M = Mg, Ca, Sr, Ba)

NASA Astrophysics Data System (ADS)

Zhuravlev, Yu. N.; Korabel'nikov, D. V.

2017-05-01

The paper deals with ab initio investigations of elastic and photoelastic properties of oxides and nitrates of alkaline-earth metals. In gradient approximation of the density functional theory (DFT), these properties are studied with the use of the linear combination of the atomic orbital technique. DFT calculations are done with the CRYSTAL 14 software package. The paper introduces the elastic and photoelastic constants, anisotropy parameters for single-crystalline phases and the elastic modules, hardness, Poisson ratio for polycrystalline phases. Such parameters as sonic speed, Debye temperature, thermal conductivity, and Gruneisen parameter are estimated herein. For the fist time, mechanical stability, anisotropy of elastic and photoelastic properties and their dependences are investigated ab initio in this paper. Experimental results on elastic and photoelastic properties of oxides and nitrates are in good agreement with theoretical calculations.

Relationship between tendon stiffness and failure: a metaanalysis

PubMed Central

LaCroix, Andrew S.; Duenwald-Kuehl, Sarah E.; Lakes, Roderic S.

2013-01-01

Tendon is a highly specialized, hierarchical tissue designed to transfer forces from muscle to bone; complex viscoelastic and anisotropic behaviors have been extensively characterized for specific subsets of tendons. Reported mechanical data consistently show a pseudoelastic, stress-vs.-strain behavior with a linear slope after an initial toe region. Many studies report a linear, elastic modulus, or Young's modulus (hereafter called elastic modulus) and ultimate stress for their tendon specimens. Individually, these studies are unable to provide a broader, interstudy understanding of tendon mechanical behavior. Herein we present a metaanalysis of pooled mechanical data from a representative sample of tendons from different species. These data include healthy tendons and those altered by injury and healing, genetic modification, allograft preparation, mechanical environment, and age. Fifty studies were selected and analyzed. Despite a wide range of mechanical properties between and within species, elastic modulus and ultimate stress are highly correlated (R2 = 0.785), suggesting that tendon failure is highly strain-dependent. Furthermore, this relationship was observed to be predictable over controlled ranges of elastic moduli, as would be typical of any individual species. With the knowledge gained through this metaanalysis, noninvasive tools could measure elastic modulus in vivo and reasonably predict ultimate stress (or structural compromise) for diseased or injured tendon. PMID:23599401

Phase field benchmark problems for dendritic growth and linear elasticity

DOE PAGES

Jokisaari, Andrea M.; Voorhees, P. W.; Guyer, Jonathan E.; ...

2018-03-26

We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from other members in the phase field community. As the integrated computational materials engineering (ICME) approach to materials design has gained traction, there is an increasing need for quantitative phase field results. New algorithms and numerical implementations increase computational capabilities, necessitating standard problems to evaluate their impact on simulated microstructure evolution as well as their computational performance. We propose one benchmark problem formore » solidifiication and dendritic growth in a single-component system, and one problem for linear elasticity via the shape evolution of an elastically constrained precipitate. We demonstrate the utility and sensitivity of the benchmark problems by comparing the results of 1) dendritic growth simulations performed with different time integrators and 2) elastically constrained precipitate simulations with different precipitate sizes, initial conditions, and elastic moduli. As a result, these numerical benchmark problems will provide a consistent basis for evaluating different algorithms, both existing and those to be developed in the future, for accuracy and computational efficiency when applied to simulate physics often incorporated in phase field models.« less

Micropolar curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-01-01

New models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin.High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors,vectors of displacements and rotation and body force shave been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking in to account micropolar couple stress and rotation effects.

Effect of Liquid Viscosity on Dispersion of Quasi-Lamb Waves in an Elastic-Layer-Viscous-Liquid-Layer System

NASA Astrophysics Data System (ADS)

Guz, A. N.; Bagno, A. M.

2017-07-01

The dispersion curves are constructed and propagation of quasi-Lamb waves are studied for wide range of frequencies based on the Navier -Stokes three-dimensional linearized equations for a viscous liquid and linear equations of the classical theory of elasticity for an elastic layer. For a thick liquid layer, the effect of the viscosity of the liquid and the thickness of elastic and liquid layers on the phase velocities and attenuation coefficients of quasi-Lamb modes is analyzed. It is shown that in the case of a thick liquid layer for all modes, there are elastic layers of certain thickness with minimal effect of liquid viscosity on the phase velocities and attenuation coefficients of modes. It is also discovered that for some modes, there are both certain thicknesses and certain ranges of thickness where the effect of liquid viscosity on the phase velocities and attenuation coefficients of these modes is considerable. We ascertain that liquid viscosity promotes decrease of the penetration depth of the lowest quasi-Lamb mode into the liquid. The developed approach and the obtained results make it possible to ascertain for wave processes the limits of applicability of the model of ideal compressible fluid. Numerical results in the form of graphs are adduced and analyzed.

Experimental investigation of Rayleigh Taylor instability in elastic-plastic materials

NASA Astrophysics Data System (ADS)

Haley, Aaron Alan; Banerjee, Arindam

2010-11-01

The interface of an elastic-plastic plate accelerated by a fluid of lower density is Rayleigh Taylor (RT) unstable, the growth being mitigated by the mechanical strength of the plate. The instability is observed when metal plates are accelerated by high explosives, in explosive welding, and in volcanic island formation due to the strength of the inner crust. In contrast to the classical case involving Newtonian fluids, RT instability in accelerated solids is not well understood. The difficulties for constructing a theory for the linear growth phase in solids is essentially due to the character of elastic-plastic constitutive properties which has a nonlinear dependence on the magnitude of the rate of deformation. Experimental investigation of the phenomena is difficult due to the exceedingly small time scales (in high energy density experiments) and large measurement uncertainties of material properties. We performed experiments on our Two-Wheel facility to study the linear stage of the incompressible RT instability in elastic-plastic materials (yogurt) whose properties were well characterized. Rotation of the wheels imparted a constant centrifugal acceleration on the material interface that was cut with a small sinusoidal ripple. The controlled initial conditions and precise acceleration amplitudes are levied to investigate transition from elastic to plastic deformation and allow accurate and detailed measurements of flow properties.

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part I: Linear Theory

NASA Technical Reports Server (NTRS)

Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

2014-01-01

Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports. The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness.

Phase field benchmark problems for dendritic growth and linear elasticity

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

Jokisaari, Andrea M.; Voorhees, P. W.; Guyer, Jonathan E.

We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from other members in the phase field community. As the integrated computational materials engineering (ICME) approach to materials design has gained traction, there is an increasing need for quantitative phase field results. New algorithms and numerical implementations increase computational capabilities, necessitating standard problems to evaluate their impact on simulated microstructure evolution as well as their computational performance. We propose one benchmark problem formore » solidifiication and dendritic growth in a single-component system, and one problem for linear elasticity via the shape evolution of an elastically constrained precipitate. We demonstrate the utility and sensitivity of the benchmark problems by comparing the results of 1) dendritic growth simulations performed with different time integrators and 2) elastically constrained precipitate simulations with different precipitate sizes, initial conditions, and elastic moduli. As a result, these numerical benchmark problems will provide a consistent basis for evaluating different algorithms, both existing and those to be developed in the future, for accuracy and computational efficiency when applied to simulate physics often incorporated in phase field models.« less

Theoretical investigations on structural, elastic and electronic properties of thallium halides

NASA Astrophysics Data System (ADS)

Singh, Rishi Pal; Singh, Rajendra Kumar; Rajagopalan, Mathrubutham

2011-04-01

Theoretical investigations on structural, elastic and electronic properties, viz. ground state lattice parameter, elastic moduli and density of states, of thallium halides (viz. TlCl and TlBr) have been made using the full potential linearized augmented plane wave method within the generalized gradient approximation (GGA). The ground state lattice parameter and bulk modulus and its pressure derivative have been obtained using optimization method. Young's modulus, shear modulus, Poisson ratio, sound velocities for longitudinal and shear waves, Debye average velocity, Debye temperature and Grüneisen parameter have also been calculated for these compounds. Calculated structural, elastic and other parameters are in good agreement with the available data.

Approximate formulas for elasticity of the Tornquist functions and some their advantages

NASA Astrophysics Data System (ADS)

Issin, Meyram

2017-09-01

In this article functions of demand for prime necessity, second necessity and luxury goods depending on the income are considered. These functions are called Tornquist functions. By means of the return model the demand for prime necessity goods and second necessity goods are approximately described. Then on the basis of a method of the smallest squares approximate formulas for elasticity of these Tornquist functions are received. To receive an approximate formula for elasticity of function of demand for luxury goods, the linear asymptotic formula is constructed for this function. Some benefits of approximate formulas for elasticity of Tornquist functions are specified.

Nanoparticle amount, and not size, determines chain alignment and nonlinear hardening in polymer nanocomposites

PubMed Central

Varol, H. Samet; Meng, Fanlong; Hosseinkhani, Babak; Malm, Christian; Bonn, Daniel; Bonn, Mischa; Zaccone, Alessio

2017-01-01

Polymer nanocomposites—materials in which a polymer matrix is blended with nanoparticles (or fillers)—strengthen under sufficiently large strains. Such strain hardening is critical to their function, especially for materials that bear large cyclic loads such as car tires or bearing sealants. Although the reinforcement (i.e., the increase in the linear elasticity) by the addition of filler particles is phenomenologically understood, considerably less is known about strain hardening (the nonlinear elasticity). Here, we elucidate the molecular origin of strain hardening using uniaxial tensile loading, microspectroscopy of polymer chain alignment, and theory. The strain-hardening behavior and chain alignment are found to depend on the volume fraction, but not on the size of nanofillers. This contrasts with reinforcement, which depends on both volume fraction and size of nanofillers, potentially allowing linear and nonlinear elasticity of nanocomposites to be tuned independently. PMID:28377517

ELASTIC NET FOR COX'S PROPORTIONAL HAZARDS MODEL WITH A SOLUTION PATH ALGORITHM.

PubMed

Wu, Yichao

2012-01-01

For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox's proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox's proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems.

First-principles study of structural stability, electronic, optical and elastic properties of binary intermetallic: PtZr

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

Pagare, Gitanjali, E-mail: gita-pagare@yahoo.co.in; Jain, Ekta, E-mail: jainekta05@gmail.com; Sanyal, S. P., E-mail: sps.physicsbu@gmail.com

2016-05-06

Structural, electronic, optical and elastic properties of PtZr have been studied using the full-potential linearized augmented plane wave (FP-LAPW) method within density functional theory (DFT). The energy against volume and enthalpy vs. pressure variation in three different structures i.e. B{sub 1}, B{sub 2} and B{sub 3} for PtZr has been presented. The equilibrium lattice parameter, bulk modulus and its pressure derivative have been obtained using optimization method for all the three phases. Furthermore, electronic structure was discussed to reveal the metallic character of the present compound. The linear optical properties are also studied under zero pressure for the first time.more » Results on elastic properties are obtained using generalized gradient approximation (GGA) for exchange correlation potentials. Ductile nature of PtZr compound is predicted in accordance with Pugh’s criteria.« less

Calculation of open and closed system elastic coefficients for multicomponent solids

NASA Astrophysics Data System (ADS)

Mishin, Y.

2015-06-01

Thermodynamic equilibrium in multicomponent solids subject to mechanical stresses is a complex nonlinear problem whose exact solution requires extensive computations. A few decades ago, Larché and Cahn proposed a linearized solution of the mechanochemical equilibrium problem by introducing the concept of open system elastic coefficients [Acta Metall. 21, 1051 (1973), 10.1016/0001-6160(73)90021-7]. Using the Ni-Al solid solution as a model system, we demonstrate that open system elastic coefficients can be readily computed by semigrand canonical Monte Carlo simulations in conjunction with the shape fluctuation approach. Such coefficients can be derived from a single simulation run, together with other thermodynamic properties needed for prediction of compositional fields in solid solutions containing defects. The proposed calculation approach enables streamlined solutions of mechanochemical equilibrium problems in complex alloys. Second order corrections to the linear theory are extended to multicomponent systems.

Force sensing using 3D displacement measurements in linear elastic bodies

NASA Astrophysics Data System (ADS)

Feng, Xinzeng; Hui, Chung-Yuen

2016-07-01

In cell traction microscopy, the mechanical forces exerted by a cell on its environment is usually determined from experimentally measured displacement by solving an inverse problem in elasticity. In this paper, an innovative numerical method is proposed which finds the "optimal" traction to the inverse problem. When sufficient regularization is applied, we demonstrate that the proposed method significantly improves the widely used approach using Green's functions. Motivated by real cell experiments, the equilibrium condition of a slowly migrating cell is imposed as a set of equality constraints on the unknown traction. Our validation benchmarks demonstrate that the numeric solution to the constrained inverse problem well recovers the actual traction when the optimal regularization parameter is used. The proposed method can thus be applied to study general force sensing problems, which utilize displacement measurements to sense inaccessible forces in linear elastic bodies with a priori constraints.

Low-temperature anomalies in the dynamic elastic moduli of cubic AIIBVI crystals with 3d-transition metal impurities

NASA Astrophysics Data System (ADS)

Lonchakov, A. T.

2011-04-01

A negative paramagnetic contribution to the dynamic elastic moduli is identified in AIIBVI:3d wide band-gap compounds for the first time. It appears as a paramagnetic elastic, or, briefly, paraelastic, susceptibility. These compounds are found to have a linear temperature dependence for the inverse paraelastic susceptibility. This is explained by a contribution from the diagonal matrix elements of the orbit-lattice interaction operators in the energy of the spin-orbital states of the 3d-ion as a function of applied stress (by analogy with the Curie contribution to the magnetic susceptibility). The inverse paraelastic susceptibility of AIIBVI crystals containing non-Kramers 3d-ions is found to deviate from linearity with decreasing temperature and reaches saturation. This effect is explained by a contribution from nondiagonal matrix elements (analogous to the well known van Vleck contribution to the magnetic susceptibility of paramagnets).

Elastic-plastic models for multi-site damage

NASA Technical Reports Server (NTRS)

Actis, Ricardo L.; Szabo, Barna A.

1994-01-01

This paper presents recent developments in advanced analysis methods for the computation of stress site damage. The method of solution is based on the p-version of the finite element method. Its implementation was designed to permit extraction of linear stress intensity factors using a superconvergent extraction method (known as the contour integral method) and evaluation of the J-integral following an elastic-plastic analysis. Coarse meshes are adequate for obtaining accurate results supported by p-convergence data. The elastic-plastic analysis is based on the deformation theory of plasticity and the von Mises yield criterion. The model problem consists of an aluminum plate with six equally spaced holes and a crack emanating from each hole. The cracks are of different sizes. The panel is subjected to a remote tensile load. Experimental results are available for the panel. The plasticity analysis provided the same limit load as the experimentally determined load. The results of elastic-plastic analysis were compared with the results of linear elastic analysis in an effort to evaluate how plastic zone sizes influence the crack growth rates. The onset of net-section yielding was determined also. The results show that crack growth rate is accelerated by the presence of adjacent damage, and the critical crack size is shorter when the effects of plasticity are taken into consideration. This work also addresses the effects of alternative stress-strain laws: The elastic-ideally-plastic material model is compared against the Ramberg-Osgood model.

A Linear Theory for Inflatable Plates of Arbitrary Shape

NASA Technical Reports Server (NTRS)

McComb, Harvey G., Jr.

1961-01-01

A linear small-deflection theory is developed for the elastic behavior of inflatable plates of which Airmat is an example. Included in the theory are the effects of a small linear taper in the depth of the plate. Solutions are presented for some simple problems in the lateral deflection and vibration of constant-depth rectangular inflatable plates.

A mathematical model to describe the nonlinear elastic properties of the gastrocnemius tendon of chickens.

PubMed

Foutz, T L

1991-03-01

A phenomenological model was developed to describe the nonlinear elastic behavior of the avian gastrocnemius tendon. Quasistatic uniaxial tensile tests were used to apply a deformation and resulting load on the tendon at a deformation rate of 5 mm/min. Plots of deformation versus load indicated a nonlinear loading response. By calculating engineering stress and engineering strain, the experimental data were normalized for tendon shape. The elastic response was determined from stress-strain curves and was found to vary with engineering strain. The response to the applied engineering strain could best be described by a mathematical model that combined a linear function and a nonlinear function. Three parameters in the model were developed to represent the nonlinear elastic behavior of the tendon, thereby allowing analysis of elasticity without prior knowledge of engineering strain. This procedure reduced the amount of data needed for the statistical analysis of nonlinear elasticity.

Finite-thickness effects on the Rayleigh-Taylor instability in accelerated elastic solids

NASA Astrophysics Data System (ADS)

Piriz, S. A.; Piriz, A. R.; Tahir, N. A.

2017-05-01

A physical model has been developed for the linear Rayleigh-Taylor instability of a finite-thickness elastic slab laying on top of a semi-infinite ideal fluid. The model includes the nonideal effects of elasticity as boundary conditions at the top and bottom interfaces of the slab and also takes into account the finite transit time of the elastic waves across the slab thickness. For Atwood number AT=1 , the asymptotic growth rate is found to be in excellent agreement with the exact solution [Plohr and Sharp, Z. Angew. Math. Mech. 49, 786 (1998), 10.1007/s000330050121], and a physical explanation is given for the reduction of the stabilizing effectiveness of the elasticity for the thinner slabs. The feedthrough factor is also calculated.

Contact mechanics for coated spheres that includes the transition from weak to strong adhesion

DOE PAGES

Reedy, Earl David

2007-09-01

Recently published results for a rigid spherical indenter contacting a thin, linear elastic coating on a rigid planar substrate have been extended to include the case of two contacting spheres, where each sphere is rigid and coated with a thin, linear elastic material. This is done by using an appropriately chosen effective radius and coating modulus. Finally, the earlier work has also been extended to provide analytical results that span the transition between the previously derived Derjaguin–Müller–Toporov (DMT)-like (work of adhesion/coating-modulus ratio is small) and Johnson–Kendall–Roberts (JKR)-like (work of adhesion/coating-modulus ratio is large) limits.

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18

NASA Technical Reports Server (NTRS)

Buttrill, Carey S.

1989-01-01

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

Nonlinear reflection of shock shear waves in soft elastic media.

PubMed

Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël

2010-02-01

For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.

Mechanical design in arteries.

PubMed

Shadwick, R E

1999-12-01

The most important mechanical property of the artery wall is its non-linear elasticity. Over the last century, this has been well-documented in vessels in many animals, from humans to lobsters. Arteries must be distensible to provide capacitance and pulse-smoothing in the circulation, but they must also be stable to inflation over a range of pressure. These mechanical requirements are met by strain-dependent increases in the elastic modulus of the vascular wall, manifest by a J-shaped stress-strain curve, as typically exhibited by other soft biological tissues. All vertebrates and invertebrates with closed circulatory systems have arteries with this non-linear behaviour, but specific tissue properties vary to give correct function for the physiological pressure range of each species. In all cases, the non-linear elasticity is a product of the parallel arrangement of rubbery and stiff connective tissue elements in the artery wall, and differences in composition and tissue architecture can account for the observed variations in mechanical properties. This phenomenon is most pronounced in large whales, in which very high compliance in the aortic arch and exceptionally low compliance in the descending aorta occur, and is correlated with specific modifications in the arterial structure.

Elastic constants and pressure derivative of elastic constants of Si1-xGex solid solution

NASA Astrophysics Data System (ADS)

Jivani, A. R.; Baria, J. K.; Vyas, P. S.; Jani, A. R.

2013-02-01

Elastic properties of Si1-xGex solid solution with arbitrary (atomic) concentration (x) are studied using the pseudo-alloy atom model based on the pseudopotential theory and on the higher-order perturbation scheme with the application of our own proposed model potential. We have used local-field correction function proposed by Sarkar et al to study Si-Ge system. The Elastic constants and pressure derivatives of elastic constants of the solid solution is investigated with different concentration x of Ge. It is found in the present study that the calculated numerical values of the aforesaid physical properties of Si-Ge system are function of x. The elastic constants (C11, C12 and C44) decrease linearly with increase in concentration x and pressure derivative of elastic constants (C11, C12 and C44) increase with the concentration x of Ge. This study provides better set of theoretical results for such solid solution for further comparison either with theoretical or experimental results.

The influence of time dependent flight and maneuver velocities and elastic or viscoelastic flexibilities on aerodynamic and stability derivatives

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

Cochrane, Alexander P.; Merrett, Craig G.; Hilton, Harry H.

2014-12-10

The advent of new structural concepts employing composites in primary load carrying aerospace structures in UAVs, MAVs, Boeing 787s, Airbus A380s, etc., necessitates the inclusion of flexibility as well as viscoelasticity in static structural and aero-viscoelastic analyses. Differences and similarities between aeroelasticity and aero-viscoelasticity have been investigated in [2]. An investigation is undertaken as to the dependence and sensitivity of aerodynamic and stability derivatives to elastic and viscoelastic structural flexibility and as to time dependent flight and maneuver velocities. Longitudinal, lateral and directional stabilities are investigated. It has been a well established fact that elastic lifting surfaces are subject tomore » loss of control effectiveness and control reversal at certain flight speeds, which depend on aerodynamic, structural and material properties [5]. Such elastic analyses are extended to linear viscoelastic materials under quasi-static, dynamic, and sudden and gradual loading conditions. In elastic wings one of the critical static parameters is the velocity at which control reversal takes place (V{sub REV}{sup E}). Since elastic formulations constitute viscoelastic initial conditions, viscoelastic reversal may occur at speeds V{sub REV<}{sup ≧}V{sub REV}{sup E}, but furthermore does so in time at 0 < t{sub REV} ≤ ∞. The influence of the twin effects of viscoelastic and elastic materials and of variable flight velocities on longitudinal, lateral, directional and spin stabilities are also investigated. It has been a well established fact that elastic lifting surfaces are subject to loss of control effectiveness and control reversal at certain flight speeds, which depend on aerodynamic, structural and material properties [5]. Such elastic analyses are here extended to linear viscoelastic materials under quasi-static, dynamic, and sudden and gradual loading conditions. In elastic wings the critical parameter is the velocity at which control reversal takes place (V{sub REV}{sup E}). Since elastic formulations constitute viscoelastic initial conditions, viscoelastic reversal may occur at speeds V{sub REV<}{sup ≧}V{sub REV}{sup E}, but furthermore does so in time at 0 < t{sub REV} ≤ ∞. This paper reports on analytical analyses and simulations of the effects of flexibility and time dependent material properties (viscoelasticity) on aerodynamic derivatives and on lateral, longitudinal, directional and spin stability derivatives. Cases of both constant and variable flight and maneuver velocities are considered. Analytical results for maneuvers involving constant and time dependent rolling velocities are analyzed, discussed and evaluated. The relationships between rolling velocity p and aileron angular displacement β as well as control effectiveness are analyzed and discussed in detail for elastic and viscoelastic wings. Such analyses establish the roll effectiveness derivatives (∂[p(t)])/(V{sub ∞}∂β(t)) . Similar studies involving other stability and aerodynamic derivatives are also undertaken. The influence of the twin effects of viscoelastic and elastic materials and of variable flight, rolling, pitching and yawing velocities on longitudinal, lateral and directional are also investigated. Variable flight velocities, encountered during maneuvers, render the usually linear problem at constant velocities into a nonlinear one.« less

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.

Rayleigh wave effects in an elastic half-space.

NASA Technical Reports Server (NTRS)

Aggarwal, H. R.

1972-01-01

Consideration of Rayleigh wave effects in a homogeneous isotropic linearly elastic half-space subject to an impulsive uniform disk pressure loading. An approximate formula is obtained for the Rayleigh wave effects. It is shown that the Rayleigh waves near the center of loading arise from the portion of the dilatational and shear waves moving toward the axis, after they originate at the edge of the load disk. A study is made of the vertical displacement due to Rayleigh waves at points on the axis near the surface of the elastic half-space.

Boundary element modelling of dynamic behavior of piecewise homogeneous anisotropic elastic solids

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Markov, I. P.; Litvinchuk, S. Yu

2018-04-01

A traditional direct boundary integral equations method is applied to solve three-dimensional dynamic problems of piecewise homogeneous linear elastic solids. The materials of homogeneous parts are considered to be generally anisotropic. The technique used to solve the boundary integral equations is based on the boundary element method applied together with the Radau IIA convolution quadrature method. A numerical example of suddenly loaded 3D prismatic rod consisting of two subdomains with different anisotropic elastic properties is presented to verify the accuracy of the proposed formulation.

Elasticity of entangled polymer loops: Olympic gels

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

Vilgis, T.A.; Otto, M.

1997-08-01

In this Rapid Communication we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the nonaffine deformation regime where the free energy scales linear with the deformation. In the large (affine) deformation regime the free energy is shown to scale as F{proportional_to}{lambda}{sup 5/2} where {lambda} is the deformation ratio. Thus a highly non-Hookian stress-strain relation is predicted. {copyright} {ital 1997} {ital The American Physical Society}

Measurement of elastic constants of monoclinic nickel-titanium and validation of first principles calculations

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

Stebner, A. P.; Brown, D. W.; Brinson, L. C.

2013-05-27

Polycrystalline, monoclinic nickel-titanium specimens were subjected to tensile and compressive deformations while neutron diffraction spectra were recorded in situ. Using these data, orientation-specific and macroscopic Young's moduli are determined from analysis of linear-elastic deformation exhibited by 13 unique orientations of monoclinic lattices and their relationships to each macroscopic stress and strain. Five of 13 elastic compliance constants are also identified: s{sub 11} = 1.15, s{sub 15} = -1.10, s{sub 22} = 1.34, s{sub 33} = 1.06, s{sub 35} = -1.54, all Multiplication-Sign 10{sup -2} GPa{sup -1}. Through these results, recent atomistic calculations of monoclinic nickel-titanium elastic constants are validated.

Linear sampling method applied to non destructive testing of an elastic waveguide: theory, numerics and experiments

NASA Astrophysics Data System (ADS)

Baronian, Vahan; Bourgeois, Laurent; Chapuis, Bastien; Recoquillay, Arnaud

2018-07-01

This paper presents an application of the linear sampling method to ultrasonic non destructive testing of an elastic waveguide. In particular, the NDT context implies that both the solicitations and the measurements are located on the surface of the waveguide and are given in the time domain. Our strategy consists in using a modal formulation of the linear sampling method at multiple frequencies, such modal formulation being justified theoretically in Bourgeois et al (2011 Inverse Problems 27 055001) for rigid obstacles and in Bourgeois and Lunéville (2013 Inverse Problems 29 025017) for cracks. Our strategy requires the inversion of some emission and reception matrices which deserve some special attention due to potential ill-conditioning. The feasibility of our method is proved with the help of artificial data as well as real data.

Non-Singular Dislocation Elastic Fields and Linear Elastic Fracture Mechanics

NASA Astrophysics Data System (ADS)

Korsunsky, Alexander M.

2010-03-01

One of the hallmarks of the traditional linear elastic fracture mechanics (LEFM) is the presence of an (integrable) inverse square root singularity of strains and stresses in the vicinity of the crack tip. It is the presence of this singularity that necessitates the introduction of the concepts of stress intensity factor (and its critical value, the fracture toughness) and the energy release rate (and material toughness). This gives rise to the Griffith theory of strength that includes, apart from applied stresses, the considerations of defect size and geometry. A highly successful framework for the solution of crack problems, particularly in the two-dimensional case, due to Muskhelishvili (1953), Bilby and Eshelby (1968) and others, relies on the mathematical concept of dislocation. Special analytical and numerical methods of dealing with the characteristic 1/r (Cauchy) singularity occupy a prominent place within this theory. Recently, in a different context of dislocation dynamics simulations, Cai et al. (2006) proposed a novel means of removing the singularity associated with the dislocation core, by introducing a blunting radius parameter a into the expressions for elastic fields. Here, using the example of two-dimensional elasticity, we demonstrate how the adoption of the similar mathematically expedient tool leads naturally to a non-singular formulation of fracture mechanics problems. This opens an efficient means of treating a variety of crack problems.

Estimating the price elasticity of expenditure for prescription drugs in the presence of non-linear price schedules: an illustration from Quebec, Canada.

PubMed

Contoyannis, Paul; Hurley, Jeremiah; Grootendorst, Paul; Jeon, Sung-Hee; Tamblyn, Robyn

2005-09-01

The price elasticity of demand for prescription drugs is a crucial parameter of interest in designing pharmaceutical benefit plans. Estimating the elasticity using micro-data, however, is challenging because insurance coverage that includes deductibles, co-insurance provisions and maximum expenditure limits create a non-linear price schedule, making price endogenous (a function of drug consumption). In this paper we exploit an exogenous change in cost-sharing within the Quebec (Canada) public Pharmacare program to estimate the price elasticity of expenditure for drugs using IV methods. This approach corrects for the endogeneity of price and incorporates the concept of a 'rational' consumer who factors into consumption decisions the price they expect to face at the margin given their expected needs. The IV method is adapted from an approach developed in the public finance literature used to estimate income responses to changes in tax schedules. The instrument is based on the price an individual would face under the new cost-sharing policy if their consumption remained at the pre-policy level. Our preferred specification leads to expenditure elasticities that are in the low range of previous estimates (between -0.12 and -0.16). Naïve OLS estimates are between 1 and 4 times these magnitudes. (c) 2005 John Wiley & Sons, Ltd.

Stress stiffening and approximate equations in flexible multibody dynamics

NASA Technical Reports Server (NTRS)

Padilla, Carlos E.; Vonflotow, Andreas H.

1993-01-01

A useful model for open chains of flexible bodies undergoing large rigid body motions, but small elastic deformations, is one in which the equations of motion are linearized in the small elastic deformations and deformation rates. For slow rigid body motions, the correctly linearized, or consistent, set of equations can be compared to prematurely linearized, or inconsistent, equations and to 'oversimplified,' or ruthless, equations through the use of open loop dynamic simulations. It has been shown that the inconsistent model should never be used, while the ruthless model should be used whenever possible. The consistent and inconsistent models differ by stress stiffening terms. These are due to zeroth-order stresses effecting virtual work via nonlinear strain-displacement terms. In this paper we examine in detail the nature of these stress stiffening terms and conclude that they are significant only when the associated zeroth-order stresses approach 'buckling' stresses. Finally it is emphasized that when the stress stiffening terms are negligible the ruthlessly linearized equations should be used.

Characterization of the Nonlinear Elastic Properties of Graphite/Epoxy Composites Using Ultrasound

NASA Technical Reports Server (NTRS)

Prosser, William H.; Green, Robert E., Jr.

1990-01-01

The normalized change in ultrasonic "natural" velocity as a function of stress and temperature was measured in a unidirectional laminate of T300/5208 graphite/epoxy composite using a pulsed phase locked loop ultrasonic interferometer. These measurements were used together with the linear (second order) elastic moduli to calculate some of the nonlinear (third order) moduli of this material.

Forced in-plane vibration of a thick ring on a unilateral elastic foundation

NASA Astrophysics Data System (ADS)

Wang, Chunjian; Ayalew, Beshah; Rhyne, Timothy; Cron, Steve; Dailliez, Benoit

2016-10-01

Most existing studies of a deformable ring on elastic foundation rely on the assumption of a linear foundation. These assumptions are insufficient in cases where the foundation may have a unilateral stiffness that vanishes in compression or tension such as in non-pneumatic tires and bushing bearings. This paper analyzes the in-plane dynamics of such a thick ring on a unilateral elastic foundation, specifically, on a two-parameter unilateral elastic foundation, where the stiffness of the foundation is treated as linear in the circumferential direction but unilateral (i.e. collapsible or tensionless) in the radial direction. The thick ring is modeled as an orthotropic and extensible circular Timoshenko beam. An arbitrarily distributed time-varying in-plane force is considered as the excitation. The Equations of Motion are explicitly derived and a solution method is proposed that uses an implicit Newmark scheme for the time domain solution and an iterative compensation approach to determine the unilateral zone of the foundation at each time step. The dynamic axle force transmission is also analyzed. Illustrative forced vibration responses obtained from the proposed model and solution method are compared with those obtained from a finite element model.

Effects of Initial Geometric Imperfections On the Non-Linear Response of the Space Shuttle Superlightweight Liquid-Oxygen Tank

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Young, Richard D.; Collins, Timothy J.; Starnes, James H., Jr.

2002-01-01

The results of an analytical study of the elastic buckling and nonlinear behavior of the liquid-oxygen tank for the new Space Shuttle superlightweight external fuel tank are presented. Selected results that illustrate three distinctly different types of non-linear response phenomena for thin-walled shells which are subjected to combined mechanical and thermal loads are presented. These response phenomena consist of a bifurcation-type buckling response, a short-wavelength non-linear bending response and a non-linear collapse or "snap-through" response associated with a limit point. The effects of initial geometric imperfections on the response characteristics are emphasized. The results illustrate that the buckling and non-linear response of a geometrically imperfect shell structure subjected to complex loading conditions may not be adequately characterized by an elastic linear bifurcation buckling analysis, and that the traditional industry practice of applying a buckling-load knock-down factor can result in an ultraconservative design. Results are also presented that show that a fluid-filled shell can be highly sensitive to initial geometric imperfections, and that the use a buckling-load knock-down factor is needed for this case.

Negative stiffness honeycombs as tunable elastic metamaterials

NASA Astrophysics Data System (ADS)

Goldsberry, Benjamin M.; Haberman, Michael R.

2018-03-01

Acoustic and elastic metamaterials are media with a subwavelength structure that behave as effective materials displaying atypical effective dynamic properties. These material systems are of interest because the design of their sub-wavelength structure allows for direct control of macroscopic wave dispersion. One major design limitation of most metamaterial structures is that the dynamic response cannot be altered once the microstructure is manufactured. However, the ability to modify wave propagation in the metamaterial with an external stimulus is highly desirable for numerous applications and therefore remains a significant challenge in elastic metamaterials research. In this work, a honeycomb structure composed of a doubly periodic array of curved beams, known as a negative stiffness honeycomb (NSH), is analyzed as a tunable elastic metamaterial. The nonlinear static elastic response that results from large deformations of the NSH unit cell leads to a large variation in linear elastic wave dispersion associated with infinitesimal motion superposed on the externally imposed pre-strain. A finite element model is utilized to model the static deformation and subsequent linear wave motion at the pre-strained state. Analysis of the slowness surface and group velocity demonstrates that the NSH exhibits significant tunability and a high degree of anisotropy which can be used to guide wave energy depending on static pre-strain levels. In addition, it is shown that partial band gaps exist where only longitudinal waves propagate. The NSH therefore behaves as a meta-fluid, or pentamode metamaterial, which may be of use for applications of transformation elastodynamics such as cloaking and gradient index lens devices.

Reflection and transmission of elastic waves through a couple-stress elastic slab sandwiched between two half-spaces

NASA Astrophysics Data System (ADS)

Wang, Changda; Chen, Xuejun; Wei, Peijun; Li, Yueqiu

2017-12-01

The reflection and transmission of elastic waves through a couple-stress elastic slab that is sandwiched between two couple-stress elastic half-spaces are studied in this paper. Because of the couple-stress effects, there are three types of elastic waves in the couple-stress elastic solid, two of which are dispersive. The interface conditions between two couple-stress solids involve the surface couple and rotation apart from the surface traction and displacement. The nontraditional interface conditions between the slab and two solid half-spaces are used to obtain the linear algebraic equation sets from which the amplitude ratios of reflection and transmission waves to the incident wave can be determined. Then, the energy fluxes carried by the various reflection and transmission waves are calculated numerically and the normal energy flux conservation is used to validate the numerical results. The special case, couple-stress elastic slab sandwiched by the classical elastic half-spaces, is also studied and compared with the situation that the classical elastic slab sandwiched by the classical elastic half-spaces. Incident longitudinal wave (P wave) and incident transverse wave (SV wave) are both considered. The influences of the couple-stress are mainly discussed based on the numerical results. It is found that the couple-stress mainly influences the transverse modes of elastic waves.

A virtual surgical training system that simulates cutting of soft tissue using a modified pre-computed elastic model.

PubMed

Toe, Kyaw Kyar; Huang, Weimin; Yang, Tao; Duan, Yuping; Zhou, Jiayin; Su, Yi; Teo, Soo-Kng; Kumar, Selvaraj Senthil; Lim, Calvin Chi-Wan; Chui, Chee Kong; Chang, Stephen

2015-08-01

This work presents a surgical training system that incorporates cutting operation of soft tissue simulated based on a modified pre-computed linear elastic model in the Simulation Open Framework Architecture (SOFA) environment. A precomputed linear elastic model used for the simulation of soft tissue deformation involves computing the compliance matrix a priori based on the topological information of the mesh. While this process may require a few minutes to several hours, based on the number of vertices in the mesh, it needs only to be computed once and allows real-time computation of the subsequent soft tissue deformation. However, as the compliance matrix is based on the initial topology of the mesh, it does not allow any topological changes during simulation, such as cutting or tearing of the mesh. This work proposes a way to modify the pre-computed data by correcting the topological connectivity in the compliance matrix, without re-computing the compliance matrix which is computationally expensive.

ELASTIC NET FOR COX’S PROPORTIONAL HAZARDS MODEL WITH A SOLUTION PATH ALGORITHM

PubMed Central

Wu, Yichao

2012-01-01

For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox’s proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox’s proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems. PMID:23226932

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.

Interpolation problem for the solutions of linear elasticity equations based on monogenic functions

NASA Astrophysics Data System (ADS)

Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii

2017-11-01

Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.

Compressible Fluids Interacting with a Linear-Elastic Shell

NASA Astrophysics Data System (ADS)

Breit, Dominic; Schwarzacher, Sebastian

2018-05-01

We study the Navier-Stokes equations governing the motion of an isentropic compressible fluid in three dimensions interacting with a flexible shell of Koiter type. The latter one constitutes a moving part of the boundary of the physical domain. Its deformation is modeled by a linearized version of Koiter's elastic energy. We show the existence of weak solutions to the corresponding system of PDEs provided the adiabatic exponent satisfies {γ > 12/7} ({γ >1 } in two dimensions). The solution exists until the moving boundary approaches a self-intersection. This provides a compressible counterpart of the results in Lengeler and Růžičkaka (Arch Ration Mech Anal 211(1):205-255, 2014) on incompressible Navier-Stokes equations.

The elastic theory of shells using geometric algebra

PubMed Central

Lasenby, J.; Agarwal, A.

2017-01-01

We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible. PMID:28405404

The elastic theory of shells using geometric algebra.

PubMed

Gregory, A L; Lasenby, J; Agarwal, A

2017-03-01

We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible.

Study of Graphite/Epoxy Composites for Material Flaw Criticality.

DTIC Science & Technology

1980-11-01

criticality of disbonds with two-dimensional planforms located in laminated graphite/epoxy composites has been examined. Linear elastic fracture...mechanics approach, semi-empirical growth laws and methods of stress analysis based on a modified laminated plate theory have been studied for assessing...growth rates of disbonds in a transverse shear environ- ment. Elastic stability analysis has been utilized for laminates with disbonds subjected to in

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

High elastic modulus polymer electrolytes suitable for preventing thermal runaway in lithium batteries

DOEpatents

Mullin, Scott; Panday, Ashoutosh; Balsara, Nitash Pervez; Singh, Mohit; Eitouni, Hany Basam; Gomez, Enrique Daniel

2014-04-22

A polymer that combines high ionic conductivity with the structural properties required for Li electrode stability is useful as a solid phase electrolyte for high energy density, high cycle life batteries that do not suffer from failures due to side reactions and dendrite growth on the Li electrodes, and other potential applications. The polymer electrolyte includes a linear block copolymer having a conductive linear polymer block with a molecular weight of at least 5000 Daltons, a structural linear polymer block with an elastic modulus in excess of 1.times.10.sup.7 Pa and an ionic conductivity of at least 1.times.10.sup.-5 Scm.sup.-1. The electrolyte is made under dry conditions to achieve the noted characteristics. In another aspect, the electrolyte exhibits a conductivity drop when the temperature of electrolyte increases over a threshold temperature, thereby providing a shutoff mechanism for preventing thermal runaway in lithium battery cells.

Non-linear heterogeneous FE approach for FRP strengthened masonry arches

NASA Astrophysics Data System (ADS)

Bertolesi, Elisa; Milani, Gabriele; Fedele, Roberto

2015-12-01

A fast and reliable non-linear heterogeneous FE approach specifically conceived for the analysis of FRP-reinforced masonry arches is presented. The approach proposed relies into the reduction of mortar joints to interfaces exhibiting a non-linear holonomic behavior, with a discretization of bricks by means of four-noded elastic elements. The FRP reinforcement is modeled by means of truss elements with elastic-brittle behavior, where the peak tensile strength is estimated by means of a consolidated approach provided by the Italian guidelines CNR-DT200 on masonry strengthening with fiber materials, where the delamination of the strip from the support is taken into account. The model is validated against some recent experimental results relying into circular masonry arches reinforced at both the intrados and the extrados. Some sensitivity analyses are conducted varying the peak tensile strength of the trusses representing the FRP reinforcement.

Elastic properties and optical absorption studies of mixed alkali borogermanate glasses

NASA Astrophysics Data System (ADS)

Taqiullah, S. M.; Ahmmad, Shaik Kareem; Samee, M. A.; Rahman, Syed

2018-05-01

First time the mixed alkali effect (MAE) has been investigated in the glass system xNa2O-(30-x)Li2O-40B2O3- 30GeO2 (0≤x≤30 mol%) through density and optical absorption studies. The present glasses were prepared by melt quench technique. The density of the present glasses varies non-linearly exhibiting mixed alkali effect. Using the density data, the elastic moduli namely Young's modulus, bulk and shear modulus show strong linear dependence as a function of compositional parameter. From the absorption edge studies, the values of optical band gap energies for all transitions have been evaluated. It was established that the type of electronic transition in the present glass system is indirect allowed. The indirect optical band gap exhibit non-linear behavior with compositional parameter showing the mixed alkali effect.

Theoretical study of strength of elastic-plastic water-saturated interface under constrained shear

NASA Astrophysics Data System (ADS)

Dimaki, Andrey V.; Shilko, Evgeny V.; Psakhie, Sergey G.

2016-11-01

This paper presents a theoretical study of shear strength of an elastic-plastic water-filled interface between elastic permeable blocks under compression. The medium is described within the discrete element method. The relationship between the stress-strain state of the solid skeleton and pore pressure of a liquid is described in the framework of the Biot's model of poroelasticity. The simulation demonstrates that shear strength of an elastic-plastic interface depends non-linearly on the values of permeability and loading to a great extent. We have proposed an empirical relation that approximates the obtained results of the numerical simulation in assumption of the interplay of dilation of the material and mass transfer of the liquid.

The effect of topography of upper-mantle discontinuities on SS precursors

NASA Astrophysics Data System (ADS)

Koroni, Maria; Trampert, Jeannot

2016-01-01

Using the spectral-element method, we explored the effect of topography of upper-mantle discontinuities on the traveltimes of SS precursors recorded on transverse component seismograms. The latter are routinely used to infer the topography of mantle transition zone discontinuities. The step from precursory traveltimes to topographic changes is mainly done using linearised ray theory, or sometimes using finite-frequency kernels. We simulated exact seismograms in 1-D and 3-D elastic models of the mantle. In a second simulation, we added topography to the discontinuities. We compared the waveforms obtained with and without topography by cross correlation of the SS precursors. Since we did not add noise, the precursors are visible in individual seismograms without the need of stacking. The resulting time anomalies were then converted into topographic variations and compared to the original topographic models. Based on the correlation between initial and inferred models, and provided that ray coverage is good, we found that linearised ray theory gives a relatively good idea on the location of the uplifts and depressions of the discontinuities. It seriously underestimates the amplitude of the topographic variations by a factor ranging between 2 and 7. Real data depend on the 3-D elastic structure and the topography. All studies to date correct for the 3-D elastic effects assuming that the traveltimes can be linearly decomposed into a structure and a discontinuity part. We found a strong non-linearity in this decomposition which cannot be modelled without a fully non-linear inversion for elastic structure and discontinuities simultaneously.

Linear and nonlinear stiffness and friction in biological rhythmic movements.

PubMed

Beek, P J; Schmidt, R C; Morris, A W; Sim, M Y; Turvey, M T

1995-11-01

Biological rhythmic movements can be viewed as instances of self-sustained oscillators. Auto-oscillatory phenomena must involve a nonlinear friction function, and usually involve a nonlinear elastic function. With respect to rhythmic movements, the question is: What kinds of nonlinear friction and elastic functions are involved? The nonlinear friction functions of the kind identified by Rayleigh (involving terms such as theta3) and van der Pol (involving terms such as theta2theta), and the nonlinear elastic functions identified by Duffing (involving terms such as theta3), constitute elementary nonlinear components for the assembling of self-sustained oscillators, Recently, additional elementary nonlinear friction and stiffness functions expressed, respectively, through terms such as theta2theta3 and thetatheta2, and a methodology for evaluating the contribution of the elementary components to any given cyclic activity have been identified. The methodology uses a quantification of the continuous deviation of oscillatory motion from ideal (harmonic) motion. Multiple regression of this quantity on the elementary linear and nonlinear terms reveals the individual contribution of each term to the oscillator's non-harmonic behavior. In the present article the methodology was applied to the data from three experiments in which human subjects produced pendular rhythmic movements under manipulations of rotational inertia (experiment 1), rotational inertia and frequency (experiment 2), and rotational inertia and amplitude (experiment 3). The analysis revealed that the pendular oscillators assembled in the three experiments were compositionally rich, braiding linear and nonlinear friction and elastic functions in a manner that depended on the nature of the task.

Rotating elastic string loops in flat and black hole spacetimes: stability, cosmic censorship and the Penrose process

NASA Astrophysics Data System (ADS)

Natário, José; Queimada, Leonel; Vicente, Rodrigo

2018-04-01

We rederive the equations of motion for relativistic strings, that is, one-dimensional elastic bodies whose internal energy depends only on their stretching, and use them to study circular string loops rotating in the equatorial plane of flat and black hole spacetimes. We start by obtaining the conditions for equilibrium, and find that: (i) if the string’s longitudinal speed of sound does not exceed the speed of light then its radius when rotating in Minkowski’s spacetime is always larger than its radius when at rest; (ii) in Minkowski’s spacetime, equilibria are linearly stable for rotation speeds below a certain threshold, higher than the string’s longitudinal speed of sound, and linearly unstable for some rotation speeds above it; (iii) equilibria are always linearly unstable in Schwarzschild’s spacetime. Moreover, we study interactions of a rotating string loop with a Kerr black hole, namely in the context of the weak cosmic censorship conjecture and the Penrose process. We find that: (i) elastic string loops that satisfy the null energy condition cannot overspin extremal black holes; (ii) elastic string loops that satisfy the dominant energy condition cannot increase the maximum efficiency of the usual particle Penrose process; (iii) if the dominant energy condition (but not the weak energy condition) is violated then the efficiency can be increased. This last result hints at the interesting possibility that the dominant energy condition may underlie the well known upper bounds for the efficiencies of energy extraction processes (including, for example, superradiance).

Equations for normal-mode statistics of sound scattering by a rough elastic boundary in an underwater waveguide, including backscattering.

PubMed

Morozov, Andrey K; Colosi, John A

2017-09-01

Underwater sound scattering by a rough sea surface, ice, or a rough elastic bottom is studied. The study includes both the scattering from the rough boundary and the elastic effects in the solid layer. A coupled mode matrix is approximated by a linear function of one random perturbation parameter such as the ice-thickness or a perturbation of the surface position. A full two-way coupled mode solution is used to derive the stochastic differential equation for the second order statistics in a Markov approximation.

Cointegration of output, capital, labor, and energy

NASA Astrophysics Data System (ADS)

Stresing, R.; Lindenberger, D.; Kã¼mmel, R.

2008-11-01

Cointegration analysis is applied to the linear combinations of the time series of (the logarithms of) output, capital, labor, and energy for Germany, Japan, and the USA since 1960. The computed cointegration vectors represent the output elasticities of the aggregate energy-dependent Cobb-Douglas function. The output elasticities give the economic weights of the production factors capital, labor, and energy. We find that they are for labor much smaller and for energy much larger than the cost shares of these factors. In standard economic theory output elasticities equal cost shares. Our heterodox findings support results obtained with LINEX production functions.

Radiation-damage-induced transitions in zircon: Percolation theory applied to hardness and elastic moduli as a function of density

NASA Astrophysics Data System (ADS)

Beirau, Tobias; Nix, William D.; Ewing, Rodney C.; Pöllmann, Herbert; Salje, Ekhard K. H.

2018-05-01

Two in literature predicted percolation transitions in radiation-damaged zircon (ZrSiO4) were observed experimentally by measurement of the indentation hardness as a function of density and their correlation with the elastic moduli. Percolations occur near 30% and 70% amorphous fractions, where hardness deviates from its linear correlation with the elastic modulus (E), the shear modulus (G) and the bulk modulus (K). The first percolation point pc1 generates a cusp in the hardness versus density evolution, while the second percolation point is seen as a change of slope.

Nanoscale characterization of the biomechanical properties of collagen fibrils in the sclera

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

Papi, M.; Paoletti, P.; Geraghty, B.

We apply the PeakForce Quantitative Nanomechanical Property Mapping (PFQNM) atomic force microscopy mode for the investigation of regional variations in the nanomechanical properties of porcine sclera. We examine variations in the collagen fibril diameter, adhesion, elastic modulus and dissipation in the posterior, equatorial and anterior regions of the sclera. The mean fibril diameter, elastic modulus and dissipation increased from the posterior to the anterior region. Collagen fibril diameter correlated linearly with elastic modulus. Our data matches the known macroscopic mechanical behavior of the sclera. We propose that PFQNM has significant potential in ocular biomechanics and biophysics research.

Towards an Aero-Propulso-Servo-Elasticity Analysis of a Commercial Supersonic Transport

NASA Technical Reports Server (NTRS)

Connolly, Joseph W.; Kopasakis, George; Chwalowski, Pawel; Sanetrik, Mark D.; Carlson, Jan-Renee; Silva, Walt A.; McNamara, Jack

2016-01-01

This paper covers the development of an aero-propulso-servo-elastic (APSE) model using computational fluid dynamics (CFD) and linear structural deformations. The APSE model provides the integration of the following two previously developed nonlinear dynamic simulations: a variable cycle turbofan engine and an elastic supersonic commercial transport vehicle. The primary focus of this study is to provide a means to include relevant dynamics of a turbomachinery propulsion system into the aeroelastic studies conducted during a vehicle design, which have historically neglected propulsion effects. A high fidelity CFD tool is used here for the integration platform. The elastic vehicle neglecting the propulsion system serves as a comparison of traditional approaches to the APSE results. An overview of the methodology is presented for integrating the propulsion system and elastic vehicle. Static aeroelastic analysis comparisons between the traditional and developed APSE models for a wing tip detection indicate that the propulsion system impact on the vehicle elastic response could increase the detection by approximately ten percent.

Preparation and Elastic Moduli of Germanate Glass Containing Lead and Bismuth

PubMed Central

Sidek, Hj A. A.; Bahari, Hamid R.; Halimah, Mohamed K.; Yunus, Wan M. M.

2012-01-01

This paper reports the rapid melt quenching technique preparation for the new family of bismuth-lead germanate glass (BPG) systems in the form of (GeO2)60–(PbO)40−x–(½Bi2O3)x where x = 0 to 40 mol%. Their densities with respect of Bi2O3 concentration were determined using Archimedes’ method with acetone as a floatation medium. The current experimental data are compared with those of bismuth lead borate (B2O3)20–(PbO)80−x–(Bi2O3)x. The elastic properties of BPG were studied using the ultrasonic pulse-echo technique where both longitudinal and transverse sound wave velocities have been measured in each glass samples at a frequency of 15 MHz and at room temperature. Experimental data shows that all the physical parameters of BPG including density and molar volume, both longitudinal and transverse velocities increase linearly with increasing of Bi2O3 content in the germanate glass network. Their elastic moduli such as longitudinal, shear and Young’s also increase linearly with addition of Bi2O3 but the bulk modulus did not. The Poisson’s ratio and fractal dimensionality are also found to vary linearly with the Bi2O3 concentration. PMID:22606000

Preparation and elastic moduli of germanate glass containing lead and bismuth.

PubMed

Sidek, Hj A A; Bahari, Hamid R; Halimah, Mohamed K; Yunus, Wan M M

2012-01-01

This paper reports the rapid melt quenching technique preparation for the new family of bismuth-lead germanate glass (BPG) systems in the form of (GeO(2))(60)-(PbO)(40-) (x)-(½Bi(2)O(3))(x) where x = 0 to 40 mol%. Their densities with respect of Bi(2)O(3) concentration were determined using Archimedes' method with acetone as a floatation medium. The current experimental data are compared with those of bismuth lead borate (B(2)O(3))(20)-(PbO)(80-) (x)-(Bi(2)O(3))(x). The elastic properties of BPG were studied using the ultrasonic pulse-echo technique where both longitudinal and transverse sound wave velocities have been measured in each glass samples at a frequency of 15 MHz and at room temperature. Experimental data shows that all the physical parameters of BPG including density and molar volume, both longitudinal and transverse velocities increase linearly with increasing of Bi(2)O(3) content in the germanate glass network. Their elastic moduli such as longitudinal, shear and Young's also increase linearly with addition of Bi(2)O(3) but the bulk modulus did not. The Poisson's ratio and fractal dimensionality are also found to vary linearly with the Bi(2)O(3) concentration.

The effect of stent graft oversizing on radial forces considering nitinol wire behavior and vessel characteristics.

PubMed

Senf, B; von Sachsen, S; Neugebauer, R; Drossel, W-G; Florek, H-J; Mohr, F W; Etz, C D

2014-11-01

Stent graft fixation in the vessel affects the success of endovascular aneurysm repair. Thereby the radial forces of the stent, which are dependent on several factors, play a significant role. In the presented work, a finite element sensitivity study was performed. The radial forces are 29% lower when using the hyperelastic approach for the vessel compared with linear elastic assumptions. Without the linear elastic modeled plaque, the difference increases to 35%. Modeling plaque with linear elastic material approach results in 8% higher forces than with a hyperelastic characteristic. The significant differences resulting from the investigated simplifications of the material lead to the conclusion that it is important to apply an anisotropic nonlinear approach for the vessel. The oversizing study shows that radial forces increase by 64% (0.54 N) when raising the oversize from 10 to 22%, and no further increase in force can be observed beyond these values (vessel diameter D=12 mm). Starting from an oversize of 24%, the radial force steadily decreases. The findings of the investigation show that besides the oversizing the material properties, the ring design and the vessel characteristics have an influence on radial forces. Copyright © 2014 IPEM. Published by Elsevier Ltd. All rights reserved.

Thermophoretically induced large-scale deformations around microscopic heat centers

NASA Astrophysics Data System (ADS)

Puljiz, Mate; Orlishausen, Michael; Köhler, Werner; Menzel, Andreas M.

2016-05-01

Selectively heating a microscopic colloidal particle embedded in a soft elastic matrix is a situation of high practical relevance. For instance, during hyperthermic cancer treatment, cell tissue surrounding heated magnetic colloidal particles is destroyed. Experiments on soft elastic polymeric matrices suggest a very long-ranged, non-decaying radial component of the thermophoretically induced displacement fields around the microscopic heat centers. We theoretically confirm this conjecture using a macroscopic hydrodynamic two-fluid description. Both thermophoretic and elastic effects are included in this theory. Indeed, we find that the elasticity of the environment can cause the experimentally observed large-scale radial displacements in the embedding matrix. Additional experiments confirm the central role of elasticity. Finally, a linearly decaying radial component of the displacement field in the experiments is attributed to the finite size of the experimental sample. Similar results are obtained from our theoretical analysis under modified boundary conditions.

Fluid-structure interaction in Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Kempf, Martin Horst Willi

1998-10-01

The linear stability of a viscous fluid between two concentric, rotating cylinders is considered. The inner cylinder is a rigid boundary and the outer cylinder has an elastic layer exposed to the fluid. The subject is motivated by flow between two adjoining rollers in a printing press. The governing equations of the fluid layer are the incompressible Navier-Stokes equations, and the governing equations of the elastic layer are Navier's equations. A narrow gap, neutral stability, and axisymmetric disturbances are assumed. The solution involves a novel technique for treating two layer stability problems, where an exact solution in the elastic layer is used to isolate the problem in the fluid layer. The results show that the presence of the elastic layer has only a slight effect on the critical Taylor numbers for the elastic parameters of modern printing presses. However, there are parameter values where the critical Taylor number is dramatically different than the classical Taylor-Couette problem.

Measurement of Shear Elastic Moduli in Quasi-Incompressible Soft Solids

NASA Astrophysics Data System (ADS)

Rénier, Mathieu; Gennisson, Jean-Luc; Barrière, Christophe; Catheline, Stefan; Tanter, Mickaël; Royer, Daniel; Fink, Mathias

2008-06-01

Recently a nonlinear equation describing the plane shear wave propagation in isotropic quasi-incompressible media has been developed using a new expression of the strain energy density, as a function of the second, third and fourth order shear elastic constants (respectively μ, A, D) [1]. In such a case, the shear nonlinearity parameter βs depends only from these last coefficients. To date, no measurement of the parameter D have been carried out in soft solids. Using a set of two experiments, acoustoelasticity and finite amplitude shear waves, the shear elastic moduli up to the fourth order of soft solids are measured. Firstly, this theoretical background is applied to the acoustoelasticity theory, giving the variations of the shear wave speed as a function of the stress applied to the medium. From such variations, both linear (μ) and third order shear modulus (A) are deduced in agar-gelatin phantoms. Experimentally the radiation force induced by a focused ultrasound beam is used to generate quasi-plane linear shear waves within the medium. Then the shear wave propagation is imaged with an ultrafast ultrasound scanner. Secondly, in order to give rise to finite amplitude plane shear waves, the radiation force generation technique is replaced by a vibrating plate applied at the surface of the phantoms. The propagation is also imaged using the same ultrafast scanner. From the assessment of the third harmonic amplitude, the nonlinearity parameter βS is deduced. Finally, combining these results with the acoustoelasticity experiment, the fourth order modulus (D) is deduced. This set of experiments provides the characterization, up to the fourth order, of the nonlinear shear elastic moduli in quasi-incompressible soft media. Measurements of the A moduli reveal that while the behaviors of both soft solids are close from a linear point of view, the corresponding nonlinear moduli A are quite different. In a 5% agar-gelatin phantom, the fourth order elastic constant D is found to be 30±10 kPa.

A design concept of parallel elasticity extracted from biological muscles for engineered actuators.

PubMed

Chen, Jie; Jin, Hongzhe; Iida, Fumiya; Zhao, Jie

2016-08-23

Series elastic actuation that takes inspiration from biological muscle-tendon units has been extensively studied and used to address the challenges (e.g. energy efficiency, robustness) existing in purely stiff robots. However, there also exists another form of passive property in biological actuation, parallel elasticity within muscles themselves, and our knowledge of it is limited: for example, there is still no general design strategy for the elasticity profile. When we look at nature, on the other hand, there seems a universal agreement in biological systems: experimental evidence has suggested that a concave-upward elasticity behaviour is exhibited within the muscles of animals. Seeking to draw possible design clues for elasticity in parallel with actuators, we use a simplified joint model to investigate the mechanisms behind this biologically universal preference of muscles. Actuation of the model is identified from general biological joints and further reduced with a specific focus on muscle elasticity aspects, for the sake of easy implementation. By examining various elasticity scenarios, one without elasticity and three with elasticity of different profiles, we find that parallel elasticity generally exerts contradictory influences on energy efficiency and disturbance rejection, due to the mechanical impedance shift thus caused. The trade-off analysis between them also reveals that concave parallel elasticity is able to achieve a more advantageous balance than linear and convex ones. It is expected that the results could contribute to our further understanding of muscle elasticity and provide a theoretical guideline on how to properly design parallel elasticity behaviours for engineering systems such as artificial actuators and robotic joints.

Wrinkle-to-fold transition in soft layers under equi-biaxial strain: A weakly nonlinear analysis

NASA Astrophysics Data System (ADS)

Ciarletta, P.

2014-12-01

Soft materials can experience a mechanical instability when subjected to a finite compression, developing wrinkles which may eventually evolve into folds or creases. The possibility to control the wrinkling network morphology has recently found several applications in many developing fields, such as scaffolds for biomaterials, stretchable electronics and surface micro-fabrication. Albeit much is known of the pattern initiation at the linear stability order, the nonlinear effects driving the pattern selection in soft materials are still unknown. This work aims at investigating the nature of the elastic bifurcation undertaken by a growing soft layer subjected to a equi-biaxial strain. Considering a skin effect at the free surface, the instability thresholds are found to be controlled by a characteristic length, defined by the ratio between capillary energy and bulk elasticity. For the first time, a weakly nonlinear analysis of the wrinkling instability is performed here using the multiple-scale perturbation method applied to the incremental theory in finite elasticity. The Ginzburg-Landau equations are derived for different superposing linear modes. This study proves that a subcritical pitchfork bifurcation drives the observed wrinkle-to-fold transition in swelling gels experiments, favoring the emergence of hexagonal creased patterns, albeit quasi-hexagonal patterns might later emerge because of an expected symmetry break. Moreover, if the surface energy is somewhat comparable to the bulk elastic energy, it has the same stabilizing effect as for fluid instabilities, driving the formation of stable wrinkles, as observed in elastic bi-layered materials.

A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

NASA Astrophysics Data System (ADS)

Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

2017-12-01

Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.

Crack Initiation and Propagation Properties of HY 130 Steel Weldments Following Temper Embrittlement.

DTIC Science & Technology

1982-09-01

mechanics ( EPFM ) may be applied to engineering problems to determine material properties related to crack initiation and propagation. Specifically, these...Introduction The application of linear elastic fracture mechanics (LEFM) to engineering fracture analyses has become increasingly widespread and the use...structures to which the particular material was to be applied. The advent of elastic-plastic fracture mechanics ( EPFM ) has proven valuable because a

Microstructural dependence on relevant physical-mechanical properties on SiO2-Na2O-CaO-P2O5 biological glasses.

PubMed

Rajendran, V; Begum, A Nishara; Azooz, M A; el Batal, F H

2002-11-01

Bioactive glasses of the system SiO2-Na2O-CaO-P2O5 have been prepared by the normal melting and annealing technique. The elastic moduli, attenuation, Vickers hardness, fracture toughness and fracture surface energy have been obtained using the known method at room temperature. The temperature dependence of elastic moduli and attenuation measurements have been extended over a wide range of temperature from 150 to 500 K. The SiO2 content dependence of velocities, attenuation, elastic moduli, and other parameters show an interesting observation at 45 wt% of SiO2 by exhibiting an anomalous behaviour. A linear relation is developed for Tg, which explores the influence of Na2O on SiO2-Na2O-CaO-P2O5 bioactive glasses. The measured hardness, fracture toughness and fracture surface energy show a linear relation with Young's modulus. It is also interesting to note that the observed results are functions of polymerisation and the number of non-bridging oxygens (NBO) prevailing in the network with change in SiO2 content. The temperature dependence of velocities, attenuation and elastic moduli show the existence of softening in the glass network structure as temperature increases.

Lax-Wendroff and TVD finite volume methods for unidimensional thermomechanical numerical simulations of impacts on elastic-plastic solids

NASA Astrophysics Data System (ADS)

Heuzé, Thomas

2017-10-01

We present in this work two finite volume methods for the simulation of unidimensional impact problems, both for bars and plane waves, on elastic-plastic solid media within the small strain framework. First, an extension of Lax-Wendroff to elastic-plastic constitutive models with linear and nonlinear hardenings is presented. Second, a high order TVD method based on flux-difference splitting [1] and Superbee flux limiter [2] is coupled with an approximate elastic-plastic Riemann solver for nonlinear hardenings, and follows that of Fogarty [3] for linear ones. Thermomechanical coupling is accounted for through dissipation heating and thermal softening, and adiabatic conditions are assumed. This paper essentially focuses on one-dimensional problems since analytical solutions exist or can easily be developed. Accordingly, these two numerical methods are compared to analytical solutions and to the explicit finite element method on test cases involving discontinuous and continuous solutions. This allows to study in more details their respective performance during the loading, unloading and reloading stages. Particular emphasis is also paid to the accuracy of the computed plastic strains, some differences being found according to the numerical method used. Lax-Wendoff two-dimensional discretization of a one-dimensional problem is also appended at the end to demonstrate the extensibility of such numerical scheme to multidimensional problems.

Computational Modeling of Micro-Crack Induced Attenuation in CFRP Composites

NASA Technical Reports Server (NTRS)

Roberts, R. A.; Leckey, C. A. C.

2012-01-01

A computational study is performed to determine the contribution to ultrasound attenuation in carbon fiber reinforced polymer composite laminates of linear elastic scattering by matrix micro-cracking. Multiple scattering approximations are benchmarked against exact computational approaches. Results support linear scattering as the source of observed increased attenuation in the presence of micro-cracking.

Constitutive error based parameter estimation technique for plate structures using free vibration signatures

NASA Astrophysics Data System (ADS)

Guchhait, Shyamal; Banerjee, Biswanath

2018-04-01

In this paper, a variant of constitutive equation error based material parameter estimation procedure for linear elastic plates is developed from partially measured free vibration sig-natures. It has been reported in many research articles that the mode shape curvatures are much more sensitive compared to mode shape themselves to localize inhomogeneity. Complying with this idea, an identification procedure is framed as an optimization problem where the proposed cost function measures the error in constitutive relation due to incompatible curvature/strain and moment/stress fields. Unlike standard constitutive equation error based procedure wherein a solution of a couple system is unavoidable in each iteration, we generate these incompatible fields via two linear solves. A simple, yet effective, penalty based approach is followed to incorporate measured data. The penalization parameter not only helps in incorporating corrupted measurement data weakly but also acts as a regularizer against the ill-posedness of the inverse problem. Explicit linear update formulas are then developed for anisotropic linear elastic material. Numerical examples are provided to show the applicability of the proposed technique. Finally, an experimental validation is also provided.

The Dispersion of the Axisymmetric Longitudinal Waves in the Pre-Strained Bi-Material Hollow Cylinder with the Imperfect Interface Conditions

NASA Astrophysics Data System (ADS)

Akbarov, S. D.; Ipek, C.

This work studies the influence of the imperfectness of the interface conditions on the dispersion of the axisymmetric longitudinal waves in the pre-strained bi-material hollow cylinder. The investigations are made within the 3D linearized theory of elastic waves in elastic bodies with initial stresses. It is assumed that the materials of the layers of the hollow cylinder are made from hyper elastic compressible materials and the elasticity relations of those are given through the harmonic potential. The shear spring type imperfectness of the interface conditions is considered and the degree of this imperfectness is estimated by the shear-spring parameter. Numerical results on the influence of this parameter on the behavior of the dispersion curves are presented and discussed.

The boundary element method applied to 3D magneto-electro-elastic dynamic problems

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Markov, I. P.; Kuznetsov, Iu A.

2017-11-01

Due to the coupling properties, the magneto-electro-elastic materials possess a wide number of applications. They exhibit general anisotropic behaviour. Three-dimensional transient analyses of magneto-electro-elastic solids can hardly be found in the literature. 3D direct boundary element formulation based on the weakly-singular boundary integral equations in Laplace domain is presented in this work for solving dynamic linear magneto-electro-elastic problems. Integral expressions of the three-dimensional fundamental solutions are employed. Spatial discretization is based on a collocation method with mixed boundary elements. Convolution quadrature method is used as a numerical inverse Laplace transform scheme to obtain time domain solutions. Numerical examples are provided to illustrate the capability of the proposed approach to treat highly dynamic problems.

Discontinuous Galerkin method for coupled problems of compressible flow and elastic structures

NASA Astrophysics Data System (ADS)

Kosík, A.; Feistauer, M.; Hadrava, M.; Horáček, J.

2013-10-01

This paper is concerned with the numerical simulation of the interaction of 2D compressible viscous flow and an elastic structure. We consider the model of dynamical linear elasticity. Each individual problem is discretized in space by the discontinuous Galerkin method (DGM). For the time discretization we can use either the BDF (backward difference formula) method or also the DGM. The time dependence of the domain occupied by the fluid is given by the deformation of the elastic structure adjacent to the flow domain. It is treated with the aid of the Arbitrary Lagrangian-Eulerian (ALE) method. The fluid-structure interaction, given by transient conditions, is realized by an iterative process. The developed method is applied to the simulation of the biomechanical problem containing the onset of the voice production.

First principles predictions of electronic and elastic properties of BaPb2As2 in the ThCr2Si2-type structure

NASA Astrophysics Data System (ADS)

Bourourou, Y.; Amari, S.; Yahiaoui, I. E.; Bouhafs, B.

2018-01-01

A first-principles approach is used to predicts the electronic and elastic properties of BaPb2As2 superconductor compound, using full-potential linearized augmented plane wave plus local orbitals (FP-L/APW+lo) scheme within the local density approximation LDA. The calculated equilibrium structural parameter a agree well with the experiment while the c/a ratio is far away from the experimental result. The band structure, density of states, together with the charge density and chemical bonding are discussed. The calculated elastic constants for our compound indicate that it is mechanically stable at ambient pressure. Polycrystalline elastic moduli (Young's, Bulk, shear Modulus and the Poisson's ratio) were calculated according to the Voigte-Reusse-Hill (VRH) average.

Structural, elastic and electronic properties of transition metal carbides ZnC, NbC and their ternary alloys ZnxNb1-xC

NASA Astrophysics Data System (ADS)

Zidi, Y.; Méçabih, S.; Abbar, B.; Amari, S.

2018-02-01

We have investigated the structural, electronic and elastic properties of transition-metal carbides ZnxNb1-xC alloys in the range of 0 ≤ x ≤ 1 using the density functional theory (DFT). The full potential linearized augmented plane wave (FP-LAPW) method within a framework of the generalized gradient approximation (GGA) and GGA + U (where U is the Hubbard correlation terms) approach is used to perform the calculations presented here. The lattice parameters, the bulk modulus, its pressure derivative and the elastic constants were determined. We have obtained Young's modulus, shear modulus, Poisson's ratio, anisotropy factor by the aid of the calculated elastic constants. We discuss the total and partial densities of states and charge densities.

3D Modeling Effect of Spherical Inclusions on the Magnetostriction of Bulk Superconductors

NASA Astrophysics Data System (ADS)

Zhao, Yufeng; Pan, Baocai

2018-02-01

In this paper, the dependence of the effective magnetostriction of bulk superconductors on the elastic parameters including the volume fraction and elastic modulus ratio is studied by a three-dimensional model consisting of a spherical inclusion-superconducting matrix system. The effect of the elastic modulus and volume fraction on the magnetostriction is also obtained through the magnetostriction loop. The results indicate that the elastic modulus and volume fraction have obvious effects on the effective magnetostriction of the superconducting composite, which gives an explanation about the differences between the experimental and the theoretical results. Furthermore, it is worth pointing out that the linear field dependence of magnetostriction is unique to the Bean model by comparing the curve shapes of the magnetostriction loop with and without inclusion.

The influence of geometric imperfections on the stability of three-layer beams with foam core

NASA Astrophysics Data System (ADS)

Wstawska, Iwona

2017-01-01

The main objective of this work is the numerical analysis (FE analysis) of stability of three-layer beams with metal foam core (alumina foam core). The beams were subjected to pure bending. The analysis of the local buckling was performed. Furthermore, the influence of geometric parameters of the beam and material properties of the core (linear and non-linear model) on critical loads values and buckling shape were also investigated. The calculations were made on a family of beams with different mechanical properties of the core (elastic and elastic-plastic material). In addition, the influence of geometric imperfections on deflection and normal stress values of the core and the faces has been evaluated.

Simulative design in macroscale for prospective application to micro-catheters.

PubMed

Ha, Cheol Woo

2018-02-09

In this paper, a motion-transforming element is applied to the development of a new catheter device. The motion-transforming element structure allows a reduction of linear movement and converts linear movement to rotational movement. The simulative design of micro-catheters is based on a proposed structure called the Operating Mini Station (OMS). OMS is operated by movement of a motion-transforming element. A new motion-transforming element is designed using multiple links that are connected by hinged joints based on an elastic design. The design of the links and the hinges are optimized for precise and reliable movement of the motion-transforming element. Because of the elastic design, it is possible to realize a catheter that allows various movements in small spaces like capillaries.

On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

NASA Astrophysics Data System (ADS)

BOERTJENS, G. J.; VAN HORSSEN, W. T.

2000-08-01

In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.

Microdomain Yield Behaviour in an Ultra-High Strength Low Alloy Steel for Marine Use with Low Sensitivity of SCC

NASA Astrophysics Data System (ADS)

Yin, Jiang; Tao, Anxiang; Xu, Pingguang; Ping, Dehai

The present paper involves a fundamental research on microdomain yield behavior of an ultrahigh strength low alloy steel with high temperature tempered bainite. The smooth cylinder specimen was took from deep water mooring chain links from the steel with the chemical composition of 0.23C-0.25Si -0.70Mn-3.55 (Cr+Ni+Mo) -0.13 (V+Nb+Ti) (mass %) ,which was quenched from 1253K and then tempered at 873K Its macroscopic yield strength is 1120MPa and the tensile strength is 1250MPa In-situ neutron diffraction measurements of loading tension have suggested that a good linear elastic deformation can be kept up to 500MPa stress, and then (200) priority non-linear elastic strain, that is the yield of crystal lattice occur at 700MPa and the (110) non-linear elastic strain was found at 800MPa. The (200) and (110) nonlinear elastic strain increases gradually when the stress was further increased, however, the (211) kept its linear elastic deformation stage as before. The sub-microstructural analysis carried out using TEM and additional determine the nature and quantitative analysis has revealed that there are three kinds of alloy carbides: (1) θ-M3C cementites with an average particle size of less than 50 nm which inside laths and lath boundaries; (2) ɛ-M2C formed uniformly within the ferrites with a length of less than 200 nm and width of less than 20 nm; (3) ultra-fine high density MC cohered with matrix α-Fe and its particle size is about 2 nm. The whole microdomain yield behaviour of the material was possibly influenced by the fcc-MC with high density. The results of CLT (constant load), SSRT (slow strain rate) and KIscc test of the present chain in seawater solution indicate, that threshold value of SCC (stress corrosion cracking) stress exceed 0.8 tensile strength and the chain's KIscc value is double of KIscc value of 4340 steel type parts. MC not only form strong hydrogen trap, but also slow down microdomain yield likely by means of increasing yield strength of crystal lattice, thus reduce SCC sensibility of the steel.

Structural, electronic and elastic properties of heavy fermion YbRh2 Laves phase compound

NASA Astrophysics Data System (ADS)

Pawar, Harsha; Shugani, Mani; Aynyas, Mahendra; Sanyal, Sankar P.

2018-05-01

The structural, electronic and elastic properties of YbRh2 Laves phase intermetallic compound which crystallize in cubic (MgCu2-type) structure have been investigated using ab-initio full potential linearized augmented plane wave (FP- LAPW) method with LDA and LDA+U approximation. The calculated ground state properties such as lattice parameter (a0), bulk modulus (B) and its pressure derivative (B') are in good agreement with available experimental and theoretical data. The electronic properties are analyzed from band structures and density of states. Elastic constants are predicted first time for this compound which obeys the stability criteria for cubic system.

Identification and control of structures in space

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Quinn, R. D.; Norris, M. A.

1984-01-01

The derivation of the equations of motion for the Spacecraft Control Laboratory Experiment (SCOLE) is reported and the equations of motion of a similar structure orbiting the earth are also derived. The structure is assumed to undergo large rigid-body maneuvers and small elastic deformations. A perturbation approach is proposed whereby the quantities defining the rigid-body maneuver are assumed to be relatively large, with the elastic deformations and deviations from the rigid-body maneuver being relatively small. The perturbation equations have the form of linear equations with time-dependent coefficients. An active control technique can then be formulated to permit maneuvering of the spacecraft and simultaneously suppressing the elastic vibration.

The effect of carbon concentration and plastic deformation on ultrasonic higher order elastic properties of steel

NASA Technical Reports Server (NTRS)

Heyman, J. S.; Allison, S. G.; Salama, K.

1985-01-01

The behavior of higher order elastic properties, which are much more sensitive to material state than are second order properties, has been studied for steel alloys AISI 1016, 1045, 1095, and 8620 by measuring the stress derivative of the acoustic natural velocity to determine the stress acoustic constants (SAC's). Results of these tests show a 20 percent linear variation of SAC's with carbon content as well as even larger variations with prestrain (plastic deformation). The use of higher order elastic characterization permits quantitative evaluation of solids and may prove useful in studies of fatigue and fracture.

Effect of large deformation and surface stiffening on the transmission of a line load on a neo-Hookean half space.

PubMed

Wu, Haibin; Liu, Zezhou; Jagota, Anand; Hui, Chung-Yuen

2018-03-07

A line force acting on a soft elastic solid, say due to the surface tension of a liquid drop, can cause significant deformation and the formation of a kink close to the point of force application. Analysis based on linearized elasticity theory shows that sufficiently close to its point of application, the force is borne entirely by the surface stress, not by the elasticity of the substrate; this local balance of three forces is called Neumann's triangle. However, it is not difficult to imagine realistic properties for which this force balance cannot be satisfied. For example, if the line force corresponds to surface tension of water, the numerical values of (unstretched) solid-vapor and solid-liquid surface stresses can easily be such that their sum is insufficient to balance the applied force. In such cases conventional (or naïve) Neumann's triangle of surface forces must break down. Here we study how force balance is rescued from the breakdown of naïve Neumann's triangle by a combination of (a) large hyperelastic deformations of the underlying bulk solid, and (b) increase in surface stress due to surface elasticity (surface stiffening). For a surface with constant surface stress (no surface stiffening), we show that the linearized theory remains accurate if the applied force is less than about 1.3 times the solid surface stress. For a surface in which the surface stress increases linearly with the surface stretch, we find that the Neumann's triangle construction works well as long as we replace the constant surface stress in the naïve Neumann triangle by the actual surface stress underneath the line load.

Biomechanical properties of low back myofascial tissue in younger adult ankylosing spondylitis patients and matched healthy control subjects.

PubMed

White, Allison; Abbott, Hannah; Masi, Alfonse T; Henderson, Jacqueline; Nair, Kalyani

2018-06-06

Ankylosing spondylitis is a degenerative and inflammatory rheumatologic disorder that primarily affects the spine. Delayed diagnosis leads to debilitating spinal damage. This study examines biomechanical properties of non-contracting (resting) human lower lumbar myofascia in ankylosing spondylitis patients and matched healthy control subjects. Biomechanical properties of stiffness, frequency, decrement, stress relaxation time, and creep were quantified from 24 ankylosing spondylitis patients (19 male, 5 female) and 24 age- and sex-matched control subjects in prone position on both sides initially and after 10 min rest. Concurrent surface electromyography measurements were performed to ensure resting state. Statistical analyses were conducted, and significance was set at p < 0.05. Decreased lumbar muscle elasticity (inverse of decrement) was primarily correlated with disease duration in ankylosing spondylitis subjects, whereas BMI was the primary correlate in control subjects. In ankylosing spondylitis and control groups, significant positive correlations were observed between the linear elastic properties of stiffness and frequency as well as between the viscoelastic parameters of stress relaxation time and creep. The preceding groups also showed significant negative correlations between the linear elastic and viscoelastic properties. Findings indicate that increased disease duration is associated with decreased tissue elasticity or myofascial degradation. Both ankylosing spondylitis and healthy subjects revealed similar correlations between the linear and viscoelastic properties which suggest that the disease does not directly alter their inherent interrelations. The novel results that stiffness is greater in AS than normal subjects, whereas decrement is significantly correlated with AS disease duration deserves further investigation of the biomechanical properties and their underlying mechanisms. Copyright © 2018 Elsevier Ltd. All rights reserved.

Simulation of Blast Loading on an Ultrastructurally-based Computational Model of the Ocular Lens

DTIC Science & Technology

2016-12-01

organelles. Additionally, the cell membranes demonstrated the classic ball-and-socket loops . For the SEM images, they were placed in two fixatives and mounted...considered (fibrous network and matrix), both components are modelled using a hyper - elastic framework, and the resulting constitutive model is embedded in a...within the framework of hyper - elasticity). Full details on the linearization procedures that were adopted in these previous models or the convergence

Asymptotic analysis of hierarchical martensitic microstructure

NASA Astrophysics Data System (ADS)

Cesana, Pierluigi; Porta, Marcel; Lookman, Turab

2014-12-01

We consider a hierarchical nested microstructure, which also contains a point of singularity (disclination) at the origin, observed in lead orthovanadate. We show how to exactly compute the energy cost and associated displacement field within linearized elasticity by enforcing geometric compatibility of strains across interfaces of the three-phase mixture of distortions (variants) in the microstructure. We prove that the mechanical deformation is purely elastic and discuss the behavior of the system close to the origin.

A new method for the visualization and quantification of internal skin elasticity by ultrasound imaging.

PubMed

Osanai, Osamu; Ohtsuka, Mayumi; Hotta, Mitsuyuki; Kitaharai, Takashi; Takema, Yoshinori

2011-08-01

Skin elasticity has been assessed previously only in the surface layer. We developed a new method that uses tissue strain imaging (TSI) technology, and the aim of this study was to test this new method to assess internal skin elasticity. Using a pressure device with a 12 MHz ultrasound transducer, constant and linear compressions were applied to the cheek skin of 35 volunteers (aged: 20-60 years). The elasticity of each layer (dermis, subcutaneous and muscle) was measured and analyzed using the TSI application software incorporated into the Toshiba Aplio(™) XV ultrasound system. A skin tissue-equivalent phantom, which is a block of material with the acoustic velocity (1530 m/s) of human skin, was collaboratively developed by OST Inc. This phantom was placed between the skin and the transducer as a reference material. Skin elasticity was clearly visualized and quantified in each layer of the skin. Age-dependent decreases in elasticity were determined in all layers of the skin. Among the three internal skin layers, the highest elasticity was determined in the subcutaneous layer followed by the muscle layer. These findings support the validity and sensitivity of the TSI method to assess the elasticity of various layers of skin. © 2011 John Wiley & Sons A/S.

Inverse finite element methods for extracting elastic-poroviscoelastic properties of cartilage and other soft tissues from indentation

NASA Astrophysics Data System (ADS)

Namani, Ravi

Mechanical properties are essential for understanding diseases that afflict various soft tissues, such as osteoarthritic cartilage and hypertension which alters cardiovascular arteries. Although the linear elastic modulus is routinely measured for hard materials, standard methods are not available for extracting the nonlinear elastic, linear elastic and time-dependent properties of soft tissues. Consequently, the focus of this work is to develop indentation methods for soft biological tissues; since analytical solutions are not available for the general context, finite element simulations are used. First, parametric studies of finite indentation of hyperelastic layers are performed to examine if indentation has the potential to identify nonlinear elastic behavior. To answer this, spherical, flat-ended conical and cylindrical tips are examined and the influence of thickness is exploited. Also the influence of the specimen/substrate boundary condition (slip or non-slip) is clarified. Second, a new inverse method---the hyperelastic extraction algorithm (HPE)---was developed to extract two nonlinear elastic parameters from the indentation force-depth data, which is the basic measurement in an indentation test. The accuracy of the extracted parameters and the influence of noise in measurements on this accuracy were obtained. This showed that the standard Berkovitch tip could only extract one parameter with sufficient accuracy, since the indentation force-depth curve has limited sensitivity to both nonlinear elastic parameters. Third, indentation methods for testing tissues from small animals were explored. New methods for flat-ended conical tips are derived. These account for practical test issues like the difficulty in locating the surface or soft specimens. Also, finite element simulations are explored to elucidate the influence of specimen curvature on the indentation force-depth curve. Fourth, the influence of inhomogeneity and material anisotropy on the extracted "average" linear elastic modulus was studied. The focus here is on murine tibial cartilage, since recent experiments have shown that the modulus measured by a 15 mum tip is considerably larger than that obtained from a 90 mum tip. It is shown that a depth-dependent modulus could give rise to such a size effect. Lastly, parametric studies were performed within the small strain setting to understand the influence of permeability and viscoelastic properties on the indentation stress-relaxation response. The focus here is on cartilage, and specific test protocols (single-step vs. multi-step stress relaxation) are explored. An inverse algorithm was developed to extract the poroviscoelastic parameters. A sensitivity study using this algorithm shows that the instantaneous elastic modulus (which is a measure of the viscous relaxation) can be extracted with very good accuracy, but the permeability and long-time relaxation constant cannot be extracted with good accuracy. The thesis concludes with implications of these studies. The potential and limitations of indentation tests for studying cartilage and other soft tissues is discussed.

Influence of third-degree geometric nonlinearities on the vibration and stability of pretwisted, preconed, rotating blades

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1986-01-01

The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree geometric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.

A novel pressure variation study on electronic structure, mechanical stability and thermodynamic properties of potassium based fluoroperovskite

NASA Astrophysics Data System (ADS)

Erum, Nazia; Azhar Iqbal, Muhammad

2017-09-01

The effect of pressure variation on stability, structural parameters, elastic constants, mechanical, electronic and thermodynamic properties of cubic SrKF3 fluoroperovskite have been investigated by using the full-potential linearized augmented plane wave (FP-LAPW) method combined with Quasi-harmonic Debye model in which the phonon effects are considered. The calculated lattice parameters show a prominent decrease in lattice constant and bonds length with the increase in pressure. The application of pressure from 0 to 25 GPa reveals a predominant characteristic associated with widening of bandgap with GGA and GGA plus Tran-Blaha modified Becke-Johnson (TB-mBJ) potential. The influence of pressure on elastic constants and their related mechanical parameters have been discussed in detail. Apart of linear dependence of elastic coefficients, transition from brittle to ductile behavior is also observed at elevated pressure ranges. We have successfully computed variation of lattice constant, volume expansion, bulk modulus, Debye temperature and specific heat capacities at pressure and temperature in the range of 0-25 GPa and 0-600 K.

On the Opening of Thick Walled Elastic Tubes: A Fluid-Structure Model for Acid Reflux

NASA Astrophysics Data System (ADS)

Ghosh, Sudip; Kahrilas, Peter

2005-11-01

A coupled fluid-structure mathematical model was developed to quantify rapid opening of thick-walled elastic tubes, a phenomenon underlying biological flows such as gastroesophageal reflux disease (GERD). The wall was modeled using non-linear finite deformation theory to predict space-time radial distention of an axisymmetric tube with luminal fluid flow. Anisotropic azimuthal and longitudinal muscle-induced stresses were incorporated, and interstitial material properties were assumed isotropic and linearly elastic. Fluid flow was modeled using lubrication theory with inertial correction. Opening and flow were driven by a specified inflow pressure and zero pressure gradient was specified at outflow. No-slip and surface force balance were applied at the fluid-wall interface. Viscoelasticity was modeled with ad hoc damping and the evolution of the tube geometry was predicted at mid-layer. A potentially important discovery was made when applied to studies of initiation of opening with GERD: while material stiffness is of minor consequence, small changes in resting lumen distension (˜2 mm diameter) may be a sensitive distinguishing feature of the disease.

Process Modelling of Curing Process-Induced Internal Stress and Deformation of Composite Laminate Structure with Elastic and Viscoelastic Models

NASA Astrophysics Data System (ADS)

Li, Dongna; Li, Xudong; Dai, Jianfeng

2018-06-01

In this paper, two kinds of transient models, the viscoelastic model and the linear elastic model, are established to analyze the curing deformation of the thermosetting resin composites, and are calculated by COMSOL Multiphysics software. The two models consider the complicated coupling between physical and chemical changes during curing process of the composites and the time-variant characteristic of material performance parameters. Subsequently, the two proposed models are implemented respectively in a three-dimensional composite laminate structure, and a simple and convenient method of local coordinate system is used to calculate the development of residual stresses, curing shrinkage and curing deformation for the composite laminate. Researches show that the temperature, degree of curing (DOC) and residual stresses during curing process are consistent with the study in literature, so the curing shrinkage and curing deformation obtained on these basis have a certain referential value. Compared the differences between the two numerical results, it indicates that the residual stress and deformation calculated by the viscoelastic model are more close to the reference value than the linear elastic model.

Lattice dynamic properties of Rh2XAl (X=Fe and Y) alloys

NASA Astrophysics Data System (ADS)

Al, Selgin; Arikan, Nihat; Demir, Süleyman; Iyigör, Ahmet

2018-02-01

The electronic band structure, elastic and vibrational spectra of Rh2FeAl and Rh2YAl alloys were computed in detail by employing an ab-initio pseudopotential method and a linear-response technique based on the density-functional theory (DFT) scheme within a generalized gradient approximation (GGA). Computed lattice constants, bulk modulus and elastic constants were compared. Rh2YAl exhibited higher ability to resist volume change than Rh2FeAl. The elastic constants, shear modulus, Young modulus, Poisson's ratio, B/G ratio electronic band structure, total and partial density of states, and total magnetic moment of alloys were also presented. Rh2FeAl showed spin up and spin down states whereas Rh2YAl showed none due to being non-magnetic. The calculated total densities of states for both materials suggest that both alloys are metallic in nature. Full phonon spectra of Rh2FeAl and Rh2YA1 alloys in the L21 phase were collected using the ab-initio linear response method. The obtained phonon frequencies were in the positive region indicating that both alloys are dynamically stable.

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.

Buckling delamination of the circular sandwich plate with piezoelectric face and elastic core layers under rotationally symmetric external pressure

NASA Astrophysics Data System (ADS)

Akbarov, Surkay D.; Cafarova, Fazile I.; Yahnioglu, Nazmiye

2017-02-01

The axisymmetric buckling delamination of the piezoelectric circular sandwich plate with piezoelectric face and elastic (metal) core layers around the interface penny-shaped cracks is investigated. The case is considered where short-circuit conditions with respect to the electrical potential on the upper and lower and also lateral surfaces of face layers are satisfied. It is assumed that the edge surfaces of the cracks have an infinitesimal rotationally symmetric initial imperfection and the development of this imperfection with rotationally symmetric compressive forces acting on the lateral surface of the plate is studied by employing the exact geometrically non-linear field equations and relations of electro-elasticity for piezoelectric materials. Solution to the considered nonlinear problem is reduced to solution of the series boundary value problems derived by applying the linearization procedure with respect to small imperfection of the sought values. Numerical results reveal the effect of piezoelectricity as well as geometrical and material parameters on the critical values are determined numerically by employing finite element method (FEM).

Viscous-elastic dynamics of power-law fluids within an elastic cylinder

NASA Astrophysics Data System (ADS)

Boyko, Evgeniy; Bercovici, Moran; Gat, Amir D.

2017-07-01

In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a tn/n +1 dependence on time (t ), suggesting the ability to indirectly measure the power-law index (n ) of shear-thinning liquids through measurements of elastic deformation.

Significance of third-order elasticity for determination of the pressure coefficient of the light emission in strained quantum wells

NASA Astrophysics Data System (ADS)

Łepkowski, S. P.

2008-10-01

We investigate the contribution arising from third-order elasticity to the pressure coefficient of the light emission (dEE/dP) in strained zinc-blende InGaAs/GaAs and InGaN/GaN quantum wells (QWs) grown in a (001) direction. In the framework of the third-order elasticity theory, we develop a model of pressure tuning of strains in these structures, which is then used to determine the coefficient dEE/dP . In the calculations of dEE/dP , we use a consistent set of the second- and third-order elastic constants which has been obtained from ab initio calculations. Our results indicate that the usage of third-order elasticity leads to significant reduction in dEE/dP in strained (001)-oriented InGaAs/GaAs and InGaN/GaN QWs, in comparison to the values of dEE/dP obtained by using the linear theory of elasticity. In the case of InGaAs/GaAs QWs, the values of dEE/dP calculated using third-order elasticity are in reasonable agreement with experimental data. For InGaN/GaN QWs, better agreement between theoretical and experimental values of dEE/dP is obtained when instead of third-order elasticity, pressure dependence of the second-order elastic constants is taken into account.

A comparison of the two approaches of the theory of critical distances based on linear-elastic and elasto-plastic analyses

NASA Astrophysics Data System (ADS)

Terekhina, A. I.; Plekhov, O. A.; Kostina, A. A.; Susmel, L.

2017-06-01

The problem of determining the strength of engineering structures, considering the effects of the non-local fracture in the area of stress concentrators is a great scientific and industrial interest. This work is aimed on modification of the classical theory of critical distance that is known as a method of failure prediction based on linear-elastic analysis in case of elasto-plastic material behaviour to improve the accuracy of estimation of lifetime of notched components. Accounting plasticity has been implemented with the use of the Simplified Johnson-Cook model. Mechanical tests were carried out using a 300 kN electromechanical testing machine Shimadzu AG-X Plus. The cylindrical un-notched specimens and specimens with stress concentrators of titanium alloy Grade2 were tested under tensile loading with different grippers travel speed, which ensured several orders of strain rate. The results of elasto-plastic analyses of stress distributions near a wide variety of notches are presented. The results showed that the use of the modification of the TCD based on elasto-plastic analysis gives us estimates falling within an error interval of ±5-10%, that more accurate predictions than the linear elastic TCD solution. The use of an improved description of the stress-strain state at the notch tip allows introducing the critical distances as a material parameter.

Design, Optimization and Evaluation of Integrally Stiffened Al 7050 Panel with Curved Stiffeners

NASA Technical Reports Server (NTRS)

Slemp, Wesley C. H.; Bird, R. Keith; Kapania, Rakesh K.; Havens, David; Norris, Ashley; Olliffe, Robert

2011-01-01

A curvilinear stiffened panel was designed, manufactured, and tested in the Combined Load Test Fixture at NASA Langley Research Center. The panel was optimized for minimum mass subjected to constraints on buckling load, yielding, and crippling or local stiffener failure using a new analysis tool named EBF3PanelOpt. The panel was designed for a combined compression-shear loading configuration that is a realistic load case for a typical aircraft wing panel. The panel was loaded beyond buckling and strains and out-of-plane displacements were measured. The experimental data were compared with the strains and out-of-plane deflections from a high fidelity nonlinear finite element analysis and linear elastic finite element analysis of the panel/test-fixture assembly. The numerical results indicated that the panel buckled at the linearly elastic buckling eigenvalue predicted for the panel/test-fixture assembly. The experimental strains prior to buckling compared well with both the linear and nonlinear finite element model.

Identification of internal properties of fibers and micro-swimmers

NASA Astrophysics Data System (ADS)

Plouraboue, Franck; Thiam, Ibrahima; Delmotte, Blaise; Climent, Eric; PSC Collaboration

2016-11-01

In this presentation we discuss the identifiability of constitutive parameters of passive or active micro-swimmers. We first present a general framework for describing fibers or micro-swimmers using a bead-model description. Using a kinematic constraint formulation to describe fibers, flagellum or cilia, we find explicit linear relationship between elastic constitutive parameters and generalised velocities from computing contact forces. This linear formulation then permits to address explicitly identifiability conditions and solve for parameter identification. We show that both active forcing and passive parameters are both identifiable independently but not simultaneously. We also provide unbiased estimators for elastic parameters as well as active ones in the presence of Langevin-like forcing with Gaussian noise using normal linear regression models and maximum likelihood method. These theoretical results are illustrated in various configurations of relaxed or actuated passives fibers, and active filament of known passive properties, showing the efficiency of the proposed approach for direct parameter identification. The convergence of the proposed estimators is successfully tested numerically.

Inelastic strain analogy for piecewise linear computation of creep residues in built-up structures

NASA Technical Reports Server (NTRS)

Jenkins, Jerald M.

1987-01-01

An analogy between inelastic strains caused by temperature and those caused by creep is presented in terms of isotropic elasticity. It is shown how the theoretical aspects can be blended with existing finite-element computer programs to exact a piecewise linear solution. The creep effect is determined by using the thermal stress computational approach, if appropriate alterations are made to the thermal expansion of the individual elements. The overall transient solution is achieved by consecutive piecewise linear iterations. The total residue caused by creep is obtained by accumulating creep residues for each iteration and then resubmitting the total residues for each element as an equivalent input. A typical creep law is tested for incremental time convergence. The results indicate that the approach is practical, with a valid indication of the extent of creep after approximately 20 hr of incremental time. The general analogy between body forces and inelastic strain gradients is discussed with respect to how an inelastic problem can be worked as an elastic problem.

Experimental and Computational Investigation of Viscoelasticity of Native and Engineered Ligament and Tendon

NASA Astrophysics Data System (ADS)

Ma, J.; Narayanan, H.; Garikipati, K.; Grosh, K.; Arruda, E. M.

The important mechanisms by which soft collagenous tissues such as ligament and tendon respond to mechanical deformation include non-linear elasticity, viscoelasticity and poroelasticity. These contributions to the mechanical response are modulated by the content and morphology of structural proteins such as type I collagen and elastin, other molecules such as glycosaminoglycans, and fluid. Our ligament and tendon constructs, engineered from either primary cells or bone marrow stromal cells and their autogenous matricies, exhibit histological and mechanical characteristics of native tissues of different levels of maturity. In order to establish whether the constructs have optimal mechanical function for implantation and utility for regenerative medicine, constitutive relationships for the constructs and native tissues at different developmental levels must be established. A micromechanical model incorporating viscoelastic collagen and non-linear elastic elastin is used to describe the non-linear viscoelastic response of our homogeneous engineered constructs in vitro. This model is incorporated within a finite element framework to examine the heterogeneity of the mechanical responses of native ligament and tendon.

Functional similarities in the mechanical design of the aorta in lower vertebrates and mammals.

PubMed

Gibbons, C A; Shadwick, R E

1989-12-01

The mechanical properties of the aorta from the toad Bufo marinus, the lizard Gekko gecko and the garter snake Thamnophis radix were compared to those of the rat, by inflation of vessel segments in vitro. The arteries of the lower vertebrates, like those of mammals, were compliant, highly resilient, and non-linearly elastic. The elastic modulus of the artery wall was similar in the lower vertebrates and mammals, at their respective mean physiological pressures. We conclude that the aorta in each of these animals is suitably designed to function effectively as an elastic pulse smoothing component in the circulation; differences in the pressure wave transmission characteristics of lower vertebrates and mammals do not result from dissimilarities in arterial elastic properties, but from substantial differences in heart rate of these two groups.

Finite element analysis of large transient elastic-plastic deformations of simple structures, with application to the engine rotor fragment containment/deflection problem

NASA Technical Reports Server (NTRS)

Wu, R. W.; Witmer, E. A.

1972-01-01

Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.

Mathematical modeling of aeroelastic systems

NASA Astrophysics Data System (ADS)

Velmisov, Petr A.; Ankilov, Andrey V.; Semenova, Elizaveta P.

2017-12-01

In the paper, the stability of elastic elements of a class of designs that are in interaction with a gas or liquid flow is investigated. The definition of the stability of an elastic body corresponds to the concept of stability of dynamical systems by Lyapunov. As examples the mathematical models of flowing channels (models of vibration devices) at a subsonic flow and the mathematical models of protective surface at a supersonic flow are considered. Models are described by the related systems of the partial differential equations. An analytic investigation of stability is carried out on the basis of the construction of Lyapunov-type functionals, a numerical investigation is carried out on the basis of the Galerkin method. The various models of the gas-liquid environment (compressed, incompressible) and the various models of a deformable body (elastic linear and elastic nonlinear) are considered.

First-Order System Least Squares for Velocity-Vorticity-Pressure Form of the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Zhiqiang; Manteuffel, Thomas A.; McCormick, Stephen F.

1996-01-01

In this paper, we study the least-squares method for the generalized Stokes equations (including linear elasticity) based on the velocity-vorticity-pressure formulation in d = 2 or 3 dimensions. The least squares functional is defined in terms of the sum of the L(exp 2)- and H(exp -1)-norms of the residual equations, which is weighted appropriately by by the Reynolds number. Our approach for establishing ellipticity of the functional does not use ADN theory, but is founded more on basic principles. We also analyze the case where the H(exp -1)-norm in the functional is replaced by a discrete functional to make the computation feasible. We show that the resulting algebraic equations can be uniformly preconditioned by well-known techniques.

Closed-form solution for Eshelby's elliptic inclusion in antiplane elasticity using complex variable

NASA Astrophysics Data System (ADS)

Chen, Y. Z.

2013-12-01

This paper provides a closed-form solution for the Eshelby's elliptic inclusion in antiplane elasticity. In the formulation, the prescribed eigenstarins are not only for the uniform distribution, but also for the linear form. After using the complex variable and the conformal mapping, the continuation condition for the traction and displacement along the interface in the physical plane can be reduced to a condition along the unit circle. The relevant complex potentials defined in the inclusion and the matrix can be separated from the continuation conditions of the traction and displacement along the interface. The expressions of the real strains and stresses in the inclusion from the assumed eigenstrains are presented. Results for the case of linear distribution of eigenstrain are first obtained in the paper.

Sensitivity of inelastic response to numerical integration of strain energy. [for cantilever beam

NASA Technical Reports Server (NTRS)

Kamat, M. P.

1976-01-01

The exact solution to the quasi-static, inelastic response of a cantilever beam of rectangular cross section subjected to a bending moment at the tip is obtained. The material of the beam is assumed to be linearly elastic-linearly strain-hardening. This solution is then compared with three different numerical solutions of the same problem obtained by minimizing the total potential energy using Gaussian quadratures of two different orders and a Newton-Cotes scheme for integrating the strain energy of deformation. Significant differences between the exact dissipative strain energy and its numerical counterpart are emphasized. The consequence of this on the nonlinear transient responses of a beam with solid cross section and that of a thin-walled beam on elastic supports under impulsive loads are examined.

Observing (non)linear lattice dynamics in graphite by ultrafast Kikuchi diffraction

PubMed Central

Liang, Wenxi; Vanacore, Giovanni M.; Zewail, Ahmed H.

2014-01-01

In materials, the nature of the strain–stress relationship, which is fundamental to their properties, is determined by both the linear and nonlinear elastic responses. Whereas the linear response can be measured by various techniques, the nonlinear behavior is nontrivial to probe and to reveal its nature. Here, we report the methodology of time-resolved Kikuchi diffraction for mapping the (non)linear elastic response of nanoscale graphite following an ultrafast, impulsive strain excitation. It is found that the longitudinal wave propagating along the c-axis exhibits echoes with a frequency of 9.1 GHz, which indicates the reflections of strain between the two surfaces of the material with a speed of ∼4 km/s. Because Kikuchi diffraction enables the probing of strain in the transverse direction, we also observed a higher-frequency mode at 75.5 GHz, which has a relatively long lifetime, on the order of milliseconds. The fluence dependence and the polarization properties of this nonlinear mode are entirely different from those of the linear, longitudinal mode, and here we suggest a localized breather motion in the a-b plane as the origin of the nonlinear shear dynamics. The approach presented in this contribution has the potential for a wide range of applications because most crystalline materials exhibit Kikuchi diffraction. PMID:24706785

A Focused Fundamental Study of Predicting Materials Degradation & Fatigue. Volume 1

DTIC Science & Technology

1997-05-31

physical properties are: bulk modulus, shear strength, coefficient of friction, modulus of elasticity/ rigidity and Poisson’s ratio. Each of these physical...acting on a subsurface crack when abrasive motion occurs on the surface using linear elastic fracture mechanics theory. Both mechanisms involve a...The body of the scattering 5 cell was a 4-way Swagelok*(Crawford Fitting Co., Solon, OH) connector with a 1.5 mm hole drilled in the top for

Dependence of laser radiation intensity on the elastic deformation of a revolving optical disk with a reflective coating

NASA Astrophysics Data System (ADS)

Gladyshev, V. O.; Portnov, D. I.

2016-12-01

The physical mechanism of alteration of intensity of linearly polarized monochromatic electromagnetic radiation with λ = 630 nm in a revolving dielectric disk with a mirror coating is examined. The effect is induced by elastic deformation due to the revolution and by thermoelastic deformation of the optically transparent disk. These deformations result in birefringence, the polarization plane rotation, and a 30-40% change in the intensity of reflected radiation.

Density and mechanical properties of calcium aluminate cement

NASA Astrophysics Data System (ADS)

Ahmed, Syed Taqi Uddin; Ahmmad, Shaik Kareem

2018-04-01

Calcium aluminate cements are a special type of cements which have their composition mainly dominated by the presence of Monocalcium Aluminates. In the present paper for the first time we have shown theoretical density and elastic constants for various calcium aluminate cements. The density of the present CAS decrease with aluminates presents in the cement. Using the density data, the elastic moduli namely Young's modulus, bulk and shear modulus show strong linear dependence as a function of compositional parameter.

Effect of Emplacement Material Properties on Chemical Explosion Spectra - Preliminary Analysis Using Synthetic Waveforms Near Elastic Radii

NASA Astrophysics Data System (ADS)

Saikia, C. K.; Ezzedine, S. M.; Vorobiev, O.; Antoun, T.; Woods, M. T.

2017-12-01

The focus of this study is to investigate the effect of the non-linear material properties on synthetic waveforms at receivers located within the elastic region near the non-linear zone around energetic chemical explosions. The primary goal is to characterize the effect of porosity and joint properties. The joint sizes are typically small compared with the wavelength represented by the computational grid, so the calculations become time consuming to properly represent the fidelity of the calculations. In this study, we use GEODYN-L Lagrangian code, where the joints are included explicitly. We simulate a suite of synthetics for chemical explosions in granite, and varying the porosity and joint orientation. Using the generated synthetic waveforms in the elastic region, we calculate displacement spectra and compare them with homogenous medium solutions (i.e., free of porosity and joints). We are attempting to develop a set of correction factors necessary to apply in various field (emplacement) conditions so that the spectral characteristics can be compared to those predicted by the Mueller-Murphy (MM, 1971; Saikia, 2017) and other source functions (Denny and Johnson, 1991; Ford and Walter, 2013) near the elastic radii. Future investigations will include similar analysis for the nuclear explosions. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Passive and active ventricular elastances of the left ventricle

PubMed Central

Zhong, Liang; Ghista, Dhanjoo N; Ng, Eddie YK; Lim, Soo T

2005-01-01

Background Description of the heart as a pump has been dominated by models based on elastance and compliance. Here, we are presenting a somewhat new concept of time-varying passive and active elastance. The mathematical basis of time-varying elastance of the ventricle is presented. We have defined elastance in terms of the relationship between ventricular pressure and volume, as: dP = EdV + VdE, where E includes passive (Ep) and active (Ea) elastance. By incorporating this concept in left ventricular (LV) models to simulate filling and systolic phases, we have obtained the time-varying expression for Ea and the LV-volume dependent expression for Ep. Methods and Results Using the patient's catheterization-ventriculogram data, the values of passive and active elastance are computed. Ea is expressed as: ; Epis represented as: . Ea is deemed to represent a measure of LV contractility. Hence, Peak dP/dt and ejection fraction (EF) are computed from the monitored data and used as the traditional measures of LV contractility. When our computed peak active elastance (Ea,max) is compared against these traditional indices by linear regression, a high degree of correlation is obtained. As regards Ep, it constitutes a volume-dependent stiffness property of the LV, and is deemed to represent resistance-to-filling. Conclusions Passive and active ventricular elastance formulae can be evaluated from a single-beat P-V data by means of a simple-to-apply LV model. The active elastance (Ea) can be used to characterize the ventricle's contractile state, while passive elastance (Ep) can represent a measure of resistance-to-filling. PMID:15707494

Structural, Electronic and Elastic Properties of Heavy Fermion YbTM2 (TM= Ir and Pt) Laves Phase Compounds

NASA Astrophysics Data System (ADS)

Pawar, H.; Shugani, M.; Aynyas, M.; Sanyal, S. P.

2018-02-01

The structural, electronic and elastic properties of YbTM2 (TM = Ir and Pt) Laves phase intermetallic compounds which crystallize in cubic (MgCu2-type) structure, have been investigated using ab-initio full potential linearized augmented plane wave (FP-LAPW) method with LDA and LDA+U approximation. The calculated ground state properties such as lattice parameter (a0), bulk modulus (B) and its pressure derivative (B‧) are in good agreement with available experimental and theoretical data. The electronic properties are analyzed from band structures and density of states. Elastic constants are predicted first time for these compounds which obey the stability criteria for cubic system.

Ab-initio thermodynamic and elastic properties of AlNi and AlNi3 intermetallic compounds

NASA Astrophysics Data System (ADS)

Yalameha, Shahram; Vaez, Aminollah

2018-04-01

In this paper, thermodynamic and elastic properties of the AlNi and AlNi3 were investigated using density functional theory (DFT). The full-potential linearized augmented plane-wave (APW) in the framework of the generalized gradient approximation as used as implemented in the Wien2k package. The temperature dependence of thermal expansion coefficient, bulk modulus and heat capacity in a wide range of temperature (0-1600 K) were investigated. The calculated elastic properties of the compounds show that both intermetallic compounds of AlNi and AlNi3 have surprisingly negative Poisson’s ratio (NPR). The results were compared with other experimental and computational data.

Hypo-Elastic Model for Lung Parenchyma

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

Freed, Alan D.; Einstein, Daniel R.

2012-03-01

A simple elastic isotropic constitutive model for the spongy tissue in lung is derived from the theory of hypoelasticity. The model is shown to exhibit a pressure dependent behavior that has been interpreted by some as indicating extensional anisotropy. In contrast, we show that this behavior arises natural from an analysis of isotropic hypoelastic invariants, and is a likely result of non-linearity, not anisotropy. The response of the model is determined analytically for several boundary value problems used for material characterization. These responses give insight into both the material behavior as well as admissible bounds on parameters. The model ismore » characterized against published experimental data for dog lung. Future work includes non-elastic model behavior.« less

Linear movement of plywood and flakeboards as related to the longitudinal movement of wood

Treesearch

B. G. Heebink; E. W. Kuenzi; A. C. Maki

1964-01-01

Veneer, plywood, and flakeboard specimens were subjected to various humidity conditions. Physical and elastic properties of the veneer were determined and the influence of these properties on the movement of plywood and flakeboards fabricated of like material was evaluated, The linear movement of the plywood and flakeboards was closely related to the longitudinal-to-...

Mechanisms Inducing Jet Rotation in Shear-Formed Shaped-Charge Liners.

DTIC Science & Technology

1990-03-01

of deviatoric strain, and compressibility affects only the equation of state , not the deviatoric stress /strain relation. An anisotropic formulation is...strains, a more accurate scalar equation of state should simultaneously be employed to account for non-linear compressibility effects . A4 A.3 Elastic... obtainable knowing the previous and present cycles’ average stress . However, many non-linear equations

Polymer concentration and properties of elastic turbulence in a von Karman swirling flow

NASA Astrophysics Data System (ADS)

Jun, Yonggun; Steinberg, Victor

2017-10-01

We report detailed experimental studies of statistical, scaling, and spectral properties of elastic turbulence (ET) in a von Karman swirling flow between rotating and stationary disks of polymer solutions in a wide, from dilute to semidilute entangled, range of polymer concentrations ϕ . The main message of the investigation is that the variation of ϕ just weakly modifies statistical, scaling, and spectral properties of ET in a swirling flow. The qualitative difference between dilute and semidilute unentangled versus semidilute entangled polymer solutions is found in the dependence of the critical Weissenberg number Wic of the elastic instability threshold on ϕ . The control parameter of the problem, the Weissenberg number Wi, is defined as the ratio of the nonlinear elastic stress to dissipation via linear stress relaxation and quantifies the degree of polymer stretching. The power-law scaling of the friction coefficient on Wi/Wic characterizes the ET regime with the exponent independent of ϕ . The torque Γ and pressure p power spectra show power-law decays with well-defined exponents, which has values independent of Wi and ϕ separately at 100 ≤ϕ ≤900 ppm and 1600 ≤ϕ ≤2300 ppm ranges. Another unexpected observation is the presence of two types of the boundary layers, horizontal and vertical, distinguished by their role in the energy pumping and dissipation, which has width dependence on Wi and ϕ differs drastically. In the case of the vertical boundary layer near the driving disk, wvv is independent of Wi/Wic and linearly decreases with ϕ /ϕ * , while in the case of the horizontal boundary layer wvh its width is independent of ϕ /ϕ * , linearly decreases with Wi/Wic , and is about five times smaller than wvv. Moreover, these Wi and ϕ dependencies of the vertical and horizontal boundary layer widths are found in accordance with the inverse turbulent intensity calculated inside the boundary layers Vθh/Vθh rms and Vθv/Vθv rms , respectively. Specifically, the dependence of Vθv/Vθv rms in the vertical boundary layer on Wi and ϕ agrees with a recent theoretical prediction [S. Belan, A. Chernych, and V. Lebedev, Boundary layer of elastic turbulence (unpublished)].

What Do Observations of Postseismic Deformation Tell us About the Rheology of the Lithoshpere?

NASA Astrophysics Data System (ADS)

Fialko, Y.

2006-12-01

Geodetic observations in epicentral areas of large shallow earthquakes reveal transient displacements that typically have the same sense as the coseismic ones, but are about an order of magnitude smaller. A number of different mechanisms has been proposed to explain the observed time-dependent deformation, including afterslip on a deep extension of the seismic rupture, viscous-like response of a substrate below the brittle-ductile transition (e.g., the lower crust or upper mantle), and re-distribution of pore fluids in the upper crust. Distinguishing the relative contributions of these relaxation mechanisms is important before one can make robust inferences about the effective rheology of the upper part of the continental lithosphere. Either the bulk visco-elastic relaxation or afterslip is required to explain large horizontal displacements observed in the aftermath of large strike-slip earthquakes. Both temporal and spatial signatures of postseismic deformation were used to demonstrate that simple linear Maxwell rheologies are not adequate. For non-linear (e.g., powerlaw) rheologies, the surface deformation field may be indistinguishable from that due to afterslip at the early stages of relaxation, when the deformation is localized in high stress areas on the downdip continuation of the earthquake fault. However, at later stages of relaxation visco-elastic models predict appreciable changes in the displacement pattern. In particular, vertical velocities may change sign after viscous flow in the ductile substrate becomes more diffuse. Thus afterslip and non-linear visco-elastic models can be in principle distinguished given a sufficiently long observation period. Fluid flow and poro-elastic effects are incapable of explaining the observed horizontal deformation, but may substantially contribute to vertical postseismic motions, further complicating a discrimination between afterslip and visco-elastic relaxation. I will present space geodetic measurements of postseismic deformation due to several large earthquakes in California and Asia, and discuss implications from these measurements for the crust and upper mantle rheology. The main conclusion is that the deformation patterns are not consistent between different events, suggesting either various contributions from different relaxation mechanisms, or significant variations in crustal rheologies.

Automatic control: the vertebral column of dogfish sharks behaves as a continuously variable transmission with smoothly shifting functions.

PubMed

Porter, Marianne E; Ewoldt, Randy H; Long, John H

2016-09-15

During swimming in dogfish sharks, Squalus acanthias, both the intervertebral joints and the vertebral centra undergo significant strain. To investigate this system, unique among vertebrates, we cyclically bent isolated segments of 10 vertebrae and nine joints. For the first time in the biomechanics of fish vertebral columns, we simultaneously characterized non-linear elasticity and viscosity throughout the bending oscillation, extending recently proposed techniques for large-amplitude oscillatory shear (LAOS) characterization to large-amplitude oscillatory bending (LAOB). The vertebral column segments behave as non-linear viscoelastic springs. Elastic properties dominate for all frequencies and curvatures tested, increasing as either variable increases. Non-linearities within a bending cycle are most in evidence at the highest frequency, 2.0 Hz, and curvature, 5 m -1 Viscous bending properties are greatest at low frequencies and high curvatures, with non-linear effects occurring at all frequencies and curvatures. The range of mechanical behaviors includes that of springs and brakes, with smooth transitions between them that allow for continuously variable power transmission by the vertebral column to assist in the mechanics of undulatory propulsion. © 2016. Published by The Company of Biologists Ltd.

An instrument to measure mechanical up-conversion phenomena in metals in the elastic regime

NASA Astrophysics Data System (ADS)

Vajente, G.; Quintero, E. A.; Ni, X.; Arai, K.; Gustafson, E. K.; Robertson, N. A.; Sanchez, E. J.; Greer, J. R.; Adhikari, R. X.

2016-06-01

Crystalline materials, such as metals, are known to exhibit deviation from a simple linear relation between strain and stress when the latter exceeds the yield stress. In addition, it has been shown that metals respond to varying external stress in a discontinuous way in this regime, exhibiting discrete releases of energy. This crackling noise has been extensively studied both experimentally and theoretically when the metals are operating in the plastic regime. In our study, we focus on the behavior of metals in the elastic regime, where the stresses are well below the yield stress. We describe an instrument that aims to characterize non-linear mechanical noise in metals when stressed in the elastic regime. In macroscopic systems, this phenomenon is expected to manifest as a non-stationary noise modulated by external disturbances applied to the material, a form of mechanical up-conversion of noise. The main motivation for this work is for the case of maraging steel components (cantilevers and wires) in the suspension systems of terrestrial gravitational wave detectors. Such instruments are planned to reach very ambitious displacement sensitivities, and therefore mechanical noise in the cantilevers could prove to be a limiting factor for the detectors' final sensitivities, mainly due to non-linear up-conversion of low frequency residual seismic motion to the frequencies of interest for the gravitational wave observations. We describe here the experimental setup, with a target sensitivity of 10-15 m/ √{ Hz } in the frequency range of 10-1000 Hz, a simple phenomenological model of the non-linear mechanical noise, and the analysis method that is inspired by this model.

Why glass elasticity affects the thermodynamics and fragility of supercooled liquids

PubMed Central

Yan, Le; Düring, Gustavo; Wyart, Matthieu

2013-01-01

Supercooled liquids are characterized by their fragility: The slowing down of the dynamics under cooling is more sudden and the jump of specific heat at the glass transition is generally larger in fragile liquids than in strong ones. Despite the importance of this quantity in classifying liquids, explaining what aspects of the microscopic structure controls fragility remains a challenge. Surprisingly, experiments indicate that the linear elasticity of the glass—a purely local property of the free energy landscape—is a good predictor of fragility. In particular, materials presenting a large excess of soft elastic modes, the so-called boson peak, are strong. This is also the case for network liquids near the rigidity percolation, known to affect elasticity. Here we introduce a model of the glass transition based on the assumption that particles can organize locally into distinct configurations that are coupled spatially via elasticity. The model captures the mentioned observations connecting elasticity and fragility. We find that materials presenting an abundance of soft elastic modes have little elastic frustration: Energy is insensitive to most directions in phase space, leading to a small jump of specific heat. In this framework strong liquids turn out to lie the closest to a critical point associated with a rigidity or jamming transition, and their thermodynamic properties are related to the problem of number partitioning and to Hopfield nets in the limit of small memory. PMID:23576746

Why glass elasticity affects the thermodynamics and fragility of supercooled liquids.

PubMed

Yan, Le; Düring, Gustavo; Wyart, Matthieu

2013-04-16

Supercooled liquids are characterized by their fragility: The slowing down of the dynamics under cooling is more sudden and the jump of specific heat at the glass transition is generally larger in fragile liquids than in strong ones. Despite the importance of this quantity in classifying liquids, explaining what aspects of the microscopic structure controls fragility remains a challenge. Surprisingly, experiments indicate that the linear elasticity of the glass--a purely local property of the free energy landscape--is a good predictor of fragility. In particular, materials presenting a large excess of soft elastic modes, the so-called boson peak, are strong. This is also the case for network liquids near the rigidity percolation, known to affect elasticity. Here we introduce a model of the glass transition based on the assumption that particles can organize locally into distinct configurations that are coupled spatially via elasticity. The model captures the mentioned observations connecting elasticity and fragility. We find that materials presenting an abundance of soft elastic modes have little elastic frustration: Energy is insensitive to most directions in phase space, leading to a small jump of specific heat. In this framework strong liquids turn out to lie the closest to a critical point associated with a rigidity or jamming transition, and their thermodynamic properties are related to the problem of number partitioning and to Hopfield nets in the limit of small memory.

Application of variational and Galerkin equations to linear and nonlinear finite element analysis

NASA Technical Reports Server (NTRS)

Yu, Y.-Y.

1974-01-01

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

Electronic structure, elasticity, bonding features and mechanical behaviour of zinc intermetallics: A DFT study

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

Fatima, Bushra, E-mail: bushrafatima25@gmail.com; Acharya, Nikita; Sanyal, Sankar P.

2016-05-06

The structural stability, electronic structure, elastic and mechanical properties of TiZn and ZrZn intermetallics have been studied using ab-initio full potential linearized augmented plane wave (FP-LAPW) method within generalized gradient approximation for exchange and correlation potentials. The various structural parameters, such as lattice constant (a{sub 0}), bulk modulus (B), and its pressure derivative (B’) are analysed and compared. The investigation of elastic constants affirm that both TiZn and ZrZn are elastically stable in CsCl (B{sub 2} phase) structure. The electronic structures have been analysed quantitatively from the band structure which reveals the metallic nature of these compounds. To better illustratemore » the nature of bonding and charge transfer, we have also studied the Fermi surfaces. The three well known criterion of ductility namely Pugh’s rule, Cauchy’s pressure and Frantsevich rule elucidate the ductile nature of these compounds.« less

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.

Non-invasive determination of the complete elastic moduli of spider silks

NASA Astrophysics Data System (ADS)

Koski, Kristie J.; Akhenblit, Paul; McKiernan, Keri; Yarger, Jeffery L.

2013-03-01

Spider silks possess nature’s most exceptional mechanical properties, with unrivalled extensibility and high tensile strength. Unfortunately, our understanding of silks is limited because the complete elastic response has never been measured—leaving a stark lack of essential fundamental information. Using non-invasive, non-destructive Brillouin light scattering, we obtain the entire stiffness tensors (revealing negative Poisson’s ratios), refractive indices, and longitudinal and transverse sound velocities for major and minor ampullate spider silks: Argiope aurantia, Latrodectus hesperus, Nephila clavipes, Peucetia viridans. These results completely quantify the linear elastic response for all possible deformation modes, information unobtainable with traditional stress-strain tests. For completeness, we apply the principles of Brillouin imaging to spatially map the elastic stiffnesses on a spider web without deforming or disrupting the web in a non-invasive, non-contact measurement, finding variation among discrete fibres, junctions and glue spots. Finally, we provide the stiffness changes that occur with supercontraction.

Dynamic elasticity measurement for prosthetic socket design.

PubMed

Kim, Yujin; Kim, Junghoon; Son, Hyeryon; Choi, Youngjin

2017-07-01

The paper proposes a novel apparatus to measure the dynamic elasticity of human limb in order to help the design and fabrication of the personalized prosthetic socket. To take measurements of the dynamic elasticity, the desired force generated as an exponential chirp signal in which the frequency increases and amplitude is maintained according to time progress is applied to human limb and then the skin deformation is recorded, ultimately, to obtain the frequency response of its elasticity. It is referred to as a Dynamic Elasticity Measurement Apparatus (DEMA) in the paper. It has three core components such as linear motor to provide the desired force, loadcell to implement the force feedback control, and potentiometer to record the skin deformation. After measuring the force/deformation and calculating the dynamic elasticity of the limb, it is visualized as 3D color map model of the limb so that the entire dynamic elasticity can be shown at a glance according to the locations and frequencies. For the visualization, the dynamic elasticities measured at specific locations and frequencies are embodied using the color map into 3D limb model acquired by using 3D scanner. To demonstrate the effectiveness, the visualized dynamic elasticities are suggested as outcome of the proposed system, although we do not have any opportunity to apply the proposed system to the amputees. Ultimately, it is expected that the proposed system can be utilized to design and fabricate the personalized prosthetic socket in order for releasing the wearing pain caused by the conventional prosthetic socket.

Elasticity and critical bending moment of model colloidal aggregates.

PubMed

Pantina, John P; Furst, Eric M

2005-04-08

The bending mechanics of singly bonded colloidal aggregates are measured using laser tweezers. We find that the colloidal bonds are capable of supporting significant torques, providing a direct measurement of the tangential interactions between particles. A critical bending moment marks the limit of linear bending elasticity, past which small-scale rearrangements occur. These mechanical properties underlie the rheology and dynamics of colloidal gels formed by diffusion-limited cluster aggregation, and give critical insight into the contact interactions between Brownian particles.

Dynamic behaviour analysis of an energy accumulation system comprising a composite flywheel

NASA Astrophysics Data System (ADS)

Portnov, G. G.; Kulakov, V. L.; Barinov, I. N.

1994-01-01

A simple system for energy accumulation comprising a rim and a massive shaft with elastic couplings was considered; the shaft runs in elastic damping bearings. Forced vibrations of the flywheel system induced by linear and angular eccentricities of composite rim were investigated. The effect of variation of different parameters of the system (stiffness of bearings, viscous friction coefficients of bearings, mass and moment of inertia of the shaft) on damping of radial and angular forced vibrations has been estimated.

Numerical solution of fluid-structure interaction represented by human vocal folds in airflow

NASA Astrophysics Data System (ADS)

Valášek, J.; Sváček, P.; Horáček, J.

2016-03-01

The paper deals with the human vocal folds vibration excited by the fluid flow. The vocal fold is modelled as an elastic body assuming small displacements and therefore linear elasticity theory is used. The viscous incompressible fluid flow is considered. For purpose of numerical solution the arbitrary Lagrangian-Euler method (ALE) is used. The whole problem is solved by the finite element method (FEM) based solver. Results of numerical experiments with different boundary conditions are presented.

Property-Structure-Processing Relations in Polymeric Materials.

DTIC Science & Technology

1981-07-31

increase indefinitely without indicating actual yield value and R which is a measure of the elastic character of the fluid, approaches a limiting value...appears to increase indefinitely without indicating an- actual yield value and R, which is a measure of the elastic character of the fluid, approaches a...a linear graph when log r is plotted against log x; i.e., ,I has a x" behavior at low x. Since a 0 1, this does not correspond to the classical yield

Fatigue-Crack-Growth Structural Analysis

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.

1986-01-01

Elastic and plastic deformations calculated under variety of loading conditions. Prediction of fatigue-crack-growth lives made with FatigueCrack-Growth Structural Analysis (FASTRAN) computer program. As cyclic loads are applied to initial crack configuration, FASTRAN predicts crack length and other parameters until complete break occurs. Loads are tensile or compressive and of variable or constant amplitude. FASTRAN incorporates linear-elastic fracture mechanics with modifications of load-interaction effects caused by crack closure. FASTRAN considered research tool, because of lengthy calculation times. FASTRAN written in FORTRAN IV for batch execution.

Concentration Dependent Physical Properties of Ge1-xSnx Solid Solution

NASA Astrophysics Data System (ADS)

Jivani, A. R.; Jani, A. R.

2011-12-01

Our own proposed potential is used to investigate few physical properties like total energy, bulk modulus, pressure derivative of bulk modulus, elastic constants, pressure derivative of elastic constants, Poisson's ratio and Young's modulus of Ge1-xSnx solid solution with x is atomic concentration of α-Sn. The potential combines linear plus quadratic types of electron-ion interaction. First time screening function proposed by Sarkar et al is used to investigate the properties of the Ge-Sn solid solution system.

Miniaturized Stretchable and High-Rate Linear Supercapacitors

NASA Astrophysics Data System (ADS)

Zhu, Wenjun; Zhang, Yang; Zhou, Xiaoshuang; Xu, Jiang; Liu, Zunfeng; Yuan, Ningyi; Ding, Jianning

2017-07-01

Linear stretchable supercapacitors have attracted much attention because they are well suited to applications in the rapidly expanding field of wearable electronics. However, poor conductivity of the electrode material, which limits the transfer of electrons in the axial direction of the linear supercapacitors, leads to a serious loss of capacity at high rates. To solve this problem, we use gold nanoparticles to decorate aligned multiwall carbon nanotube to fabricate stretchable linear electrodes. Furthermore, we have developed fine stretchable linear supercapacitors, which exhibited an extremely high elasticity up to 400% strain with a high capacitance of about 8.7 F g-1 at the discharge current of 1 A g-1.

Miniaturized Stretchable and High-Rate Linear Supercapacitors.

PubMed

Zhu, Wenjun; Zhang, Yang; Zhou, Xiaoshuang; Xu, Jiang; Liu, Zunfeng; Yuan, Ningyi; Ding, Jianning

2017-12-01

Linear stretchable supercapacitors have attracted much attention because they are well suited to applications in the rapidly expanding field of wearable electronics. However, poor conductivity of the electrode material, which limits the transfer of electrons in the axial direction of the linear supercapacitors, leads to a serious loss of capacity at high rates. To solve this problem, we use gold nanoparticles to decorate aligned multiwall carbon nanotube to fabricate stretchable linear electrodes. Furthermore, we have developed fine stretchable linear supercapacitors, which exhibited an extremely high elasticity up to 400% strain with a high capacitance of about 8.7 F g -1 at the discharge current of 1 A g -1 .

Temperature dependence of single-crystal elastic constants of flux-grown alpha-GaPO(4).

PubMed

Armand, P; Beaurain, M; Rufflé, B; Menaert, B; Papet, P

2009-06-01

The lattice parameter change with respect to temperature (T) has been measured using high-temperature powder X-ray diffraction techniques for high-temperature flux-grown GaPO(4) single crystals with the alpha-quartz structure. The lattice and the volume linear thermal expansion coefficients in the temperature range 303-1173 K were computed from the X-ray data. The percentage linear thermal expansions along the a and c axes at 1173 K are 1.5 and 0.51, respectively. The temperature dependence of the mass density rho of flux-grown GaPO(4) single crystals was evaluated using the volume thermal expansion coefficient alpha(V)(T) = 3.291 x 10(-5) - 2.786 x 10(-8) [T] + 4.598 x 10(-11)[T](2). Single-crystal high-resolution Brillouin spectroscopy measurements have been carried out at ambient pressure from 303 to 1123 K to determine the elastic constants C(IJ) of high-temperature flux-grown GaPO(4) material. The single-crystal elastic moduli were calculated using the sound velocities via the measured Brillouin frequency shifts Deltanu(B). These are, to our knowledge, the highest temperatures at which single-crystal elastic constants of alpha-GaPO(4) have been measured. Most of the room-temperature elastic constant values measured on flux-grown GaPO(4) material are higher than the ones found for hydrothermally grown GaPO(4) single crystals. The fourth-order temperature coefficients of both the Brillouin frequency shifts T(nuB)((n)) and the single-crystal elastic moduli T(C(IJ))((n)) were obtained. The first-order temperature coefficients of the C(IJ) are in excellent agreement with previous reports on low-temperature hydrothermally grown alpha-GaPO(4) single crystals, while small discrepancies in the higher-order temperature coefficients are observed. This is explained in terms of the OH content in the GaPO(4) network, which is an important parameter in the crystal thermal behavior.

Forces and torques on rigid inclusions in an elastic environment: Resulting matrix-mediated interactions, displacements, and rotations

NASA Astrophysics Data System (ADS)

Puljiz, Mate; Menzel, Andreas M.

2017-05-01

Embedding rigid inclusions into elastic matrix materials is a procedure of high practical relevance, for instance, for the fabrication of elastic composite materials. We theoretically analyze the following situation. Rigid spherical inclusions are enclosed by a homogeneous elastic medium under stick boundary conditions. Forces and torques are directly imposed from outside onto the inclusions or are externally induced between them. The inclusions respond to these forces and torques by translations and rotations against the surrounding elastic matrix. This leads to elastic matrix deformations, and in turn results in mutual long-ranged matrix-mediated interactions between the inclusions. Adapting a well-known approach from low-Reynolds-number hydrodynamics, we explicitly calculate the displacements and rotations of the inclusions from the externally imposed or induced forces and torques. Analytical expressions are presented as a function of the inclusion configuration in terms of displaceability and rotateability matrices. The role of the elastic environment is implicitly included in these relations. That is, the resulting expressions allow a calculation of the induced displacements and rotations directly from the inclusion configuration, without having to explicitly determine the deformations of the elastic environment. In contrast to the hydrodynamic case, compressibility of the surrounding medium is readily taken into account. We present the complete derivation based on the underlying equations of linear elasticity theory. In the future, the method will, for example, be helpful to characterize the behavior of externally tunable elastic composite materials, to accelerate numerical approaches, as well as to improve the quantitative interpretation of microrheological results.

Acoustic and elastic multiple scattering and radiation from cylindrical structures

NASA Astrophysics Data System (ADS)

Amirkulova, Feruza Abdukadirovna

Multiple scattering (MS) and radiation of waves by a system of scatterers is of great theoretical and practical importance and is required in a wide variety of physical contexts such as the implementation of "invisibility" cloaks, the effective parameter characterization, and the fabrication of dynamically tunable structures, etc. The dissertation develops fast, rapidly convergent iterative techniques to expedite the solution of MS problems. The formulation of MS problems reduces to a system of linear algebraic equations using Graf's theorem and separation of variables. The iterative techniques are developed using Neumann expansion and Block Toeplitz structure of the linear system; they are very general, and suitable for parallel computations and a large number of MS problems, i.e. acoustic, elastic, electromagnetic, etc., and used for the first time to solve MS problems. The theory is implemented in Matlab and FORTRAN, and the theoretical predictions are compared to computations obtained by COMSOL. To formulate the MS problem, the transition matrix is obtained by analyzing an acoustic and an elastic single scattering of incident waves by elastic isotropic and anisotropic solids. The mathematical model of wave scattering from multilayered cylindrical and spherical structures is developed by means of an exact solution of dynamic 3D elasticity theory. The recursive impedance matrix algorithm is derived for radially heterogeneous anisotropic solids. An explicit method for finding the impedance in piecewise uniform, transverse-isotropic material is proposed; the solution is compared to elasticity theory solutions involving Buchwald potentials. Furthermore, active exterior cloaking devices are modeled for acoustic and elastic media using multipole sources. A cloaking device can render an object invisible to some incident waves as seen by some external observer. The active cloak is generated by a discrete set of multipole sources that destructively interfere with an incident wave to produce zero total field over a finite spatial region. The approach precisely determines the necessary source amplitudes and enables a cloaked region to be determined using Graf's theorem. To apply the approach, the infinite series of multipole expansions are truncated, and the accuracy of cloaking is studied by modifying the truncation parameter.

Universal elastic-hardening-driven mechanical instability in α-quartz and quartz homeotypes under pressure

PubMed Central

Dong, Juncai; Zhu, Hailiang; Chen, Dongliang

2015-01-01

As a fundamental property of pressure-induced amorphization (PIA) in ice and ice-like materials (notably α-quartz), the occurrence of mechanical instability can be related to violation of Born criteria for elasticity. The most outstanding elastic feature of α-quartz before PIA has been experimentally reported to be the linear softening of shear modulus C44, which was proposed to trigger the transition through Born criteria B3. However, by using density-functional theory, we surprisingly found that both C44 and C66 in α-quartz exhibit strong nonlinearity under compression and the Born criteria B3 vanishes dominated by stiffening of C14, instead of by decreasing of C44. Further studies of archetypal quartz homeotypes (GeO2 and AlPO4) repeatedly reproduced the same elastic-hardening-driven mechanical instability, suggesting a universal feature of this family of crystals and challenging the long-standing idea that negative pressure derivatives of individual elastic moduli can be interpreted as the precursor effect to an intrinsic structural instability preceding PIA. The implications of this elastic anomaly in relation to the dispersive softening of the lowest acoustic branch and the possible transformation mechanism were also discussed. PMID:26099720

Universal elastic-hardening-driven mechanical instability in α-quartz and quartz homeotypes under pressure.

PubMed

Dong, Juncai; Zhu, Hailiang; Chen, Dongliang

2015-06-23

As a fundamental property of pressure-induced amorphization (PIA) in ice and ice-like materials (notably α-quartz), the occurrence of mechanical instability can be related to violation of Born criteria for elasticity. The most outstanding elastic feature of α-quartz before PIA has been experimentally reported to be the linear softening of shear modulus C44, which was proposed to trigger the transition through Born criteria B3. However, by using density-functional theory, we surprisingly found that both C44 and C66 in α-quartz exhibit strong nonlinearity under compression and the Born criteria B3 vanishes dominated by stiffening of C14, instead of by decreasing of C44. Further studies of archetypal quartz homeotypes (GeO2 and AlPO4) repeatedly reproduced the same elastic-hardening-driven mechanical instability, suggesting a universal feature of this family of crystals and challenging the long-standing idea that negative pressure derivatives of individual elastic moduli can be interpreted as the precursor effect to an intrinsic structural instability preceding PIA. The implications of this elastic anomaly in relation to the dispersive softening of the lowest acoustic branch and the possible transformation mechanism were also discussed.

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.

Nonlinear flap-lag axial equations of a rotating beam

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.; Kvaternik, R. G.

1977-01-01

It is possible to identify essentially four approaches by which analysts have established either the linear or nonlinear governing equations of motion for a particular problem related to the dynamics of rotating elastic bodies. The approaches include the effective applied load artifice in combination with a variational principle and the use of Newton's second law, written as D'Alembert's principle, applied to the deformed configuration. A third approach is a variational method in which nonlinear strain-displacement relations and a first-degree displacement field are used. The method introduced by Vigneron (1975) for deriving the linear flap-lag equations of a rotating beam constitutes the fourth approach. The reported investigation shows that all four approaches make use of the geometric nonlinear theory of elasticity. An alternative method for deriving the nonlinear coupled flap-lag-axial equations of motion is also discussed.

Elasto-Plastic Analysis of Tee Joints Using HOT-SMAC

NASA Technical Reports Server (NTRS)

Arnold, Steve M. (Technical Monitor); Bednarcyk, Brett A.; Yarrington, Phillip W.

2004-01-01

The Higher Order Theory - Structural/Micro Analysis Code (HOT-SMAC) software package is applied to analyze the linearly elastic and elasto-plastic response of adhesively bonded tee joints. Joints of this type are finding an increasing number of applications with the increased use of composite materials within advanced aerospace vehicles, and improved tools for the design and analysis of these joints are needed. The linearly elastic results of the code are validated vs. finite element analysis results from the literature under different loading and boundary conditions, and new results are generated to investigate the inelastic behavior of the tee joint. The comparison with the finite element results indicates that HOT-SMAC is an efficient and accurate alternative to the finite element method and has a great deal of potential as an analysis tool for a wide range of bonded joints.

Heat kernel for the elliptic system of linear elasticity with boundary conditions

NASA Astrophysics Data System (ADS)

Taylor, Justin; Kim, Seick; Brown, Russell

2014-10-01

We consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second Korn inequality holds. We construct heat kernel of the system subject to Dirichlet, Neumann, or mixed boundary condition under the assumption that weak solutions of the elliptic system are Hölder continuous in the interior. Moreover, we show that if weak solutions of the mixed problem are Hölder continuous up to the boundary, then the corresponding heat kernel has a Gaussian bound. In particular, if the domain is a two dimensional Lipschitz domain satisfying a corkscrew or non-tangential accessibility condition on the set where we specify Dirichlet boundary condition, then we show that the heat kernel has a Gaussian bound. As an application, we construct Green's function for elliptic mixed problem in such a domain.

System and method to create three-dimensional images of non-linear acoustic properties in a region remote from a borehole

DOEpatents

Vu, Cung; Nihei, Kurt T.; Schmitt, Denis P.; Skelt, Christopher; Johnson, Paul A.; Guyer, Robert; TenCate, James A.; Le Bas, Pierre-Yves

2013-01-01

In some aspects of the disclosure, a method for creating three-dimensional images of non-linear properties and the compressional to shear velocity ratio in a region remote from a borehole using a conveyed logging tool is disclosed. In some aspects, the method includes arranging a first source in the borehole and generating a steered beam of elastic energy at a first frequency; arranging a second source in the borehole and generating a steerable beam of elastic energy at a second frequency, such that the steerable beam at the first frequency and the steerable beam at the second frequency intercept at a location away from the borehole; receiving at the borehole by a sensor a third elastic wave, created by a three wave mixing process, with a frequency equal to a difference between the first and second frequencies and a direction of propagation towards the borehole; determining a location of a three wave mixing region based on the arrangement of the first and second sources and on properties of the third wave signal; and creating three-dimensional images of the non-linear properties using data recorded by repeating the generating, receiving and determining at a plurality of azimuths, inclinations and longitudinal locations within the borehole. The method is additionally used to generate three dimensional images of the ratio of compressional to shear acoustic velocity of the same volume surrounding the borehole.

Comparative study of sea ice dynamics simulations with a Maxwell elasto-brittle rheology and the elastic-viscous-plastic rheology in NEMO-LIM3

NASA Astrophysics Data System (ADS)

Raulier, Jonathan; Dansereau, Véronique; Fichefet, Thierry; Legat, Vincent; Weiss, Jérôme

2017-04-01

Sea ice is a highly dynamical environment characterized by a dense mesh of fractures or leads, constantly opening and closing over short time scales. This characteristic geomorphology is linked to the existence of linear kinematic features, which consist of quasi-linear patterns emerging from the observed strain rate field of sea ice. Standard rheologies used in most state-of-the-art sea ice models, like the well-known elastic-viscous-plastic rheology, are thought to misrepresent those linear kinematic features and the observed statistical distribution of deformation rates. Dedicated rheologies built to catch the processes known to be at the origin of the formation of leads are developed but still need evaluations on the global scale. One of them, based on a Maxwell elasto-brittle formulation, is being integrated in the NEMO-LIM3 global ocean-sea ice model (www.nemo-ocean.eu; www.elic.ucl.ac.be/lim). In the present study, we compare the results of the sea ice model LIM3 obtained with two different rheologies: the elastic-viscous-plastic rheology commonly used in LIM3 and a Maxwell elasto-brittle rheology. This comparison is focused on the statistical characteristics of the simulated deformation rate and on the ability of the model to reproduce the existence of leads within the ice pack. The impact of the lead representation on fluxes between ice, atmosphere and ocean is also assessed.

On relative distortion in fingerprint comparison.

PubMed

Kalka, Nathan D; Hicklin, R Austin

2014-11-01

When fingerprints are deposited, non-uniform pressure in conjunction with the inherent elasticity of friction ridge skin often causes linear and non-linear distortions in the ridge and valley structure. The effects of these distortions must be considered during analysis of fingerprint images. Even when individual prints are not notably distorted, relative distortion between two prints can have a serious impact on comparison. In this paper we discuss several metrics for quantifying and visualizing linear and non-linear fingerprint deformations, and software tools to assist examiners in accounting for distortion in fingerprint comparisons. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Water Holding as Determinant for the Elastically Stored Energy in Protein-Based Gels.

PubMed

Pouvreau, Laurice; van Wijlen, Emke; Klok, Jan; Urbonaite, Vaida; Munialo, Claire D; de Jongh, Harmen H J

2016-04-01

To evaluate the importance of the water holding capacity for the elastically stored energy of protein gels, a range of gels were created from proteins from different origin (plant: pea and soy proteins, and animal: whey, blood plasma, egg white proteins, and ovalbumin) varying in network morphology set by the protein concentration, pH, ionic strength, or the presence of specific ions. The results showed that the observed positive and linear relation between water holding (WH) and elastically stored energy (RE) is generic for globular protein gels studied. The slopes of this relation are comparable for all globular protein gels (except for soy protein gels) whereas the intercept is close to 0 for most of the systems except for ovalbumin and egg white gels. The slope and intercept obtained allows one to predict the impact of tuning WH, by gel morphology or network stiffness, on the mechanical deformation of the protein-based gel. Addition of charged polysaccharides to a protein system leads to a deviation from the linear relation between WH and RE and this deviation coincides with a change in phase behavior. © 2016 Institute of Food Technologists®

An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

NASA Astrophysics Data System (ADS)

Pan, E.; Chen, J. Y.; Bevis, M.; Bordoni, A.; Barletta, V. R.; Molavi Tabrizi, A.

2015-12-01

We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/r (where r is the radial coordinate) while the gravity is constant and that in the core the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth anisotropy on the LLNs.

Summertime Minimum Streamflow Elasticity to Antecendent Winter Precipitation, Peak Snow Water Equivalent and Summertime Evaporative Demand in the Western US Maritime Mountains

NASA Astrophysics Data System (ADS)

Schaperow, J.; Cooper, M. G.; Cooley, S. W.; Alam, S.; Smith, L. C.; Lettenmaier, D. P.

2017-12-01

As climate regimes shift, streamflows and our ability to predict them will change, as well. Elasticity of summer minimum streamflow is estimated for 138 unimpaired headwater river basins across the maritime western US mountains to better understand how climatologic variables and geologic characteristics interact to determine the response of summer low flows to winter precipitation (PPT), spring snow water equivalent (SWE), and summertime potential evapotranspiration (PET). Elasticities are calculated using log log linear regression, and linear reservoir storage coefficients are used to represent basin geology. Storage coefficients are estimated using baseflow recession analysis. On average, SWE, PET, and PPT explain about 1/3 of the summertime low flow variance. Snow-dominated basins with long timescales of baseflow recession are least sensitive to changes in SWE, PPT, and PET, while rainfall-dominated, faster draining basins are most sensitive. There are also implications for the predictability of summer low flows. The R2 between streamflow and SWE drops from 0.62 to 0.47 from snow-dominated to rain-dominated basins, while there is no corresponding increase in R2 between streamflow and PPT.

Experiments on stress dependent borehole acoustic waves.

PubMed

Hsu, Chaur-Jian; Kane, Michael R; Winkler, Kenneth; Wang, Canyun; Johnson, David Linton

2011-10-01

In the laboratory setup, a borehole traverses a dry sandstone formation, which is subjected to a controlled uniaxial stress in the direction perpendicular to the borehole axis. Measurements are made in a single loading-unloading stress cycle from zero to 10 MPa and then back down to zero stress. The applied stress and the presence of the borehole induce anisotropy in the bulk of the material and stress concentration around the borehole, both azimuthally and radially. Acoustic waves are generated and detected in the water-filled borehole, including compressional and shear headwaves, as well as modes of monopole, dipole, quadrupole, and higher order azimuthal symmetries. The linear and non-linear elastic parameters of the formation material are independently quantified, and utilized in conjunction with elastic theories to predict the characteristics of various borehole waves at zero and finite stress conditions. For example, an analytic theory is developed which is successfully used to estimate the changes of monopole tube mode at low frequency resulted from uniaxial stress, utilizing the measured material third order elasticity parameters. Comparisons between various measurements as well as that between experiments and theories are also presented. © 2011 Acoustical Society of America

Porosity Defect Remodeling and Tensile Analysis of Cast Steel

PubMed Central

Sun, Linfeng; Liao, Ridong; Lu, Wei; Fu, Sibo

2016-01-01

Tensile properties on ASTM A216 WCB cast steel with centerline porosity defect were studied with radiographic mapping and finite element remodeling technique. Non-linear elastic and plastic behaviors dependent on porosity were mathematically described by relevant equation sets. According to the ASTM E8 tensile test standard, matrix and defect specimens were machined into two categories by two types of height. After applying radiographic inspection, defect morphologies were mapped to the mid-sections of the finite element models and the porosity fraction fields had been generated with interpolation method. ABAQUS input parameters were confirmed by trial simulations to the matrix specimen and comparison with experimental outcomes. Fine agreements of the result curves between simulations and experiments could be observed, and predicted positions of the tensile fracture were found to be in accordance with the tests. Chord modulus was used to obtain the equivalent elastic stiffness because of the non-linear features. The results showed that elongation was the most influenced term to the defect cast steel, compared with elastic stiffness and yield stress. Additional visual explanations on the tensile fracture caused by void propagation were also given by the result contours at different mechanical stages, including distributions of Mises stress and plastic strain. PMID:28787919

Symmetry breaking in actin gels - Implications for cellular motility

NASA Astrophysics Data System (ADS)

John, Karin; Peyla, Philippe; Misbah, Chaouqi

2007-03-01

The physical origin of cell motility is not fully understood. Recently minimal model systems have shown, that polymerizing actin itself can produce a motile force, without the help of motor proteins. Pathogens like Shigella or Listeria use actin to propel themselves forward in their host cell. The same process can be mimicked with polystyrene beads covered with the activating protein ActA, which reside in a solution containing actin monomers. ActA induces the growth of an actin gel at the bead surface. Initially the gel grows symmetrically around the bead until a critical size is reached. Subsequently one observes a symmetry breaking and the gel starts to grow asymmetrically around the bead developing a tail of actin at one side. This symmetry breaking is accompanied by a directed movement of the bead, with the actin tail trailing behind the bead. Force generation relies on the combination of two properties: growth and elasticity of the actin gel. We study this phenomenon theoretically within the framework of a linear elasticity theory and linear flux-force relationships for the evolution of an elastic gel around a hard sphere. Conditions for a parity symmetry breaking are identified analytically and illustrated numerically with the help of a phasefield model.

Detection of Natural Fractures from Observed Surface Seismic Data Based on a Linear-Slip Model

NASA Astrophysics Data System (ADS)

Chen, Huaizhen; Zhang, Guangzhi

2018-03-01

Natural fractures play an important role in migration of hydrocarbon fluids. Based on a rock physics effective model, the linear-slip model, which defines fracture parameters (fracture compliances) for quantitatively characterizing the effects of fractures on rock total compliance, we propose a method to detect natural fractures from observed seismic data via inversion for the fracture compliances. We first derive an approximate PP-wave reflection coefficient in terms of fracture compliances. Using the approximate reflection coefficient, we derive azimuthal elastic impedance as a function of fracture compliances. An inversion method to estimate fracture compliances from seismic data is presented based on a Bayesian framework and azimuthal elastic impedance, which is implemented in a two-step procedure: a least-squares inversion for azimuthal elastic impedance and an iterative inversion for fracture compliances. We apply the inversion method to synthetic and real data to verify its stability and reasonability. Synthetic tests confirm that the method can make a stable estimation of fracture compliances in the case of seismic data containing a moderate signal-to-noise ratio for Gaussian noise, and the test on real data reveals that reasonable fracture compliances are obtained using the proposed method.

Elastic relaxation of a truncated circular cylinder with uniform dilatational eigenstrain in a half space

NASA Astrophysics Data System (ADS)

Glas, Frank

2003-06-01

We give a fully analytical solution for the displacement and strain fields generated by the coherent elastic relaxation of a type of misfitting inclusions with uniform dilatational eigenstrain lying in a half space, assuming linear isotropic elasticity. The inclusion considered is an infinitely long circular cylinder having an axis parallel to the free surface and truncated by two arbitrarily positioned planes parallel to this surface. These calculations apply in particular to strained semiconductor quantum wires. The calculations are illustrated by examples showing quantitatively that, depending on the depth of the wire under the free surface, the latter may significantly affect the magnitude and the distribution of the various strain components inside the inclusion as well as in the surrounding matrix.

Atomic picture of elastic deformation in a metallic glass

NASA Astrophysics Data System (ADS)

Wang, X. D.; Aryal, S.; Zhong, C.; Ching, W. Y.; Sheng, H. W.; Zhang, H.; Zhang, D. X.; Cao, Q. P.; Jiang, J. Z.

2015-03-01

The tensile behavior of a Ni60Nb40 metallic glass (MG) has been studied by using ab initio density functional theory (DFT) calculation with a large cell containing 1024 atoms (614 Ni and 410 Nb). We provide insight into how a super elastic limit can be achieved in a MG. Spatially inhomogeneous responses of single atoms and also major polyhedra are found to change greatly with increasing external stress when the strain is over 2%, causing the intrinsically viscoelastic behavior. We uncover the origin of the observed super elastic strain limit under tension (including linear and viscoelastic strains) in small-sized MG samples, mainly caused by inhomogeneous distribution of excess volumes in the form of newly formed subatomic cavities.

Atomic picture of elastic deformation in a metallic glass.

PubMed

Wang, X D; Aryal, S; Zhong, C; Ching, W Y; Sheng, H W; Zhang, H; Zhang, D X; Cao, Q P; Jiang, J Z

2015-03-17

The tensile behavior of a Ni60Nb40 metallic glass (MG) has been studied by using ab initio density functional theory (DFT) calculation with a large cell containing 1024 atoms (614 Ni and 410 Nb). We provide insight into how a super elastic limit can be achieved in a MG. Spatially inhomogeneous responses of single atoms and also major polyhedra are found to change greatly with increasing external stress when the strain is over 2%, causing the intrinsically viscoelastic behavior. We uncover the origin of the observed super elastic strain limit under tension (including linear and viscoelastic strains) in small-sized MG samples, mainly caused by inhomogeneous distribution of excess volumes in the form of newly formed subatomic cavities.

Atomic picture of elastic deformation in a metallic glass

DOE PAGES

Wang, X. D.; Aryal, S.; Zhong, C.; ...

2015-03-17

The tensile behavior of a Ni₆₀Nb₄₀ metallic glass (MG) has been studied by using ab initio density functional theory (DFT) calculation with a large cell containing 1024 atoms (614 Ni and 410 Nb). We provide insight into how a super elastic limit can be achieved in a MG. Spatially inhomogeneous responses of single atoms and also major polyhedra are found to change greatly with increasing external stress when the strain is over 2%, causing the intrinsically viscoelastic behavior. We uncover the origin of the observed super elastic strain limit under tension (including linear and viscoelastic strains) in small-sized MG samples,more » mainly caused by inhomogeneous distribution of excess volumes in the form of newly formed subatomic cavities.« less

A statistical model of brittle fracture by transgranular cleavage

NASA Astrophysics Data System (ADS)

Lin, Tsann; Evans, A. G.; Ritchie, R. O.

A MODEL for brittle fracture by transgranular cleavage cracking is presented based on the application of weakest link statistics to the critical microstructural fracture mechanisms. The model permits prediction of the macroscopic fracture toughness, KI c, in single phase microstructures containing a known distribution of particles, and defines the critical distance from the crack tip at which the initial cracking event is most probable. The model is developed for unstable fracture ahead of a sharp crack considering both linear elastic and nonlinear elastic ("elastic/plastic") crack tip stress fields. Predictions are evaluated by comparison with experimental results on the low temperature flow and fracture behavior of a low carbon mild steel with a simple ferrite/grain boundary carbide microstructure.

AB INITIO STUDY OF PHONON DISPERSION AND ELASTIC PROPERTIES OF L12 INTERMETALLICS Ti3Al AND Y3Al

NASA Astrophysics Data System (ADS)

Arikan, N.; Ersen, M.; Ocak, H. Y.; Iyigör, A.; Candan, A.; UǦUR, Ş.; UǦUR, G.; Khenata, R.; Varshney, D.

2013-12-01

In this paper, the structural, elastic and phonon properties of Ti3Al and Y3Al in L12(Cu3Al) phase are studied by performing first-principles calculations within the generalized gradient approximation. The calculated lattice constants, static bulk moduli, first-order pressure derivative of bulk moduli and elastic constants for both compounds are reported. The phonon dispersion curves along several high-symmetry lines at the Brillouin zone, together with the corresponding phonon density of states, are determined using the first-principles linear-response approach of the density functional perturbation theory. Temperature variations of specific heat in the range of 0-500 K are obtained using the quasi-harmonic model.

Structural, Electronic and Elastic Properties of Half-Heusler Alloys CrNiZ (Z = Al, Si, Ge and As)

NASA Astrophysics Data System (ADS)

Zitouni, A.; Benstaali, W.; Abbad, A.; Lantri, T.; Bouadjemi, B.; Aziz, Z.

2018-06-01

In the present work, a self-consistent ab-initio calculation using the full- potential linearized augmented plane wave (FP-LAPW) method within the framework of the spin-polarized density functional theory (DFT) was used to study the structural, electronic, magnetic and elastic properties of the half Heusler alloys CrNiZ (Z = Al, Si, Ge and As) in three phases ( α, β and γ phases). The generalized gradient approximation (GGA) described by Perdew-Burke-Ernzerhof (PBE) was used. The results obtained for the spin-polarized band structure and the density of states show a halfmetallic behavior for the four compounds. The elastic constants ( C ij ) show that our compounds are ductile, stiff and anisotropic.

Asymptotically Exact Solution of the Problem of Harmonic Vibrations of an Elastic Parallelepiped

NASA Astrophysics Data System (ADS)

Papkov, S. O.

2017-11-01

An asymptotically exact solution of the classical problem of elasticity about the steadystate forced vibrations of an elastic rectangular parallelepiped is constructed. The general solution of the vibration equations is constructed in the form of double Fourier series with undetermined coefficients, and an infinite system of linear algebraic equations is obtained for determining these coefficients. An analysis of the infinite system permits determining the asymptotics of the unknowns which are used to convolve the double series in both equations of the infinite systems and the displacement and stress components. The efficiency of this approach is illustrated by numerical examples and comparison with known solutions. The spectrum of the parallelepiped symmetric vibrations is studied for various ratios of its sides.

Pressure induced structural phase transition in metal nitrides: An effective interionic potential calculations

NASA Astrophysics Data System (ADS)

Soni, Shubhangi; Choudhary, K. K.; Kaurav, Netram

2018-05-01

Structural and elastic properties of transition metal nitrides, XN (X = Co, Fe and Cu), are investigated through an effective inter-ionic potential method. The B3(ZnS) type ambient crystal structure of these compounds undergoes to B1(NaCl) type structure with pressure. Structural phase transition pressure in CoN, FeN and CuN was 35, 55 and 35 GPa, respectively, predicated by computing Gibbs' free energy (G) as a function of pressure and has good agreement with available theoretical results. The elastic properties were also estimated as a function of pressure. It is found that the elastic constants increased linearly with increasing pressure due to stronger hybridization, bonding and covalent properties of constituent elements of a compound.

Normal Stresses, Contraction, and Stiffening in Sheared Elastic Networks

NASA Astrophysics Data System (ADS)

Baumgarten, Karsten; Tighe, Brian P.

2018-04-01

When elastic solids are sheared, a nonlinear effect named after Poynting gives rise to normal stresses or changes in volume. We provide a novel relation between the Poynting effect and the microscopic Grüneisen parameter, which quantifies how stretching shifts vibrational modes. By applying this relation to random spring networks, a minimal model for, e.g., biopolymer gels and solid foams, we find that networks contract or develop tension because they vibrate faster when stretched. The amplitude of the Poynting effect is sensitive to the network's linear elastic moduli, which can be tuned via its preparation protocol and connectivity. Finally, we show that the Poynting effect can be used to predict the finite strain scale where the material stiffens under shear.

Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

NASA Astrophysics Data System (ADS)

Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

2017-07-01

Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

NASA Astrophysics Data System (ADS)

Chakrabarti, Aloknath; Mohapatra, Smrutiranjan

2013-09-01

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates, separated by a gap of finite width, floating horizontally on water of finite depth, are investigated in the present work for a two-dimensional time-harmonic case. Within the frame of linear water wave theory, the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions. Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem. In both the problems, the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates. Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations. The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration. The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Critical Nucleation Length for Accelerating Frictional Slip

NASA Astrophysics Data System (ADS)

Aldam, Michael; Weikamp, Marc; Spatschek, Robert; Brener, Efim A.; Bouchbinder, Eran

2017-11-01

The spontaneous nucleation of accelerating slip along slowly driven frictional interfaces is central to a broad range of geophysical, physical, and engineering systems, with particularly far-reaching implications for earthquake physics. A common approach to this problem associates nucleation with an instability of an expanding creep patch upon surpassing a critical length Lc. The critical nucleation length Lc is conventionally obtained from a spring-block linear stability analysis extended to interfaces separating elastically deformable bodies using model-dependent fracture mechanics estimates. We propose an alternative approach in which the critical nucleation length is obtained from a related linear stability analysis of homogeneous sliding along interfaces separating elastically deformable bodies. For elastically identical half-spaces and rate-and-state friction, the two approaches are shown to yield Lc that features the same scaling structure, but with substantially different numerical prefactors, resulting in a significantly larger Lc in our approach. The proposed approach is also shown to be naturally applicable to finite-size systems and bimaterial interfaces, for which various analytic results are derived. To quantitatively test the proposed approach, we performed inertial Finite-Element-Method calculations for a finite-size two-dimensional elastically deformable body in rate-and-state frictional contact with a rigid body under sideway loading. We show that the theoretically predicted Lc and its finite-size dependence are in reasonably good quantitative agreement with the full numerical solutions, lending support to the proposed approach. These results offer a theoretical framework for predicting rapid slip nucleation along frictional interfaces.

Capillary fracture of soft gels.

PubMed

Bostwick, Joshua B; Daniels, Karen E

2013-10-01

A liquid droplet resting on a soft gel substrate can deform that substrate to the point of material failure, whereby fractures develop on the gel surface that propagate outwards from the contact line in a starburst pattern. In this paper, we characterize (i) the initiation process, in which the number of arms in the starburst is controlled by the ratio of the surface tension contrast to the gel's elastic modulus, and (ii) the propagation dynamics showing that once fractures are initiated they propagate with a universal power law L[proportional]t(3/4). We develop a model for crack initiation by treating the gel as a linear elastic solid and computing the deformations within the substrate from the liquid-solid wetting forces. The elastic solution shows that both the location and the magnitude of the wetting forces are critical in providing a quantitative prediction for the number of fractures and, hence, an interpretation of the initiation of capillary fractures. This solution also reveals that the depth of the gel is an important factor in the fracture process, as it can help mitigate large surface tractions; this finding is confirmed with experiments. We then develop a model for crack propagation by considering the transport of an inviscid fluid into the fracture tip of an incompressible material and find that a simple energy-conservation argument can explain the observed material-independent power law. We compare predictions for both linear elastic and neo-Hookean solids, finding that the latter better explains the observed exponent.

Numerical study of suspensions of deformable particles.

NASA Astrophysics Data System (ADS)

Brandt, Luca; Rosti, Marco Edoardo

2017-11-01

We consider a model non-Newtonian fluid consisting of a suspension of deformable particles in a Newtonian solvent. Einstein showed in his pioneering work that the relative increase in effective viscosity is a linear function of the particle volume fraction for dilute suspensions of rigid particles. Inertia has been shown to introduce deviations from the behaviour predicted by the different empirical fits, an effect that can be related to an increase of the effective volume fraction. We here focus on the effect of elasticity, i.e. visco-elastic deformable particles. To tackle the problem at hand, we perform three-dimensional Direct Numerical Simulation of a plane Couette flow with a suspension of neutrally buoyant deformable viscous hyper-elastic particles. We show that elasticity produces a shear-thinning effect in elastic suspensions (in comparison to rigid ones) and that it can be understood in terms of a reduction of the effective volume fraction of the suspension. The deformation modifies the particle motion reducing the level of mutual interaction. Normal stress differences will also be considered. European Research Council, Grant No. ERC-2013-CoG- 616186, TRITOS; SNIC (the Swedish National Infrastructure for Computing).

Gene Expression Data to Mouse Atlas Registration Using a Nonlinear Elasticity Smoother and Landmark Points Constraints

PubMed Central

Lin, Tungyou; Guyader, Carole Le; Dinov, Ivo; Thompson, Paul; Toga, Arthur; Vese, Luminita

2013-01-01

This paper proposes a numerical algorithm for image registration using energy minimization and nonlinear elasticity regularization. Application to the registration of gene expression data to a neuroanatomical mouse atlas in two dimensions is shown. We apply a nonlinear elasticity regularization to allow larger and smoother deformations, and further enforce optimality constraints on the landmark points distance for better feature matching. To overcome the difficulty of minimizing the nonlinear elasticity functional due to the nonlinearity in the derivatives of the displacement vector field, we introduce a matrix variable to approximate the Jacobian matrix and solve for the simplified Euler-Lagrange equations. By comparison with image registration using linear regularization, experimental results show that the proposed nonlinear elasticity model also needs fewer numerical corrections such as regridding steps for binary image registration, it renders better ground truth, and produces larger mutual information; most importantly, the landmark points distance and L2 dissimilarity measure between the gene expression data and corresponding mouse atlas are smaller compared with the registration model with biharmonic regularization. PMID:24273381

Elastic Model Transitions: a Hybrid Approach Utilizing Quadratic Inequality Constrained Least Squares (LSQI) and Direct Shape Mapping (DSM)

NASA Technical Reports Server (NTRS)

Jurenko, Robert J.; Bush, T. Jason; Ottander, John A.

2014-01-01

A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes both quadratically constrained least squares (LSQI) and Direct Shape Mapping (DSM) algorithms to determine physical displacements. This approach is applicable to the simulation of the elastic behavior of launch vehicles and other structures that utilize multiple LTI finite element model (FEM) derived mode sets that are propagated throughout time. The time invariant nature of the elastic data for discrete segments of the launch vehicle trajectory presents a problem of how to properly transition between models while preserving motion across the transition. In addition, energy may vary between flex models when using a truncated mode set. The LSQI-DSM algorithm can accommodate significant changes in energy between FEM models and carries elastic motion across FEM model transitions. Compared with previous approaches, the LSQI-DSM algorithm shows improvements ranging from a significant reduction to a complete removal of transients across FEM model transitions as well as maintaining elastic motion from the prior state.

A fluid-structure interaction model of soft robotics using an active strain approach

NASA Astrophysics Data System (ADS)

Hess, Andrew; Lin, Zhaowu; Gao, Tong

2017-11-01

Soft robotic swimmers exhibit rich dynamics that stem from the non-linear interplay of the fluid and immersed soft elastic body. Due to the difficulty of handling the nonlinear two-way coupling of hydrodynamic flow and deforming elastic body, studies of flexible swimmers often employ either one-way coupling strategies with imposed motions of the solid body or some simplified elasticity models. To explore the nonlinear dynamics of soft robots powered by smart soft materials, we develop a computational model to deal with the two-way fluid/elastic structure interactions using the fictitious domain method. To mimic the dynamic response of the functional soft material under external actuations, we assume the solid phase to be neo-Hookean, and employ an active strain approach to incorporate actuation, which is based on the multiplicative decomposition of the deformation gradient tensor. We demonstrate the capability of our algorithm by performing a series of numerical explorations that manipulate an elastic structure with finite thickness, starting from simple rectangular or circular plates to soft robot prototypes such as stingrays and jellyfish.

Synergistic effect of alloying elements doping and external pressure on the elastic property of Ni{sub 3}Al: A first-principles study

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

Li, C., E-mail: lichun@nwpu.edu.cn; Shang, J.; Yue, Z.

2015-07-15

In this paper, the basic electronic structures and elastic properties of Ni{sub 3}Al doping with alloying elements (Re, Cr, and Mo) under different pressures have been investigated using first-principles calculations based on density functional theory. It is shown that both alloying elements and external applied pressure contribute positively to the elastic properties of Ni{sub 3}Al, and the configurations of the compounds remain almost unchanged. The calculated elastic constants and moduli increase linearly with the pressure increasing from 0 and 40 GPa. Among the alloying elements studied in the present work, Re exhibits the most significant effect compared with the othermore » elements, showing its practical importance. Especially, if both alloying elements doping and pressure effects are considered simultaneously, which has not been considered previously, the studied compounds exhibit an even better elastic property than the simple superposition of the two influences. Such synergistic effect demonstrates promising applications of Ni-based single crystal superalloys in possible extreme mechanical environments.« less

Coupled variational formulations of linear elasticity and the DPG methodology

NASA Astrophysics Data System (ADS)

Fuentes, Federico; Keith, Brendan; Demkowicz, Leszek; Le Tallec, Patrick

2017-11-01

This article presents a general approach akin to domain-decomposition methods to solve a single linear PDE, but where each subdomain of a partitioned domain is associated to a distinct variational formulation coming from a mutually well-posed family of broken variational formulations of the original PDE. It can be exploited to solve challenging problems in a variety of physical scenarios where stability or a particular mode of convergence is desired in a part of the domain. The linear elasticity equations are solved in this work, but the approach can be applied to other equations as well. The broken variational formulations, which are essentially extensions of more standard formulations, are characterized by the presence of mesh-dependent broken test spaces and interface trial variables at the boundaries of the elements of the mesh. This allows necessary information to be naturally transmitted between adjacent subdomains, resulting in coupled variational formulations which are then proved to be globally well-posed. They are solved numerically using the DPG methodology, which is especially crafted to produce stable discretizations of broken formulations. Finally, expected convergence rates are verified in two different and illustrative examples.

Tensile and compressive stress-strain behavior of heat treated boron-aluminum

NASA Technical Reports Server (NTRS)

Kennedy, J. M.; Tenney, D. R.; Herakovich, C. T.

1978-01-01

An experimental study was conducted to assess the effects of heat treatment and cyclic mechanical loading on the tensile and compressive stress-strain behavior of six boron-aluminum composites having different laminate orientations and being subjected to different heat treatments. The heat treatments were as-fabricated, T6, and T6N consisting of T6 treatment followed by cryogenic quench in liquid nitrogen prior to testing. All laminates were tested in monotonic and cyclic compression, while the tensile-test data are taken from the literature for comparison purposes. It is shown that the linear elastic range of the T6- and T6N-condition specimens is larger than that of the as-fabricated specimens, and that cyclic loading in tension or compression strain hardens the specimens and extends the linear elastic range. For laminates containing 0-deg plies, the stress-strain behavior upon unloading is found to be nonlinear, whereas the other laminates exhibit a linear behavior upon unloading. Specimens in the T6 and T6N conditions show higher strain hardening than the as-fabricated specimens.

Drivers willingness to pay progressive rate for street parking.

DOT National Transportation Integrated Search

2015-01-01

This study finds willingness to pay and price elasticity for on-street parking demand using stated : preference data obtained from 238 respondents. Descriptive, statistical and economic analyses including : regression, generalized linear model, and f...

WE-A-17A-11: Implanted Brachytherapy Seed Movement Due to Transrectal Ultrasound Probe-Induced Prostate Deformation

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

Liu, D; Usmani, N; Sloboda, R

Purpose: To characterize the movement of implanted brachytherapy seeds due to transrectal ultrasound probe-induced prostate deformation and to estimate the effects on prostate dosimetry. Methods: Implanted probe-in and probe-removed seed distributions were reconstructed for 10 patients using C-arm fluoroscopy imaging. The prostate was delineated on ultrasound and registered to the fluoroscopy seeds using a visible subset of seeds and residual needle tracks. A linear tensor and shearing model correlated the seed movement with position. The seed movement model was used to infer the underlying prostate deformation and to simulate the prostate contour without probe compression. Changes in prostate and surrogatemore » urethra dosimetry were calculated. Results: Seed movement patterns reflecting elastic decompression, lateral shearing, and rectal bending were observed. Elastic decompression was characterized by anterior-posterior expansion and superior-inferior and lateral contractions. For lateral shearing, anterior movement up to 6 mm was observed for extraprostatic seeds in the lateral peripheral region. The average intra-prostatic seed movement was 1.3 mm, and the residual after linear modeling was 0.6 mm. Prostate D90 increased by 4 Gy on average (8 Gy max) and was correlated with elastic decompression. For selected patients, lateral shearing resulted in differential change in D90 of 7 Gy between anterior and posterior quadrants, and increase in whole prostate D90 of 4 Gy. Urethra D10 increased by 4 Gy. Conclusion: Seed movement upon probe removal was characterized. The proposed model captured the linear correlation between seed movement and position. Whole prostate dose coverage increased slightly, due to the small but systematic seed movement associated with elastic decompression. Lateral shearing movement increased dose coverage in the anterior-lateral region, at the expense of the posterior-lateral region. The effect on whole prostate D90 was smaller due to the subset of peripheral seeds involved, but lateral shearing movement can have greater consequences for local dose coverage.« less

Effects of replacing free weights with elastic band resistance in squats on trunk muscle activation.

PubMed

Saeterbakken, Atle H; Andersen, Vidar; Kolnes, Maria K; Fimland, Marius S

2014-11-01

The purpose of this study was to assess the effects of adding elastic bands to free-weight squats on the neuromuscular activation of core muscles. Twenty-five resistance trained women with 4.6 ± 2.1 years of resistance training experience participated in the study. In randomized order, the participants performed 6 repetition maximum in free-weight squats, with and without elastic bands (i.e., matched relative intensity between exercises). During free-weight squats with elastic bands, some of the free weights were replaced with 2 elastic bands attached to the lowest part of the squat rack. Surface electromyography (EMG) activity was measured from the erector spinae, external oblique, and rectus abdominis, whereas a linear encoder measured the vertical displacement. The EMG activities were compared between the 2 lifting modalities for the whole repetition and separately for the eccentric, concentric, and upper and lower eccentric and concentric phases. In the upper (greatest stretch of the elastic band), middle, and lower positions in squats with elastic bands, the resistance values were approximately 117, 105, and 93% of the free weight-only trial. Similar EMG activities were observed for the 2 lifting modalities for the erector spinae (p = 0.112-0.782), external oblique (p = 0.225-0.977), and rectus abdominis (p = 0.315-0.729) in all analyzed phases. In conclusion, there were no effects on the muscle activity of trunk muscles of substituting some resistance from free weights with elastic bands in the free-weight squat.

Local elasticity map and plasticity in a model Lennard-Jones glass.

PubMed

Tsamados, Michel; Tanguy, Anne; Goldenberg, Chay; Barrat, Jean-Louis

2009-08-01

In this work we calculate the local elastic moduli in a weakly polydispersed two-dimensional Lennard-Jones glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarse-grained microscopic expressions for the strain, displacement, and stress fields. This method allows us to calculate the local elasticity tensor and to quantify the deviation from linear elasticity (local Hooke's law) at different coarse-graining scales. From the results a clear picture emerges of an amorphous material with strongly spatially heterogeneous elastic moduli that simultaneously satisfies Hooke's law at scales larger than a characteristic length scale of the order of five interatomic distances. At this scale, the glass appears as a composite material composed of a rigid scaffolding and of soft zones. Only recently calculated in nonhomogeneous materials, the local elastic structure plays a crucial role in the elastoplastic response of the amorphous material. For a small macroscopic shear strain, the structures associated with the nonaffine displacement field appear directly related to the spatial structure of the elastic moduli. Moreover, for a larger macroscopic shear strain we show that zones of low shear modulus concentrate most of the strain in the form of plastic rearrangements. The spatiotemporal evolution of this local elasticity map and its connection with long term dynamical heterogeneity as well as with the plasticity in the material is quantified. The possibility to use this local parameter as a predictor of subsequent local plastic activity is also discussed.

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.

Resonant Column Tests and Nonlinear Elasticity in Simulated Rocks

NASA Astrophysics Data System (ADS)

Sebastian, Resmi; Sitharam, T. G.

2018-01-01

Rocks are generally regarded as linearly elastic even though the manifestations of nonlinearity are prominent. The variations of elastic constants with varying strain levels and stress conditions, disagreement between static and dynamic moduli, etc., are some of the examples of nonlinear elasticity in rocks. The grain-to-grain contact, presence of pores and joints along with other compliant features induce the nonlinear behavior in rocks. The nonlinear elastic behavior of rocks is demonstrated through resonant column tests and numerical simulations in this paper. Resonant column tests on intact and jointed gypsum samples across varying strain levels have been performed in laboratory and using numerical simulations. The paper shows the application of resonant column apparatus to obtain the wave velocities of stiff samples at various strain levels under long wavelength condition, after performing checks and incorporating corrections to the obtained resonant frequencies. The numerical simulation and validation of the resonant column tests using distinct element method are presented. The stiffness reductions of testing samples under torsional and flexural vibrations with increasing strain levels have been analyzed. The nonlinear elastic behavior of rocks is reflected in the results, which is enhanced by the presence of joints. The significance of joint orientation and influence of joint spacing during wave propagation have also been assessed and presented using the numerical simulations. It has been found that rock joints also exhibit nonlinear behavior within the elastic limit.

Simple quasi-analytical holonomic homogenization model for the non-linear analysis of in-plane loaded masonry panels: Part 1, meso-scale

NASA Astrophysics Data System (ADS)

Milani, G.; Bertolesi, E.

2017-07-01

A simple quasi analytical holonomic homogenization approach for the non-linear analysis of masonry walls in-plane loaded is presented. The elementary cell (REV) is discretized with 24 triangular elastic constant stress elements (bricks) and non-linear interfaces (mortar). A holonomic behavior with softening is assumed for mortar. It is shown how the mechanical problem in the unit cell is characterized by very few displacement variables and how homogenized stress-strain behavior can be evaluated semi-analytically.

Composite-Material Point-Stress Analysis

NASA Technical Reports Server (NTRS)

Spears, F., S.

1982-01-01

PSANAL computes composite-laminate elastic and thermal properties and allowable load levels for any combination of applied membrane and bending loads occurring at a point. Basic linear orthotropic stress/ strain relationships and standard composite-laminate theory formulas are utilized.

Modeling the elastic energy of alloys: Potential pitfalls of continuum treatments.

PubMed

Baskaran, Arvind; Ratsch, Christian; Smereka, Peter

2015-12-01

Some issues that arise when modeling elastic energy for binary alloys are discussed within the context of a Keating model and density-functional calculations. The Keating model is a simplified atomistic formulation based on modeling elastic interactions of a binary alloy with harmonic springs whose equilibrium length is species dependent. It is demonstrated that the continuum limit for the strain field are the usual equations of linear elasticity for alloys and that they correctly capture the coarse-grained behavior of the displacement field. In addition, it is established that Euler-Lagrange equation of the continuum limit of the elastic energy will yield the same strain field equation. This is the same energy functional that is often used to model elastic effects in binary alloys. However, a direct calculation of the elastic energy atomistic model reveals that the continuum expression for the elastic energy is both qualitatively and quantitatively incorrect. This is because it does not take atomistic scale compositional nonuniformity into account. Importantly, this result also shows that finely mixed alloys tend to have more elastic energy than segregated systems, which is the exact opposite of predictions made by some continuum theories. It is also shown that for strained thin films the traditionally used effective misfit for alloys systematically underestimate the strain energy. In some models, this drawback is handled by including an elastic contribution to the enthalpy of mixing, which is characterized in terms of the continuum concentration. The direct calculation of the atomistic model reveals that this approach suffers serious difficulties. It is demonstrated that elastic contribution to the enthalpy of mixing is nonisotropic and scale dependent. It is also shown that such effects are present in density-functional theory calculations for the Si-Ge system. This work demonstrates that it is critical to include the microscopic arrangements in any elastic model to achieve even qualitatively correct behavior.

Innovative energy absorbing devices based on composite tubes

NASA Astrophysics Data System (ADS)

Tiwari, Chandrashekhar

Analytical and experimental study of innovative load limiting and energy absorbing devices are presented here. The devices are based on composite tubes and can be categorized in to two groups based upon the energy absorbing mechanisms exhibited by them, namely: foam crushing and foam fracturing. The device based on foam crushing as the energy absorbing mechanism is composed of light weight elastic-plastic foam filling inside an angle ply composite tube. The tube is tailored to have a high Poisson’s ratio (>20). Upon being loaded the device experiences large transverse contraction resulting in rapid decrease in diameter. At a certain axial load the foam core begins to crush and energy is dissipated. This device is termed as crush tube device. The device based upon foam shear fracture as the energy absorbing mechanism involves an elastic-plastic core foam in annulus of two concentric extension-twist coupled composite tubes with opposite angles of fibers. The core foam is bonded to the inner and outer tube walls. Upon being loaded axially, the tubes twist in opposite directions and fracture the core foam in out of plane shear and thus dissipate the energy stored. The device is termed as sandwich core device (SCD). The devices exhibit variations in force-displacement characteristics with changes in design and material parameters, resulting in wide range of energy absorption capabilities. A flexible matrix composite system was selected, which was composed of high stiffness carbon fibers as reinforcements in relatively low stiffness polyurethane matrix, based upon large strain to failure capabilities and large beneficial elastic couplings. Linear and non-linear analytical models were developed encapsulating large deformation theory of the laminated composite shells (using non-linear strain energy formulation) to the fracture mechanics of core foam and elastic-plastic deformation theory of the foam filling. The non-linear model is capable of including material and geometric nonlinearities that arise from large deformation and fiber reorientation. Developed non-linear analysis predicts the behavior of extension-twist coupled and angle ply flexible matrix composite tubes under multi-axial loadings. The predicted results show close correlation with experimental findings. It was also found that these devices exhibit variations with respect to rate of loading. It was found that the novel energy absorbing devices are capable of providing 4-5 times higher specific energy absorption (SEA) than currently used devices for similar purposes (such as wire bender which has SEA of 3.6 J/g).

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

Effect of Initial Stress on the Dynamic Response of a Multi-Layered Plate-Strip Subjected to an Arbitrary Inclined Time-Harmonic Force

NASA Astrophysics Data System (ADS)

Daşdemir, A.

2017-08-01

The forced vibration of a multi-layered plate-strip with initial stress under the action of an arbitrary inclined time-harmonic force resting on a rigid foundation is considered. Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), a mathematical modelling is presented in plane strain state. It is assumed that there exists the complete contact interaction at the interface between the layers and the materials of the layer are linearly elastic, homogeneous and isotropic. The governing system of the partial differential equations of motion for the considered problem is solved approximately by employing the Finite Element Method (FEM). Further, the influence of the initial stress parameter on the dynamic response of the plate-strip is presented.

Methods of Investigation of Equations that Describe Waves in Tubes with Elastic Walls and Application of the Theory of Reversible and Weak Dissipative Shocks

NASA Astrophysics Data System (ADS)

Bakholdin, Igor

2018-02-01

Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.

Laser-based linear and nonlinear guided elastic waves at surfaces (2D) and wedges (1D).

PubMed

Hess, Peter; Lomonosov, Alexey M; Mayer, Andreas P

2014-01-01

The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump-probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented. Copyright © 2013 Elsevier B.V. All rights reserved.

Extension of non-linear beam models with deformable cross sections

NASA Astrophysics Data System (ADS)

Sokolov, I.; Krylov, S.; Harari, I.

2015-12-01

Geometrically exact beam theory is extended to allow distortion of the cross section. We present an appropriate set of cross-section basis functions and provide physical insight to the cross-sectional distortion from linear elastostatics. The beam formulation in terms of material (back-rotated) beam internal force resultants and work-conjugate kinematic quantities emerges naturally from the material description of virtual work of constrained finite elasticity. The inclusion of cross-sectional deformation allows straightforward application of three-dimensional constitutive laws in the beam formulation. Beam counterparts of applied loads are expressed in terms of the original three-dimensional data. Special attention is paid to the treatment of the applied stress, keeping in mind applications such as hydrogel actuators under environmental stimuli or devices made of electroactive polymers. Numerical comparisons show the ability of the beam model to reproduce finite elasticity results with good efficiency.

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.

Identification of internal properties of fibres and micro-swimmers

NASA Astrophysics Data System (ADS)

Plouraboué, Franck; Thiam, E. Ibrahima; Delmotte, Blaise; Climent, Eric

2017-01-01

In this paper, we address the identifiability of constitutive parameters of passive or active micro-swimmers. We first present a general framework for describing fibres or micro-swimmers using a bead-model description. Using a kinematic constraint formulation to describe fibres, flagellum or cilia, we find explicit linear relationship between elastic constitutive parameters and generalized velocities from computing contact forces. This linear formulation then permits one to address explicitly identifiability conditions and solve for parameter identification. We show that both active forcing and passive parameters are both identifiable independently but not simultaneously. We also provide unbiased estimators for generalized elastic parameters in the presence of Langevin-like forcing with Gaussian noise using a Bayesian approach. These theoretical results are illustrated in various configurations showing the efficiency of the proposed approach for direct parameter identification. The convergence of the proposed estimators is successfully tested numerically.

Relating Cohesive Zone Model to Linear Elastic Fracture Mechanics

NASA Technical Reports Server (NTRS)

Wang, John T.

2010-01-01

The conditions required for a cohesive zone model (CZM) to predict a failure load of a cracked structure similar to that obtained by a linear elastic fracture mechanics (LEFM) analysis are investigated in this paper. This study clarifies why many different phenomenological cohesive laws can produce similar fracture predictions. Analytical results for five cohesive zone models are obtained, using five different cohesive laws that have the same cohesive work rate (CWR-area under the traction-separation curve) but different maximum tractions. The effect of the maximum traction on the predicted cohesive zone length and the remote applied load at fracture is presented. Similar to the small scale yielding condition for an LEFM analysis to be valid. the cohesive zone length also needs to be much smaller than the crack length. This is a necessary condition for a CZM to obtain a fracture prediction equivalent to an LEFM result.

Functional helicoidal model of DNA molecule with elastic nonlinearity

NASA Astrophysics Data System (ADS)

Tseytlin, Y. M.

2013-06-01

We constructed a functional DNA molecule model on the basis of a flexible helicoidal sensor, specifically, a pretwisted hollow nano-strip. We study in this article the helicoidal nano- sensor model with a pretwisted strip axial extension corresponding to the overstretching transition of DNA from dsDNA to ssDNA. Our model and the DNA molecule have similar geometrical and nonlinear mechanical features unlike models based on an elastic rod, accordion bellows, or an imaginary combination of "multiple soft and hard linear springs", presented in some recent publications.

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.

Viscoelastic Taylor-Couette instability as analog of the magnetorotational instability.

PubMed

Bai, Yang; Crumeyrolle, Olivier; Mutabazi, Innocent

2015-09-01

A linear stability analysis and an experimental study of a viscoelastic Taylor-Couette flow corotating in the Keplerian ratio allow us to elucidate the analogy between the viscoelastic instability and the magnetorotational instability (MRI). A generalized Rayleigh criterion allows us to determine the potentially unstable zone to pure-elasticity-driven perturbations. Experiments with a viscoelastic polymer solution yield four modes: one pure-elasticity mode and three elastorotational instability (ERI) modes that represent the MRI-analog modes. The destabilization by the polymer viscosity is evidenced for the ERI modes.

Experimental device for measuring the dynamic properties of diaphragm motors

NASA Astrophysics Data System (ADS)

Fojtášek, Kamil; Dvořák, Lukáš; Mejzlík, Jan

The subject of this paper is to design and description of the experimental device for the determination dynamic properties of diaphragm pneumatic motors. These motors are structurally quite different from conventional pneumatic linear cylinders. The working fluid is typically compressed air, the piston of motor is replaced by an elastic part and during the working cycle there is a contact of two elastic environments. In the manufacturers catalogs of these motors are not given any working characteristics. Description of the dynamic behavior of diaphragm motor will be used for verification of mathematical models.

Dynamics of poroelastocapillary rise

NASA Astrophysics Data System (ADS)

Nasouri, Babak; Elfring, Gwynn

2017-11-01

The surface-tension-driven rise of a liquid between two elastic sheets can result in their deformation or coalescence depending on their flexibility. When the sheets are poroelastic, the flexibility of the immersed parts of the sheets can change considerably thereby altering the dynamical behavior of the system. To better understand this phenomenon, we study the poroelastocapillary rise of a wetting liquid between poroelastic sheets. Using the lubrication theory and linear elasticity, we quantify the effects of the change in material properties of the wet sheets on the capillary rise and the equilibrium state of the system.

Development of Nondestructive Non-Contact Acousto-Thermal Evaluation Technique for Damage Detection in Materials (Postprint)

DTIC Science & Technology

2012-09-01

and the sample to obtain a repeatable excitation for detec- tion of the damage of interest. Varieties of materials, includ- ing card stock, leather ...2) where Tan δ is the internal friction in the material, E is the Young’s modulus, and σmax is the maximum amplitude of the acoustic wave. Assuming...interior of a linear elastic material can be seen to depend on both the elastic properties (E and Tan δ) and the thermal properties (k, Cp) of the

Solitons, Bäcklund transformation and Lax pair for a (2+1)-dimensional B-type Kadomtsev-Petviashvili equation in the fluid/plasma mechanics

NASA Astrophysics Data System (ADS)

Lan, Zhong-Zhou; Gao, Yi-Tian; Yang, Jin-Wei; Su, Chuan-Qi; Wang, Qi-Min

2016-09-01

Under investigation in this paper is a (2+1)-dimensional B-type Kadomtsev-Petviashvili equation for the shallow water wave in a fluid or electrostatic wave potential in a plasma. Bilinear form, Bäcklund transformation and Lax pair are derived based on the binary Bell polynomials. Multi-soliton solutions are constructed via the Hirota’s method. Propagation and interaction of the solitons are illustrated graphically: (i) Through the asymptotic analysis, elastic and inelastic interactions between the two solitons are discussed analytically and graphically, respectively. The elastic interaction, amplitudes, velocities and shapes of the two solitons remain unchanged except for a phase shift. However, in the area of the inelastic interaction, amplitudes of the two solitons have a linear superposition. (ii) Elastic interactions among the three solitons indicate that the properties of the elastic interactions among the three solitons are similar to those between the two solitons. Moreover, oblique and overtaking interactions between the two solitons are displayed. Oblique interactions among the three solitons and interactions among the two parallel solitons and a single one are presented as well. (iii) Inelastic-elastic interactions imply that the interaction between the inelastic region and another one is elastic.

Upper Airway Elasticity Estimation in Pediatric Down Syndrome Sleep Apnea Patients Using Collapsible Tube Theory.

PubMed

Subramaniam, Dhananjay Radhakrishnan; Mylavarapu, Goutham; McConnell, Keith; Fleck, Robert J; Shott, Sally R; Amin, Raouf S; Gutmark, Ephraim J

2016-05-01

Elasticity of the soft tissues surrounding the upper airway lumen is one of the important factors contributing to upper airway disorders such as snoring and obstructive sleep apnea. The objective of this study is to calculate patient specific elasticity of the pharynx from magnetic resonance (MR) images using a 'tube law', i.e., the relationship between airway cross-sectional area and transmural pressure difference. MR imaging was performed under anesthesia in children with Down syndrome (DS) and obstructive sleep apnea (OSA). An airway segmentation algorithm was employed to evaluate changes in airway cross-sectional area dilated by continuous positive airway pressure (CPAP). A pressure-area relation was used to make localized estimates of airway wall stiffness for each patient. Optimized values of patient specific Young's modulus for tissue in the velopharynx and oropharynx, were estimated from finite element simulations of airway collapse. Patient specific deformation of the airway wall under CPAP was found to exhibit either a non-linear 'hardening' or 'softening' behavior. The localized airway and tissue elasticity were found to increase with increasing severity of OSA. Elasticity based patient phenotyping can potentially assist clinicians in decision making on CPAP and airway or tissue elasticity can supplement well-known clinical measures of OSA severity.

Feasibility of coded vibration in a vibro-ultrasound system for tissue elasticity measurement.

PubMed

Zhao, Jinxin; Wang, Yuanyuan; Yu, Jinhua; Li, Tianjie; Zheng, Yong-Ping

2016-07-01

The ability of various methods for elasticity measurement and imaging is hampered by the vibration amplitude on biological tissues. Based on the inference that coded excitation will improve the performance of the cross-correlation function of the tissue displacement waves, the idea of exerting encoded external vibration on tested samples for measuring its elasticity is proposed. It was implemented by integrating a programmable vibration generation function into a customized vibro-ultrasound system to generate Barker coded vibration for elasticity measurement. Experiments were conducted on silicone phantoms and porcine muscles. The results showed that coded excitation of the vibration enhanced the accuracy and robustness of the elasticity measurement especially in low signal-to-noise ratio scenarios. In the phantom study, the measured shear modulus values with coded vibration had an R(2 )= 0.993 linear correlation to that of referenced indentation, while for single-cycle pulse the R(2) decreased to 0.987. In porcine muscle study, the coded vibration also obtained a shear modulus value which is more accurate than the single-cycle pulse by 0.16 kPa and 0.33 kPa at two different depths. These results demonstrated the feasibility and potentiality of the coded vibration for enhancing the quality of elasticity measurement and imaging.

Analysis of complex elastic structures by a Rayleigh-Ritz component modes method using Lagrange multipliers. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Klein, L. R.

1974-01-01

The free vibrations of elastic structures of arbitrary complexity were analyzed in terms of their component modes. The method was based upon the use of the normal unconstrained modes of the components in a Rayleigh-Ritz analysis. The continuity conditions were enforced by means of Lagrange Multipliers. Examples of the structures considered are: (1) beams with nonuniform properties; (2) airplane structures with high or low aspect ratio lifting surface components; (3) the oblique wing airplane; and (4) plate structures. The method was also applied to the analysis of modal damping of linear elastic structures. Convergence of the method versus the number of modes per component and/or the number of components is discussed and compared to more conventional approaches, ad-hoc methods, and experimental results.

Ab Initio Study of Electronic Structure, Elastic and Transport Properties of Fluoroperovskite LiBeF3

NASA Astrophysics Data System (ADS)

Benmhidi, H.; Rached, H.; Rached, D.; Benkabou, M.

2017-04-01

The aim of this work is to investigate the electronic, mechanical, and transport properties of the fluoroperovskite compound LiBeF3 by first-principles calculations using the full-potential linear muffin-tin orbital method based on density functional theory within the local density approximation. The independent elastic constants and related mechanical properties including the bulk modulus ( B), shear modulus ( G), Young's modulus ( E), and Poisson's ratio ( ν) have been studied, yielding the elastic moduli, shear wave velocities, and Debye temperature. According to the electronic properties, this compound is an indirect-bandgap material, in good agreement with available theoretical data. The electron effective mass, hole effective mass, and energy bandgaps with their volume and pressure dependence are investigated for the first time.

Efficient finite element modeling of radiation forces on elastic particles of arbitrary size and geometry.

PubMed

Glynne-Jones, Peter; Mishra, Puja P; Boltryk, Rosemary J; Hill, Martyn

2013-04-01

A finite element based method is presented for calculating the acoustic radiation force on arbitrarily shaped elastic and fluid particles. Importantly for future applications, this development will permit the modeling of acoustic forces on complex structures such as biological cells, and the interactions between them and other bodies. The model is based on a non-viscous approximation, allowing the results from an efficient, numerical, linear scattering model to provide the basis for the second-order forces. Simulation times are of the order of a few seconds for an axi-symmetric structure. The model is verified against a range of existing analytical solutions (typical accuracy better than 0.1%), including those for cylinders, elastic spheres that are of significant size compared to the acoustic wavelength, and spheroidal particles.

Elastic, plastic, fracture analysis of masonry arches: A multi-span bridge case study

NASA Astrophysics Data System (ADS)

Lacidogna, Giuseppe; Accornero, Federico

2018-01-01

In this work a comparison is presented between elastic, plastic, and fracture analysis of the monumental arch bridge of Porta Napoli, Taranto (Italy). By means of a FEM model and applying the Mery's Method, the behavior of the curved structure under service loads is verified, while considering the Safe Theorem approach byHeyman, the ultimate carrying capacity of the structure is investigated. Moreover, by using Fracture Mechanics concepts, the damage process which takes place when the conditions assessed through linear elastic analysis are no longer valid, and before the set-in of the conditions established by means of the plastic limit analysis, is numerically analyzed. The study of these transitions returns an accurate and effective whole service life assessment of the Porta Napoli masonry arch bridge.

Decoupling nonclassical nonlinear behavior of elastic wave types

DOE PAGES

Remillieux, Marcel C.; Guyer, Robert A.; Payan, Cedric; ...

2016-03-01

In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. As a result, this could lead to furthermore » understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.« less

Comparative study on the mechanical property of silk thread from cocoons of Bombyx mori L.

PubMed

Iizuka, E; Hachimori, A; Abe, K; Sunohara, M; Hiraide, Y; Ueyama, A; Kamo, K; Fujiwara, T; Nakamura, F; Uno, T

1983-01-01

Specimens of bave (undegummed silk thread) were collected from cocoons of various origins of parent silkworm races, such as Japanese, Chinese, European, Korean and tropical origins, and from as many races as possible. An apparatus was set up to measure the dynamic elastic modulus of these specimens. In all the categories of the races tested, the elastic modulus was linearly related to the size of bave, regardless of the portion of cocoon layer from which the specimens were taken. This correlation was concluded to be universal to the silk thread of Bombyx mori L. species; however, values of the regression coefficient and of the elastic modulus were susceptible to the origin of silkworm races, depending on whether they were native or improved.

Plate and butt-weld stresses beyond elastic limit, material and structural modeling

NASA Technical Reports Server (NTRS)

Verderaime, V.

1991-01-01

Ultimate safety factors of high performance structures depend on stress behavior beyond the elastic limit, a region not too well understood. An analytical modeling approach was developed to gain fundamental insights into inelastic responses of simple structural elements. Nonlinear material properties were expressed in engineering stresses and strains variables and combined with strength of material stress and strain equations similar to numerical piece-wise linear method. Integrations are continuous which allows for more detailed solutions. Included with interesting results are the classical combined axial tension and bending load model and the strain gauge conversion to stress beyond the elastic limit. Material discontinuity stress factors in butt-welds were derived. This is a working-type document with analytical methods and results applicable to all industries of high reliability structures.

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.

Applying a probabilistic seismic-petrophysical inversion and two different rock-physics models for reservoir characterization in offshore Nile Delta

NASA Astrophysics Data System (ADS)

Aleardi, Mattia

2018-01-01

We apply a two-step probabilistic seismic-petrophysical inversion for the characterization of a clastic, gas-saturated, reservoir located in offshore Nile Delta. In particular, we discuss and compare the results obtained when two different rock-physics models (RPMs) are employed in the inversion. The first RPM is an empirical, linear model directly derived from the available well log data by means of an optimization procedure. The second RPM is a theoretical, non-linear model based on the Hertz-Mindlin contact theory. The first step of the inversion procedure is a Bayesian linearized amplitude versus angle (AVA) inversion in which the elastic properties, and the associated uncertainties, are inferred from pre-stack seismic data. The estimated elastic properties constitute the input to the second step that is a probabilistic petrophysical inversion in which we account for the noise contaminating the recorded seismic data and the uncertainties affecting both the derived rock-physics models and the estimated elastic parameters. In particular, a Gaussian mixture a-priori distribution is used to properly take into account the facies-dependent behavior of petrophysical properties, related to the different fluid and rock properties of the different litho-fluid classes. In the synthetic and in the field data tests, the very minor differences between the results obtained by employing the two RPMs, and the good match between the estimated properties and well log information, confirm the applicability of the inversion approach and the suitability of the two different RPMs for reservoir characterization in the investigated area.

Cortical bone fracture analysis using XFEM - case study.

PubMed

Idkaidek, Ashraf; Jasiuk, Iwona

2017-04-01

We aim to achieve an accurate simulation of human cortical bone fracture using the extended finite element method within a commercial finite element software abaqus. A two-dimensional unit cell model of cortical bone is built based on a microscopy image of the mid-diaphysis of tibia of a 70-year-old human male donor. Each phase of this model, an interstitial bone, a cement line, and an osteon, are considered linear elastic and isotropic with material properties obtained by nanoindentation, taken from literature. The effect of using fracture analysis methods (cohesive segment approach versus linear elastic fracture mechanics approach), finite element type, and boundary conditions (traction, displacement, and mixed) on cortical bone crack initiation and propagation are studied. In this study cohesive segment damage evolution for a traction separation law based on energy and displacement is used. In addition, effects of the increment size and mesh density on analysis results are investigated. We find that both cohesive segment and linear elastic fracture mechanics approaches within the extended finite element method can effectively simulate cortical bone fracture. Mesh density and simulation increment size can influence analysis results when employing either approach, and using finer mesh and/or smaller increment size does not always provide more accurate results. Both approaches provide close but not identical results, and crack propagation speed is found to be slower when using the cohesive segment approach. Also, using reduced integration elements along with the cohesive segment approach decreases crack propagation speed compared with using full integration elements. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Surface instability of an imperfectly bonded thin elastic film under surface van der Waals forces

NASA Astrophysics Data System (ADS)

Wang, Xu; Jing, Rong

2017-02-01

This paper studies surface instability of a thin elastic film imperfectly bonded to a rigid substrate interacting with a rigid contactor through van der Waals forces under plane strain conditions. The film-substrate interface is modeled as a linear spring with vanishing thickness described in terms of the normal and tangential interface parameters. Depending on the ratio of the two imperfect interface parameters, the critical value of the Poisson's ratio for the occurrence of surface wrinkling in the absence of surface energy can be greater than, equal to, or smaller than 0.25, which is the critical Poisson's ratio for a perfect film-substrate interface. The critical surface energy for the inhibition of the surface wrinkling is also obtained. Finally, we propose a very simple and effective method to study the surface instability of a multilayered elastic film with imperfect interfaces interacting with a rigid contactor or with another multilayered elastic film (or a multilayered simply supported plate) with imperfect interfaces.

Thermal and structural tests of Rene 41 honeycomb integral-tank concept for future space transportation systems

NASA Technical Reports Server (NTRS)

Shideler, John L.; Fields, Roger A.; Reardon, Lawrence F.; Gong, Leslie

1992-01-01

Two flat 12 by 72 inch Rene 41 honeycomb sandwich panels were tested in a manner to produce combined thermal and mechanical longitudinal stresses that simulated those that would occur in a larger, more complex integral tank and fuselage structure of an earth to orbit vehicle. Elastic strains measured at temperatures below 400 F are compared with calculated values obtained from a linear elastic finite element analysis to verify the analytical model and to establish confidence in the calculated strains. Elastic strain measurement at higher temperatures (between 600 F and 1400 F), where strain measurement is more difficult and less certain, are also compared with calculated strains. Agreement between measured and calculated strains for the lower temperatures is good, but agreement for the higher temperatures is poor because of unreliable strain measurements. Test results indicate that an ascent and entry life cycle of 500 is attainable under high combined thermal and mechanical elastic strains.

A cohesive granular material with tunable elasticity

PubMed Central

Hemmerle, Arnaud; Schröter, Matthias; Goehring, Lucas

2016-01-01

By mixing glass beads with a curable polymer we create a well-defined cohesive granular medium, held together by solidified, and hence elastic, capillary bridges. This material has a geometry similar to a wet packing of beads, but with an additional control over the elasticity of the bonds holding the particles together. We show that its mechanical response can be varied over several orders of magnitude by adjusting the size and stiffness of the bridges, and the size of the particles. We also investigate its mechanism of failure under unconfined uniaxial compression in combination with in situ x-ray microtomography. We show that a broad linear-elastic regime ends at a limiting strain of about 8%, whatever the stiffness of the agglomerate, which corresponds to the beginning of shear failure. The possibility to finely tune the stiffness, size and shape of this simple material makes it an ideal model system for investigations on, for example, fracturing of porous rocks, seismology, or root growth in cohesive porous media. PMID:27774988

Receiving sensitivity and transmitting voltage response of a fluid loaded spherical piezoelectric transducer with an elastic coating.

PubMed

George, Jineesh; Ebenezer, D D; Bhattacharyya, S K

2010-10-01

A method is presented to determine the response of a spherical acoustic transducer that consists of a fluid-filled piezoelectric sphere with an elastic coating embedded in infinite fluid to electrical and plane-wave acoustic excitations. The exact spherically symmetric, linear, differential, governing equations are used for the interior and exterior fluids, and elastic and piezoelectric materials. Under acoustic excitation and open circuit boundary condition, the equation governing the piezoelectric sphere is homogeneous and the solution is expressed in terms of Bessel functions. Under electrical excitation, the equation governing the piezoelectric sphere is inhomogeneous and the complementary solution is expressed in terms of Bessel functions and the particular integral is expressed in terms of a power series. Numerical results are presented to illustrate the effect of dimensions of the piezoelectric sphere, fluid loading, elastic coating and internal material losses on the open-circuit receiving sensitivity and transmitting voltage response of the transducer.

Compaction trends of full stiffness tensor and fluid permeability in artificial shales

NASA Astrophysics Data System (ADS)

Beloborodov, Roman; Pervukhina, Marina; Lebedev, Maxim

2018-03-01

We present a methodology and describe a set-up that allows simultaneous acquisition of all five elastic coefficients of a transversely isotropic (TI) medium and its permeability in the direction parallel to the symmetry axis during mechanical compaction experiments. We apply the approach to synthetic shale samples and investigate the role of composition and applied stress on their elastic and transport properties. Compaction trends for the five elastic coefficients that fully characterize TI anisotropy of artificial shales are obtained for a porosity range from 40 per cent to 15 per cent. A linear increase of elastic coefficients with decreasing porosity is observed. The permeability acquired with the pressure-oscillation technique exhibits exponential decrease with decreasing porosity. Strong correlations are observed between an axial fluid permeability and seismic attributes, namely, VP/VS ratio and acoustic impedance, measured in the same direction. These correlations might be used to derive permeability of shales from seismic data given that their mineralogical composition is known.

A cohesive granular material with tunable elasticity.

PubMed

Hemmerle, Arnaud; Schröter, Matthias; Goehring, Lucas

2016-10-24

By mixing glass beads with a curable polymer we create a well-defined cohesive granular medium, held together by solidified, and hence elastic, capillary bridges. This material has a geometry similar to a wet packing of beads, but with an additional control over the elasticity of the bonds holding the particles together. We show that its mechanical response can be varied over several orders of magnitude by adjusting the size and stiffness of the bridges, and the size of the particles. We also investigate its mechanism of failure under unconfined uniaxial compression in combination with in situ x-ray microtomography. We show that a broad linear-elastic regime ends at a limiting strain of about 8%, whatever the stiffness of the agglomerate, which corresponds to the beginning of shear failure. The possibility to finely tune the stiffness, size and shape of this simple material makes it an ideal model system for investigations on, for example, fracturing of porous rocks, seismology, or root growth in cohesive porous media.

Advantages of formulating an evolution equation directly for elastic distortional deformation in finite deformation plasticity

NASA Astrophysics Data System (ADS)

Rubin, M. B.; Cardiff, P.

2017-11-01

Simo (Comput Methods Appl Mech Eng 66:199-219, 1988) proposed an evolution equation for elastic deformation together with a constitutive equation for inelastic deformation rate in plasticity. The numerical algorithm (Simo in Comput Methods Appl Mech Eng 68:1-31, 1988) for determining elastic distortional deformation was simple. However, the proposed inelastic deformation rate caused plastic compaction. The corrected formulation (Simo in Comput Methods Appl Mech Eng 99:61-112, 1992) preserves isochoric plasticity but the numerical integration algorithm is complicated and needs special methods for calculation of the exponential map of a tensor. Alternatively, an evolution equation for elastic distortional deformation can be proposed directly with a simplified constitutive equation for inelastic distortional deformation rate. This has the advantage that the physics of inelastic distortional deformation is separated from that of dilatation. The example of finite deformation J2 plasticity with linear isotropic hardening is used to demonstrate the simplicity of the numerical algorithm.

Theoretical study of phonon dispersion, elastic, mechanical and thermodynamic properties of barium chalcogenides

NASA Astrophysics Data System (ADS)

Musari, A. A.; Orukombo, S. A.

2018-03-01

Barium chalcogenides are known for their high-technological importance and great scientific interest. Detailed studies of their elastic, mechanical, dynamical and thermodynamic properties were carried out using density functional theory and plane-wave pseudo potential method within the generalized gradient approximation. The optimized lattice constants were in good agreement when compared with experimental data. The independent elastic constants, calculated from a linear fit of the computed stress-strain function, were used to determine the Young’s modulus (E), bulk modulus (B), shear modulus (G), Poisson’s ratio (σ) and Zener’s anisotropy factor (A). Also, the Debye temperature and sound velocities for barium chalcogenides were estimated from the three independent elastic constants. The calculations of phonon dispersion showed that there are no negative frequencies throughout the Brillouin zone. Hence barium chalcogenides have dynamically stable NaCl-type crystal structure. Finally, their thermodynamic properties were calculated in the temperature range of 0-1000 K and their constant-volume specific heat capacities at room-temperature were reported.

Modeling of rail track substructure linear elastic coupling

DOT National Transportation Integrated Search

2015-09-30

Most analyses of rail dynamics neglect contribution of the soil, or treat it in a very simple manner such as using spring elements. This can cause accuracy issues in examining dynamics for passenger comfort, derailment, substructure analysis, or othe...

B and F Projection Methods for Nearly Incompressible Linear and Nonlinear Elasticity and Plasticity using Higher-order NURBS Elements

DTIC Science & Technology

2007-08-01

Infinite plate with a hole: sequence of meshes produced by h-refinement. The geometry of the coarsest mesh...recalled with an emphasis on k -refinement. In Section 3, the use of high-order NURBS within a projection technique is studied in the geometri - cally linear...case with a B̄ method to investigate the choice of approximation and projection spaces with NURBS.

Understanding of Materials State and its Degradation using Non-Linear Ultrasound (NLU) Approaches

DTIC Science & Technology

2011-01-01

Traditional ultrasonic NDE is based on linear theory and normally relies on measuring some particular parameter (sound velocity , attenuation... velocity in the material. In most cases this technique is not considered to be very practical as very small changes in velocity has to be measured. Hence...nonlinear elasticity) of the material the input wave distorts as it propagates. This is attributed to the difference in the wave velocities of the

Elasticity Imaging of Polymeric Media

PubMed Central

Sridhar, Mallika; Liu, Jie; Insana, Michael F.

2009-01-01

Viscoelastic properties of soft tissues and hydropolymers depend on the strength of molecular bonding forces connecting the polymer matrix and surrounding fluids. The basis for diagnostic imaging is that disease processes alter molecular-scale bonding in ways that vary the measurable stiffness and viscosity of the tissues. This paper reviews linear viscoelastic theory as applied to gelatin hydrogels for the purpose of formulating approaches to molecular-scale interpretation of elasticity imaging in soft biological tissues. Comparing measurements acquired under different geometries, we investigate the limitations of viscoelastic parameters acquired under various imaging conditions. Quasistatic (step-and-hold and low-frequency harmonic) stimuli applied to gels during creep and stress relaxation experiments in confined and unconfined geometries reveal continuous, bimodal distributions of respondance times. Within the linear range of responses, gelatin will behave more like a solid or fluid depending on the stimulus magnitude. Gelatin can be described statistically from a few parameters of low-order rheological models that form the basis of viscoelastic imaging. Unbiased estimates of imaging parameters are obtained only if creep data are acquired for greater than twice the highest retardance time constant and any steady-state viscous response has been eliminated. Elastic strain and retardance time images are found to provide the best combination of contrast and signal strength in gelatin. Retardance times indicate average behavior of fast (1–10 s) fluid flows and slow (50–400 s) matrix restructuring in response to the mechanical stimulus. Insofar as gelatin mimics other polymers, such as soft biological tissues, elasticity imaging can provide unique insights into complex structural and biochemical features of connectives tissues affected by disease. PMID:17408331

Stress Dependence of Ultrasonic Velocity in Unidirectional Graphite/Epoxy Composites for Longitudinal Waves Propagating Along the Direction of Stress

NASA Technical Reports Server (NTRS)

Prosser, William H.

1990-01-01

The first measurements of the stress induced velocity changes for propagation directions along the direction of applied stress in gr/ep composites have been presented. For propagation and stress direction perpendicular to the fiber direction, the data demonstrated a linear relation between normalized velocity shift and stress. After corrections for the delay line were made, the slope or SAC was determined and compared favorably with the expected value calculated from the previously determined nonlinear coefficients of this material. The ratio of the SAC to the elastic compliance for this direction of loading was evaluated and found to have a value similar to numerous other materials which have very different linear elastic properties. Measurements with stress and propagation along the fibers yielded unusual behavior. The curves were very nonlinear and even shifted direction at higher loads. The large scatter in the data due to bond variations made separation of material effects from bond induced artifacts impossible. Thus the SAC, R, and the remaining two unknown TOEC's could not be determined for this direction of propagation. These measurements further expand the basis of determining nonlinear elastic properties of composite materials. These properties may be useful in developing much needed NDE techniques to determine such important parameters as residual stress after cure and residual strength after impact damage. Additional study is needed to measure the nonlinear behavior in other composite materials including angle ply laminates. Also, other techniques to measure elastic nonlinearity such as harmonic generation should be applied to composites to improve the understanding of these properties and their importance.

The structural response of unsymmetrically laminated composite cylinders

NASA Technical Reports Server (NTRS)

Butler, T. A.; Hyer, M. W.

1989-01-01

The responses of an unsymmetrically laminated fiber-reinforced composite cylinder to an axial compressive load, a torsional load, and the temperature change associated with cooling from the processing temperature to the service temperature are investigated. These problems are considered axisymmetric and the response is studied in the context of linear elastic material behavior and geometrically linear kinematics. Four different laminates are studied: a general unsymmetric laminate; two unsymmetric but more conventional laminates; and a conventional quasi-isotropic symmetric laminate. The responses based on closed-form solutions for different boundary conditions are computed and studied in detail. Particular emphasis is directed at understanding the influence of elastic couplings in the laminates. The influence of coupling decreased from a large effect in the general unsymmetric laminate, to practically no effect in the quasi-isotropic laminate. For example, the torsional loading of the general unsymmetric laminate resulted in a radial displacement. The temperature change also caused a significant radial displacement to occur near the ends of the cylinder. On the other hand, the more conventional unsymmetric laminate and the quasi-isotropic cylinder did not deform radially when subjected to a torsional load. From the results obtained, it is clear the degree of elastic coupling can be controlled and indeed designed into a cylinder, the degree and character of the coupling being dictated by the application.

Adhesive Properties of Polyacrylate Gels

NASA Astrophysics Data System (ADS)

Flanigan, Cynthia; Shull, Kenneth

1998-03-01

Soft, low-modulus gels provide an interesting opportunity to examine small adhesive interactions between two bodies in contact. As shown through dynamic rheological studies, our materials undergo a rapid gelation as they are cooled from a viscous liquid at elevated temperatures to a soft, elastic solid at room temperature. At low temperatures, the gels exhibit a linearly elastic response and display moduli close to 100Pa, thereby forming materials with great potential for quantifying weak adhesive interactions with a variety of bodies ranging from polymer surfaces to biological entities. Our current studies focus on investigating interfacial effects by performing axisymmetric adhesion tests with a model polyacrylate gel formed by diluting the copolymer poly(methyl methacrylate)-poly(n-butyl acrylate)-poly(methyl methacrylate) to a 5-15 percent solution in 2-ethyl hexanol, a selective solvent for the midblock. We have explored two different experimental geometries including a hemispherical rigid indenter of glass pressed into a gel layer of varying thicknesses, and a soft, gel cap in contact with a rigid polymer surface. By simultaneously measuring the applied load, displacement between the two bodies, and contact area during loading cycles, we are able to employ a linearly elastic fracture mechanics analysis to obtain estimates of the gel's modulus over a range of polymer concentrations, and G, the energy release rate.

Elastic Multilayer Bandages for Chronic Venous Insufficiency: Features of Our Technique

PubMed Central

2012-01-01

Objectives: To evaluate the interface pressure (IP) and stiffness of our elastic multilayer bandages (eMLB). Methods: Three medical staff wrapped the legs of 10 healthy volunteers with one to six rolls of elastic bandages. The IP was measured at the medial aspect of the lower leg at the level of transposition of the medial gastrocnemius muscle into the Achilles tendon (level of B1) with the patient supine and then standing, for each number of bandages worn. The static stiffness index (SSI) was calculated as a difference between these IPs. Results: The IPs in the standing position increased linearly for up to five bandages (21.8 ± 7.2, 32.5 ± 6.1, 41.8 ± 8.5, 52.0 ± 10.4, 60.3 ± 11.8, and 66.7 ± 13.4 mmHg, with one to six bandages). SSI also increased linearly for up to five bandages (6.8 ± 5.1, 10.2 ± 4.8, 13.4 ± 7.2, 17.4 ± 8.8, 19.7 ± 9.1, and 20.4 ± 9.4 mmHg, with one to six bandages). No significant technical variation in the IP was observed among the three operators. Conclusions: Our eMLB provided stable, predictable and sufficient IPs and SSIs in healthy volunteers. PMID:23555535

Mechanical and magneto-opto-electronic investigation of transition metal based fluoro-perovskites: An ab-initio DFT study

NASA Astrophysics Data System (ADS)

Erum, Nazia; Azhar Iqbal, Muhammad

2017-09-01

Detailed ab-initio calculations are performed to investigate structural, elastic, mechanical, magneto-electronic and optical properties of the KXF3 (X = V, Fe, Co, Ni) fluoro-perovskites using Full Potential Linearized Augmented Plane Wave (FP-LAPW) method within the framework of density functional theory (DFT). The calculated structural parameters by DFT and analytical methods are found consistent with the experimental results. From the elastic and mechanical properties, it can be inferred that these compounds are elastically stable and anisotropic while KCoF3 is harder than rest of the compounds. Furthermore, thermal behavior of these compounds is analyzed by calculating Debye temperature (θD). The calculated spin dependent magneto-electronic properties in these compounds reveal that exchange splitting is dominated by N-3d orbital. The stable magnetic phase optimizations verify the experimental observations at low temperature. Type of chemical bonding is analyzed with the help of variations in electron density difference distribution that is induced due to changes of the second cation. The linear optical properties are also discussed in terms of optical spectra. The present methodology represents an influential approach to calculate the whole set of mechanical and magneto-opto-electronic parameters, which would support to understand various physical phenomena and empower device engineers for implementing these materials in spintronic applications.

Multiphoton photochemical crosslinking-based fabrication of protein micropatterns with controllable mechanical properties for single cell traction force measurements

NASA Astrophysics Data System (ADS)

Tong, Ming Hui; Huang, Nan; Zhang, Wei; Zhou, Zhuo Long; Ngan, Alfonso Hing Wan; Du, Yanan; Chan, Barbara Pui

2016-01-01

Engineering 3D microstructures with predetermined properties is critical for stem cell niche studies. We have developed a multiphoton femtosecond laser-based 3D printing platform, which generates complex protein microstructures in minutes. Here, we used the platform to test a series of fabrication and reagent parameters in precisely controlling the mechanical properties of protein micropillars. Atomic force microscopy was utilized to measure the reduced elastic modulus of the micropillars, and transmission electron microscopy was used to visualize the porosity of the structures. The reduced elastic modulus of the micropillars associated positively and linearly with the scanning power. On the other hand, the porosity and pore size of the micropillars associated inversely and linearly with the scanning power and reagent concentrations. While keeping the elastic modulus constant, the stiffness of the micropillars was controlled by varying their height. Subsequently, the single cell traction forces of rabbit chondrocytes, human dermal fibroblasts, human mesenchymal stem cells, and bovine nucleus pulposus cells (bNPCs) were successfully measured by culturing the cells on micropillar arrays of different stiffness. Our results showed that the traction forces of all groups showed positive relationship with stiffness, and that the chondrocytes and bNPCs generated the highest and lowest traction forces, respectively.

Dynamic shear rheology of colloidal suspensions of surface-modified silica nanoparticles in PEG

NASA Astrophysics Data System (ADS)

Swarna; Pattanayek, Sudip Kumar; Ghosh, Anup Kumar

2018-03-01

The present work illustrates the effect of surface modification of silica nanoparticles (500 nm) with 3-(glycidoxypropyl)trimethoxy silane which was carried out at different reaction times. The suspensions prepared from modified and unmodified silica nanoparticles were evaluated for their shear rate-dependent viscosity and strain-frequency-dependent modulus. The linear viscoelastic moduli, viz., storage modulus and loss modulus, were compared with those of nonlinear moduli. The shear-thickened suspensions displayed strain thinning at low-frequency smaller strains and a strong strain overshoot at higher strains, characteristics of a continuous shear thickening fluids. The shear-thinned suspension, conversely, exhibited a strong elastic dominance at smaller strains, but at higher strains, its strain softened observed in the steady shear viscosity plot indicating characteristics of yielding material. Considering higher order harmonic components, the decomposed elastic and viscous stress revealed a pronounced elastic response up to 10% strain and a high viscous damping at larger strains. The current work is one of a kind in demonstrating the effect of silica surface functionalization on the linear and nonlinear viscoelasticity of suspensions showing a unique rheological fingerprint. The suspensions can thus be predicted through rheological studies for their applicability in energy absorbing and damping materials with respect to their mechanical properties.

Measuring nanoscale viscoelastic parameters of cells directly from AFM force-displacement curves.

PubMed

Efremov, Yuri M; Wang, Wen-Horng; Hardy, Shana D; Geahlen, Robert L; Raman, Arvind

2017-05-08

Force-displacement (F-Z) curves are the most commonly used Atomic Force Microscopy (AFM) mode to measure the local, nanoscale elastic properties of soft materials like living cells. Yet a theoretical framework has been lacking that allows the post-processing of F-Z data to extract their viscoelastic constitutive parameters. Here, we propose a new method to extract nanoscale viscoelastic properties of soft samples like living cells and hydrogels directly from conventional AFM F-Z experiments, thereby creating a common platform for the analysis of cell elastic and viscoelastic properties with arbitrary linear constitutive relations. The method based on the elastic-viscoelastic correspondence principle was validated using finite element (FE) simulations and by comparison with the existed AFM techniques on living cells and hydrogels. The method also allows a discrimination of which viscoelastic relaxation model, for example, standard linear solid (SLS) or power-law rheology (PLR), best suits the experimental data. The method was used to extract the viscoelastic properties of benign and cancerous cell lines (NIH 3T3 fibroblasts, NMuMG epithelial, MDA-MB-231 and MCF-7 breast cancer cells). Finally, we studied the changes in viscoelastic properties related to tumorigenesis including TGF-β induced epithelial-to-mesenchymal transition on NMuMG cells and Syk expression induced phenotype changes in MDA-MB-231 cells.

The asymptotic homogenization elasticity tensor properties for composites with material discontinuities

NASA Astrophysics Data System (ADS)

Penta, Raimondo; Gerisch, Alf

2017-01-01

The classical asymptotic homogenization approach for linear elastic composites with discontinuous material properties is considered as a starting point. The sharp length scale separation between the fine periodic structure and the whole material formally leads to anisotropic elastic-type balance equations on the coarse scale, where the arising fourth rank operator is to be computed solving single periodic cell problems on the fine scale. After revisiting the derivation of the problem, which here explicitly points out how the discontinuity in the individual constituents' elastic coefficients translates into stress jump interface conditions for the cell problems, we prove that the gradient of the cell problem solution is minor symmetric and that its cell average is zero. This property holds for perfect interfaces only (i.e., when the elastic displacement is continuous across the composite's interface) and can be used to assess the accuracy of the computed numerical solutions. These facts are further exploited, together with the individual constituents' elastic coefficients and the specific form of the cell problems, to prove a theorem that characterizes the fourth rank operator appearing in the coarse-scale elastic-type balance equations as a composite material effective elasticity tensor. We both recover known facts, such as minor and major symmetries and positive definiteness, and establish new facts concerning the Voigt and Reuss bounds. The latter are shown for the first time without assuming any equivalence between coarse and fine-scale energies ( Hill's condition), which, in contrast to the case of representative volume elements, does not identically hold in the context of asymptotic homogenization. We conclude with instructive three-dimensional numerical simulations of a soft elastic matrix with an embedded cubic stiffer inclusion to show the profile of the physically relevant elastic moduli (Young's and shear moduli) and Poisson's ratio at increasing (up to 100 %) inclusion's volume fraction, thus providing a proxy for the design of artificial elastic composites.

Control of mechanical response of freestanding PbZr0.52Ti0.48O3 films through texture

NASA Astrophysics Data System (ADS)

Das, Debashish; Sanchez, Luz; Martin, Joel; Power, Brian; Isaacson, Steven; Polcawich, Ronald G.; Chasiotis, Ioannis

2016-09-01

The texture of piezoelectric lead zirconate titanate (PZT) thin films plays a key role in their mechanical response and linearity in the stress vs. strain behavior. The open circuit mechanical properties of PZT films with controlled texture varying from 100% (001) to 100% (111) were quantified with the aid of direct strain measurements from freestanding thin film specimens. The texture was tuned using a highly {111}-textured Pt substrate and excess-Pb in the PbTiO3 seed layer. The mechanical and ferroelastic properties of 500 nm thick PZT (52/48) films were found to be strongly dependent on grain orientation: the lowest elastic modulus of 90 ± 2 GPa corresponded to pure (001) texture, and its value increased linearly with the percentage of (111) texture reaching 122 ± 3 GPa for pure (111) texture. These elastic modulus values were between those computed for transversely isotropic textured PZT films by using the soft and hard bulk PZT compliance coefficients. Pure (001) texture exhibited maximum non-linearity and ferroelastic domain switching, contrary to pure (111) texture that exhibited more linearity and the least amount of switching. A micromechanics model was employed to calculate the strain due to domain switching. The model fitted well the non-linearities in the experimental stress-strain curves of (001) and (111) textured PZT films, predicting 17% and 10% of switched 90° domains that initially were favorably aligned with the applied stress in (001) and (111) textured PZT films, respectively.

Composite polymer systems with control of local substrate elasticity and their effect on cytoskeletal and morphological characteristics of adherent cells.

PubMed

Chou, Szu-Yuan; Cheng, Chao-Min; LeDuc, Philip R

2009-06-01

At the interface between extracellular substrates and biological materials, substrate elasticity strongly influences cell morphology and function. The associated biological ramifications comprise a diversity of critical responses including apoptosis, differentiation, and motility, which can affect medical devices such as stents. The interactions of the extracellular environment with the substrate are also affected by local properties wherein cells sense and respond to different physical inputs. To investigate the effects of having localized elasticity control of substrate microenvironments on cell response, we have developed a method to control material interface interactions with cells by dictating local substrate elasticity. This system is created by generating a composite material system with alternating, linear regions of polymers that have distinct stiffness characteristics. This approach was used to examine cytoskeletal and morphological changes in NIH 3T3 fibroblasts with emphasis on both local and global properties, noting that cells sense and respond to distinct material elasticities. Isolated cells sense and respond to these local differences in substrate elasticity by extending processes along the interface. Also, cells grown on softer elastic regions at higher densities (in contact with each other) have a higher projected area than isolated cells. Furthermore, when using chemical agents such as cytochalasin-D to disrupt the actin cytoskeleton, there is a significant increase in projected area for cells cultured on softer elastic regions This method has the potential to promote understanding of biomaterial-affected responses in a diversity of areas including morphogenesis, mechanotransduction, stents, and stem cell differentiation.

On the acoustic signature of tandem airfoils: The sound of an elastic airfoil in the wake of a vortex generator

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

Manela, A.

The acoustic signature of an acoustically compact tandem airfoil setup in uniform high-Reynolds number flow is investigated. The upstream airfoil is considered rigid and is actuated at its leading edge with small-amplitude harmonic pitching motion. The downstream airfoil is taken passive and elastic, with its motion forced by the vortex-street excitation of the upstream airfoil. The non-linear near-field description is obtained via potential thin-airfoil theory. It is then applied as a source term into the Powell-Howe acoustic analogy to yield the far-field dipole radiation of the system. To assess the effect of downstream-airfoil elasticity, results are compared with counterpart calculationsmore » for a non-elastic setup, where the downstream airfoil is rigid and stationary. Depending on the separation distance between airfoils, airfoil-motion and airfoil-wake dynamics shift between in-phase (synchronized) and counter-phase behaviors. Consequently, downstream airfoil elasticity may act to amplify or suppress sound through the direct contribution of elastic-airfoil motion to the total signal. Resonance-type motion of the elastic airfoil is found when the upstream airfoil is actuated at the least stable eigenfrequency of the downstream structure. This, again, results in system sound amplification or suppression, depending on the separation distance between airfoils. With increasing actuation frequency, the acoustic signal becomes dominated by the direct contribution of the upstream airfoil motion, whereas the relative contribution of the elastic airfoil to the total signature turns negligible.« less

The NASA High Speed ASE Project: Computational Analyses of a Low-Boom Supersonic Configuration

NASA Technical Reports Server (NTRS)

Silva, Walter A.; DeLaGarza, Antonio; Zink, Scott; Bounajem, Elias G.; Johnson, Christopher; Buonanno, Michael; Sanetrik, Mark D.; Yoo, Seung Y.; Kopasakis, George; Christhilf, David M.;

Enhanced calculation of eigen-stress field and elastic energy in atomistic interdiffusion of alloys

NASA Astrophysics Data System (ADS)

Cecilia, José M.; Hernández-Díaz, A. M.; Castrillo, Pedro; Jiménez-Alonso, J. F.

2017-02-01

The structural evolution of alloys is affected by the elastic energy associated to eigen-stress fields. However, efficient calculations of the elastic energy in evolving geometries are actually a great challenge in promising atomistic simulation techniques such as Kinetic Monte Carlo (KMC) methods. In this paper, we report two complementary algorithms to calculate the eigen-stress field by linear superposition (a.k.a. LSA, Lineal Superposition Algorithm) and the elastic energy modification in atomistic interdiffusion of alloys (the Atom Exchange Elastic Energy Evaluation (AE4) Algorithm). LSA is shown to be appropriated for fast incremental stress calculation in highly nanostructured materials, whereas AE4 provides the required input for KMC and, additionally, it can be used to evaluate the accuracy of the eigen-stress field calculated by LSA. Consequently, they are suitable to be used on-the-fly with KMC. Both algorithms are massively parallel by their definition and thus well-suited for their parallelization on modern Graphics Processing Units (GPUs). Our computational studies confirm that we can obtain significant improvements compared to conventional Finite Element Methods, and the utilization of GPUs opens up new possibilities for the development of these methods in atomistic simulation of materials.

Torsion of a Cosserat elastic bar with square cross section: theory and experiment

NASA Astrophysics Data System (ADS)

Drugan, W. J.; Lakes, R. S.

2018-04-01

An approximate analytical solution for the displacement and microrotation vector fields is derived for pure torsion of a prismatic bar with square cross section comprised of homogeneous, isotropic linear Cosserat elastic material. This is accomplished by analytical simplification coupled with use of the principle of minimum potential energy together with polynomial representations for the desired field components. Explicit approximate expressions are derived for cross section warp and for applied torque versus angle of twist of the bar. These show that torsional rigidity exceeds the classical elasticity value, the difference being larger for slender bars, and that cross section warp is less than the classical amount. Experimental measurements on two sets of 3D printed square cross section polymeric bars, each set having a different microstructure and four different cross section sizes, revealed size effects not captured by classical elasticity but consistent with the present analysis for physically sensible values of the Cosserat moduli. The warp can allow inference of Cosserat elastic constants independently of any sensitivity the material may have to dilatation gradients; warp also facilitates inference of Cosserat constants that are difficult to obtain via size effects.

A Maxwell elasto-brittle rheology for sea ice modelling

NASA Astrophysics Data System (ADS)

Dansereau, Véronique; Weiss, Jérôme; Saramito, Pierre; Lattes, Philippe

2016-07-01

A new rheological model is developed that builds on an elasto-brittle (EB) framework used for sea ice and rock mechanics, with the intent of representing both the small elastic deformations associated with fracturing processes and the larger deformations occurring along the faults/leads once the material is highly damaged and fragmented. A viscous-like relaxation term is added to the linear-elastic constitutive law together with an effective viscosity that evolves according to the local level of damage of the material, like its elastic modulus. The coupling between the level of damage and both mechanical parameters is such that within an undamaged ice cover the viscosity is infinitely large and deformations are strictly elastic, while along highly damaged zones the elastic modulus vanishes and most of the stress is dissipated through permanent deformations. A healing mechanism is also introduced, counterbalancing the effects of damaging over large timescales. In this new model, named Maxwell-EB after the Maxwell rheology, the irreversible and reversible deformations are solved for simultaneously; hence drift velocities are defined naturally. First idealized simulations without advection show that the model reproduces the main characteristics of sea ice mechanics and deformation: strain localization, anisotropy, intermittency and associated scaling laws.

Effects of a high mean stress on the high cycle fatigue life of PWA 1480 and correlation of data by linear elastic fracture mechanics

NASA Technical Reports Server (NTRS)

Majumdar, S.; Kwasny, R.

1985-01-01

High-cycle fatigue tests using 5-mm-diameter smooth specimens were performed on the single crystal alloy PWA 1480 (001 axis) at 70F (room temperature) in air and at 100F (538C) in vacuum (10 to the -6 power torr). Tests were conducted at zero mean stress as well as at high tensile mean stress. The results indicate that, although a tensile mean stress, in general, reduces life, the reduction in fatigue strength, for a given mean stress at a life of one million cycles, is much less than what is predicted by the usual linear Goodman plot. Further, the material appears to be significantly more resistant to mean stress effects at 1000F than at 70F. Metallographic examinations of failed specimens indicate that failures in all cases are initiated from micropores of sizes of the order of 30 to 40 microns. Since the macroscopic stress-strain response in all cases was observed to be linear elastic, linear elastic fracture mechanics (LEFM) analyses were carried out to determine the crack growth curves of the material assuming that crack initiation from a micropore (a sub o = 40 microns) occurs very early in life. The results indicate that the calculated crack growth rates at an R (defined as the ratio between minimum stress to maximum stress) value of zero are approximately the same at 70F as at 1000F. However, the calculated crack growth rates at other R ratios, both positive and negative, tend to be higher at 70F than at 1000F. Calculated threshold effects at large R values tend to be independent of temperature in the temperature regime studied. They are relatively constant with increasing R ratio up to a value of about 0.6, beyond which the calculated threshold stress intensity factor range decreases rapidly with increasing R ratios.

Optimal development of matrix elasticity

PubMed Central

Majkut, Stephanie; Idema, Timon; Swift, Joe; Krieger, Christine; Liu, Andrea; Discher, Dennis E.

2014-01-01

Summary In development and differentiation, morphological changes often accompany mechanical changes [1], but it is unclear if or when cells in embryos sense tissue elasticity. The earliest embryo is uniformly pliable while adult tissues vary widely in mechanics from soft brain and stiff heart to rigid bone [2], but the sensitivity of cells to microenvironment elasticity is debated [3]. Regenerative cardiology provides strong motivation because rigid post-infarct regions limit pumping by the adult heart [4]. Here we focus on embryonic heart and isolated cardiomyocytes, which both beat spontaneously. Tissue elasticity, Et, increases daily for heart to 1-2 kiloPascal by embryonic day-4 (E4), and although this is ∼10-fold softer than adult heart, the beating contractions of E4-cardiomyocytes prove optimal at ∼Et,E4 both in vivo and in vitro. Proteomics reveals daily increases in a small subset of proteins, namely collagen plus cardiac-specific excitation-contraction proteins. Rapid softening of the heart's matrix with collagenase or stiffening it with enzymatic crosslinking suppresses beating. Sparsely cultured E4-cardiomyocytes on collagen-coated gels likewise show maximal contraction on matrices with native E4 stiffness, highlighting cell-intrinsic mechanosensitivity. While an optimal elasticity for striation proves consistent with the mathematics of force-driven sarcomere registration, contraction wave-speed is linear in Et as theorized for Excitation-Contraction Coupled to Matrix Elasticity. Mechanosensitive stem cell cardiogenesis helps generalize tissue results, which demonstrate how myosin-II organization and contractile function is optimally matched to the load presented by matrix elasticity. PMID:24268417

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

A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

DOE PAGES

Gao, Kai; Chung, Eric T.; Gibson, Richard L.; ...

2015-06-05

The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elasticmore » wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.« less

Growth Kinematics of Opening-Mode Fractures

NASA Astrophysics Data System (ADS)

Eichhubl, P.; Alzayer, Y.; Laubach, S.; Fall, A.

2014-12-01

Fracture aperture is a primary control on flow in fractured reservoirs of low matrix permeability including unconventional oil and gas reservoirs and most geothermal systems. Guided by principles of linear elastic fracture mechanics, fracture aperture is generally assumed to be a linear function of fracture length and elastic material properties. Natural opening-mode fractures with significant preserved aperture are observed in core and outcrop indicative of fracture opening strain accommodated by permanent solution-precipitation creep. Fracture opening may thus be decoupled from length growth if the material effectively weakens after initial elastic fracture growth by either non-elastic deformation processes or changes in elastic properties. To investigate the kinematics of fracture length and aperture growth, we reconstructed the opening history of three opening-mode fractures that are bridged by crack-seal quartz cement in Travis Peak Sandstone of the SFOT-1 well, East Texas. Similar crack-seal cement bridges had been interpreted to form by repeated incremental fracture opening and subsequent precipitation of quartz cement. We imaged crack-seal cement textures for bridges sampled at varying distance from the tips using scanning electron microscope cathodoluminescence, and determined the number and thickness of crack-seal cement increments as a function of position along the fracture length and height. Observed trends in increment number and thickness are consistent with an initial stage of fast fracture propagation relative to aperture growth, followed by a stage of slow propagation and pronounced aperture growth. Consistent with fluid inclusion observations indicative of fracture opening and propagation occurring over 30-40 m.y., we interpret the second phase of pronounced aperture growth to result from fracture opening strain accommodated by solution-precipitation creep and concurrent slow, possibly subcritical, fracture propagation. Similar deformation mechanisms are envisioned to govern fracture growth over shorter timescales in reactive chemical subsurface environments including CO2 reservoirs, organic-rich shales, and geothermal systems.

Measurement of compartment elasticity using pressure related ultrasound: a method to identify patients with potential compartment syndrome.

PubMed

Sellei, R M; Hingmann, S J; Kobbe, P; Weber, C; Grice, J E; Zimmerman, F; Jeromin, S; Gansslen, A; Hildebrand, F; Pape, H C

2015-01-01

PURPOSE OF THE STUDY Decision-making in treatment of an acute compartment syndrome is based on clinical assessment, supported by invasive monitoring. Thus, evolving compartment syndrome may require repeated pressure measurements. In suspected cases of potential compartment syndromes clinical assessment alone seems to be unreliable. The objective of this study was to investigate the feasibility of a non-invasive application estimating whole compartmental elasticity by ultrasound, which may improve accuracy of diagnostics. MATERIAL AND METHODS In an in-vitro model, using an artificial container simulating dimensions of the human anterior tibial compartment, intracompartmental pressures (p) were raised subsequently up to 80 mm Hg by infusion of saline solution. The compartmental depth (mm) in the cross-section view was measured before and after manual probe compression (100 mm Hg) upon the surface resulting in a linear compartmental displacement (Δd). This was repeated at rising compartmental pressures. The resulting displacements were related to the corresponding intra-compartmental pressures simulated in our model. A hypothesized relationship between pressures related compartmental displacement and the elasticity at elevated compartment pressures was investigated. RESULTS With rising compartmental pressures, a non-linear, reciprocal proportional relation between the displacement (mm) and the intra-compartmental pressure (mm Hg) occurred. The Pearson's coefficient showed a high correlation (r2 = -0.960). The intraobserver reliability value kappa resulted in a statistically high reliability (κ = 0.840). The inter-observer value indicated a fair reliability (κ = 0.640). CONCLUSIONS Our model reveals that a strong correlation between compartmental strain displacements assessed by ultrasound and the intra-compartmental pressure changes occurs. Further studies are required to prove whether this assessment is transferable to human muscle tissue. Determining the complete compartmental elasticity by ultrasound enhancement, this application may improve detection of early signs of potential compartment syndrome. Key words: compartment syndrome, intra-compartmental pressure, non-invasive diagnostic, elasticity measurement, elastography.

Measurement of the viscoelastic compliance of the eustachian tube using a modified forced-response test.

PubMed

Ghadiali, Samir N; Federspiel, William J; Swarts, J Douglas; Doyle, William J

2002-01-01

Eustachian tube compliance (ETC) was suggested to be an important determinate of function. Previous attempts to quantify ETC used summary measures that are not clearly related to the physical properties of the system. Here, we present a new method for measuring ETC that conforms more closely to the engineering definition of compliance. The forced response test was modified to include oscillations in applied flow after the forced tubal opening. Pressure and flow were recorded during the standard and modified test in 12 anesthetized cynomolgus monkeys. The resulting pressure-flow, hysteresis loops were compared with those predicted by a simple fluid-structure model of the Eustachian tube with linear-elastic or viscoelastic properties. The tubal compliance index (TCI) and a viscoelastic compliance (C(v)) were calculated from these data for each monkey. The behavior of a viscoelastic, but not a linear elastic model accurately reproduced the experimental data for the monkey. The TCI and C(v) were linearly related, but the shared variance in these measures was only 63%. This new method for measuring ETC captures all information contained in the traditional TCI, but also provides information regarding the contribution of wall viscosity to Eustachian tube mechanics.

High Resolution, Large Deformation 3D Traction Force Microscopy

PubMed Central

López-Fagundo, Cristina; Reichner, Jonathan; Hoffman-Kim, Diane; Franck, Christian

2014-01-01

Traction Force Microscopy (TFM) is a powerful approach for quantifying cell-material interactions that over the last two decades has contributed significantly to our understanding of cellular mechanosensing and mechanotransduction. In addition, recent advances in three-dimensional (3D) imaging and traction force analysis (3D TFM) have highlighted the significance of the third dimension in influencing various cellular processes. Yet irrespective of dimensionality, almost all TFM approaches have relied on a linear elastic theory framework to calculate cell surface tractions. Here we present a new high resolution 3D TFM algorithm which utilizes a large deformation formulation to quantify cellular displacement fields with unprecedented resolution. The results feature some of the first experimental evidence that cells are indeed capable of exerting large material deformations, which require the formulation of a new theoretical TFM framework to accurately calculate the traction forces. Based on our previous 3D TFM technique, we reformulate our approach to accurately account for large material deformation and quantitatively contrast and compare both linear and large deformation frameworks as a function of the applied cell deformation. Particular attention is paid in estimating the accuracy penalty associated with utilizing a traditional linear elastic approach in the presence of large deformation gradients. PMID:24740435

Soft tissue strain measurement using an optical method

NASA Astrophysics Data System (ADS)

Toh, Siew Lok; Tay, Cho Jui; Goh, Cho Hong James

2008-11-01

Digital image correlation (DIC) is a non-contact optical technique that allows the full-field estimation of strains on a surface under an applied deformation. In this project, the application of an optimized DIC technique is applied, which can achieve efficiency and accuracy in the measurement of two-dimensional deformation fields in soft tissue. This technique relies on matching the random patterns recorded in images to directly obtain surface displacements and to get displacement gradients from which the strain field can be determined. Digital image correlation is a well developed technique that has numerous and varied engineering applications, including the application in soft and hard tissue biomechanics. Chicken drumstick ligaments were harvested and used during the experiments. The surface of the ligament was speckled with black paint to allow for correlation to be done. Results show that the stress-strain curve exhibits a bi-linear behavior i.e. a "toe region" and a "linear elastic region". The Young's modulus obtained for the toe region is about 92 MPa and the modulus for the linear elastic region is about 230 MPa. The results are within the values for mammalian anterior cruciate ligaments of 150-300 MPa.

Solving the Problem of Linear Viscoelasticity for Piecewise-Homogeneous Anisotropic Plates

NASA Astrophysics Data System (ADS)

Kaloerov, S. A.; Koshkin, A. A.

2017-11-01

An approximate method for solving the problem of linear viscoelasticity for thin anisotropic plates subject to transverse bending is proposed. The method of small parameter is used to reduce the problem to a sequence of boundary problems of applied theory of bending of plates solved using complex potentials. The general form of complex potentials in approximations and the boundary conditions for determining them are obtained. Problems for a plate with elliptic elastic inclusions are solved as an example. The numerical results for a plate with one, two elliptical (circular), and linear inclusions are analyzed.

Stability analysis of nanoscale surface patterns in stressed solids

NASA Astrophysics Data System (ADS)

Kostyrko, Sergey A.; Shuvalov, Gleb M.

2018-05-01

Here, we use the theory of surface elasticity to extend the morphological instability analysis of stressed solids developed in the works of Asaro, Tiller, Grinfeld, Srolovitz and many others. Within the framework of Gurtin-Murdoch model, the surface phase is assumed to be a negligibly thin layer with the elastic properties which differ from those of the bulk material. We consider the mass transport mechanism driven by the variation of surface and bulk energy along undulated surface of stressed solid. The linearized surface evolution equation is derived in the case of plane strain conditions and describes the amplitude change of surface perturbations with time. A parametric analysis of this equation leads to the definition of critical conditions which depend on undulation wavelength, residual surface stress, applied loading, surface and bulk elastic constants and predict the surface morphological stability.

Effect of hydrostatic pressure on physical properties of strontium based fluoroperovskites for novel applications

NASA Astrophysics Data System (ADS)

Erum, Nazia; Azhar Iqbal, Muhammad

2018-02-01

Density functional theory (DFT) is employed to calculate the effect of pressure variation on electronic structure, elastic parameters, mechanical durability, and thermodynamic aspects of SrRbF3, in combination with Quasi-harmonic Debye model. The pressure effects are determined in the range of 0-25 GPa, in which cubic stability of SrRbF3 fluoroperovskite remains valid. Significant influence of compression on wide range of elastic parameters and related mechanical properties have been discussed, to utilize this material in low birefringence lens fabrication technology. Apart of linear dependence on elastic coefficients, transition from brittle to ductile behavior is also observed at elevated pressure ranges. Moreover, successful prediction of important thermodynamic aspects such as volume expansion coefficient (α), Debye temperature (θ D), heat capacities (Cp and Cv) are also done within wide pressure and temperature ranges.

Interface crack in a nonhomogeneous elastic medium

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1988-01-01

The linear elasticity problem for an interface crack between two bonded half planes is reconsidered. It is assumed that one of the half planes is homogeneous and the second is nonhomogeneous in such a way that the elastic properties are continuous throughout the plane and have discontinuous derivatives along the interface. The problem is formulated in terms of a system of integral equations and the asymptotic behavior of the stress state near the crack tip is determined. The results lead to the conclusion that the singular behavior of stresses in the nonhomogeneous medium is identical to that in a homogeneous material provided the spacial distribution of material properties is continuous near and at the crack tip. The problem is solved for various values of the nonhomogeneity parameter and for four different sets of crack surface tractions, and the corresponding stress intensity factors are tabulated.

Preliminary investigation of crack arrest in composite laminates containing buffer strips

NASA Technical Reports Server (NTRS)

Goree, J. G.

1978-01-01

The mechanical properties of some hybrid buffer strip laminates and the crack arrest potential of laminates containing buffer strips were determined. The hybrid laminates consisted of graphite with either S-glass, E-glass, or Kevlar. Unnotched tensile coupons and center-cracked fracture coupons were tested. Elastic properties, complete stress/strain curves, and critical stress intensity values are given. The measured elastic properties compare well with those calculated by classical lamination theory for laminates with linear stress/strain behavior. The glass hybrids had more delamination and higher fracture toughness than the all-graphite or the Kevlar hybrid.

Application of a transonic potential flow code to the static aeroelastic analysis of three-dimensional wings

NASA Technical Reports Server (NTRS)

Whitlow, W., Jr.; Bennett, R. M.

1982-01-01

Since the aerodynamic theory is nonlinear, the method requires the coupling of two iterative processes - an aerodynamic analysis and a structural analysis. A full potential analysis code, FLO22, is combined with a linear structural analysis to yield aerodynamic load distributions on and deflections of elastic wings. This method was used to analyze an aeroelastically-scaled wind tunnel model of a proposed executive-jet transport wing and an aeroelastic research wing. The results are compared with the corresponding rigid-wing analyses, and some effects of elasticity on the aerodynamic loading are noted.

Dust coagulation in ISM

NASA Technical Reports Server (NTRS)

Chokshi, Arati; Tielens, Alexander G. G. M.; Hollenbach, David

1989-01-01

Coagulation is an important mechanism in the growth of interstellar and interplanetary dust particles. The microphysics of the coagulation process was theoretically analyzed as a function of the physical properties of the coagulating grains, i.e., their size, relative velocities, temperature, elastic properties, and the van der Waal interaction. Numerical calculations of collisions between linear chains provide the wave energy in individual particles and the spectrum of the mechanical vibrations set up in colliding particles. Sticking probabilities are then calculated using simple estimates for elastic deformation energies and for the attenuation of the wave energy due to absorption and scattering processes.

A Textile-Based Wearable Sensing Device Designed for Monitoring the Flexion Angle of Elbow and Knee Movements

PubMed Central

Shyr, Tien-Wei; Shie, Jing-Wen; Jiang, Chang-Han; Li, Jung-Jen

2014-01-01

In this work a wearable gesture sensing device consisting of a textile strain sensor, using elastic conductive webbing, was designed for monitoring the flexion angle of elbow and knee movements. The elastic conductive webbing shows a linear response of resistance to the flexion angle. The wearable gesture sensing device was calibrated and then the flexion angle-resistance equation was established using an assembled gesture sensing apparatus with a variable resistor and a protractor. The proposed device successfully monitored the flexion angle during elbow and knee movements. PMID:24577526

Ab-initio study of B{sub 2}-type technetium AB (A=Tc, B=Nb and Ta) intermetallic compounds

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

Acharya, Nikita, E-mail: acharyaniks30@gmail.com; Fatima, Bushra; Sanyal, Sankar P.

2016-05-06

The structural, electronic and elastic properties of AB type (A = Tc, B = Nb and Ta) technetium intermetallic compounds are studied using full potential linearized plane wave (FP-LAPW) method within generalized gradient approximation (GGA). The calculated lattice parameters agree well with the experimental results. The elastic constants obey the stability criteria for cubic system. Ductility for these compounds has been analyzed using the Pugh’s rule and Cauchy’s pressure and found that all the compounds are ductile in nature. Bonding nature is discussed in terms of Fermi surface and band structures.

Rock elastic properties and near-surface structure at Taurus-Littrow. [strain measurement of lunar basalt and breccia

NASA Technical Reports Server (NTRS)

Trice, R.; Warren, N.; Anderson, O. L.

1974-01-01

Linear strain measurements are presented for two lunar basalts, 14310,82 and 71055,15 and one breccia, 15498,23 to 5 kb hydrostatic pressure. Compressional and shear acoustic velocities to 5 kb are also presented for the basalts, 14310,82 and 71055,15. These elastic properties, along with geological, seismological and rock mechanics considerations are consistent with a model of the structure of the Taurus-Littrow valley as follows, a thin surface regolith overlying a fractured mixture of basalt flows and ejecta material which in turn overlies a coherent breccia of highland ejecta debris.

Crack growth in bonded elastic half planes

NASA Technical Reports Server (NTRS)

Goree, J. G.

1975-01-01

Two solutions were developed for the two dimensional problem of bonded linearly elastic half-planes. For each solution, numerical results are presented for the stress intensity factors, strain energy release rate, stresses, and displacements. The behavior predicted by the studies was investigated experimentally using polymers for the material pairs. Close agreement was found for the critical stress intensity factor at fracture for the perpendicular crack near the interface. Fracture along the interface proved to be inconclusive due to difficulties in obtaining a brittle bond. Some interesting and predictable behavior regarding the potential for the crack to cross the interface was observed and is discussed.

Flexible polyurethane foam modelling and identification of viscoelastic parameters for automotive seating applications

NASA Astrophysics Data System (ADS)

Deng, R.; Davies, P.; Bajaj, A. K.

2003-05-01

A hereditary model and a fractional derivative model for the dynamic properties of flexible polyurethane foams used in automotive seat cushions are presented. Non-linear elastic and linear viscoelastic properties are incorporated into these two models. A polynomial function of compression is used to represent the non-linear elastic behavior. The viscoelastic property is modelled by a hereditary integral with a relaxation kernel consisting of two exponential terms in the hereditary model and by a fractional derivative term in the fractional derivative model. The foam is used as the only viscoelastic component in a foam-mass system undergoing uniaxial compression. One-term harmonic balance solutions are developed to approximate the steady state response of the foam-mass system to the harmonic base excitation. System identification procedures based on the direct non-linear optimization and a sub-optimal method are formulated to estimate the material parameters. The effects of the choice of the cost function, frequency resolution of data and imperfections in experiments are discussed. The system identification procedures are also applied to experimental data from a foam-mass system. The performances of the two models for data at different compression and input excitation levels are compared, and modifications to the structure of the fractional derivative model are briefly explored. The role of the viscous damping term in both types of model is discussed.

Transient Non Lin Deformation in Fractured Rock

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

Sartori, Enrico

1998-10-14

MATLOC is a nonlinear, transient, two-dimensional (planer and axisymmetric), thermal stress, finite-element code designed to determine the deformation within a fractured rock mass. The mass is modeled as a nonlinear anistropic elastic material which can exhibit stress-dependent bi-linear locking behavior.

Temperature and Pressure Dependences of the Elastic Properties of Tantalum Single Crystals Under <100> Tensile Loading: A Molecular Dynamics Study

NASA Astrophysics Data System (ADS)

Li, Wei-bing; Li, Kang; Fan, Kan-qi; Zhang, Da-xing; Wang, Wei-dong

2018-04-01

Atomistic simulations are capable of providing insights into physical mechanisms responsible for mechanical properties of the transition metal of Tantalum (Ta). By using molecular dynamics (MD) method, temperature and pressure dependences of the elastic properties of Ta single crystals are investigated through <100> tensile loading. First of all, a comparative study between two types of embedded-atom method (EAM) potentials is made in term of the elastic properties of Ta single crystals. The results show that Ravelo-EAM (Physical Review B, 2013, 88: 134101) potential behaves well at different hydrostatic pressures. Then, the MD simulation results based on the Ravelo-EAM potential show that Ta will experience a body-centered-cubic (BCC) to face-centered-cubic (FCC) phase transition before fracture under <100> tensile loading at 1 K temperature, and model size and strain rate have no obvious effects on tensile behaviors of Ta. Next, from the simulation results at the system temperature from 1 to 1500 K, it can be derived that the elastic modulus of E 100 linearly decrease with the increasing temperature, while the yielding stress decrease with conforming a quadratic polynomial formula. Finally, the pressure dependence of the elastic properties is performed from 0 to 140 GPa and the observations show that the elastic modulus increases with the increasing pressure overall.

Temperature and Pressure Dependences of the Elastic Properties of Tantalum Single Crystals Under <100> Tensile Loading: A Molecular Dynamics Study.

PubMed

Li, Wei-Bing; Li, Kang; Fan, Kang-Qi; Zhang, Da-Xing; Wang, Wei-Dong

2018-04-24

Atomistic simulations are capable of providing insights into physical mechanisms responsible for mechanical properties of the transition metal of Tantalum (Ta). By using molecular dynamics (MD) method, temperature and pressure dependences of the elastic properties of Ta single crystals are investigated through <100> tensile loading. First of all, a comparative study between two types of embedded-atom method (EAM) potentials is made in term of the elastic properties of Ta single crystals. The results show that Ravelo-EAM (Physical Review B, 2013, 88: 134101) potential behaves well at different hydrostatic pressures. Then, the MD simulation results based on the Ravelo-EAM potential show that Ta will experience a body-centered-cubic (BCC) to face-centered-cubic (FCC) phase transition before fracture under <100> tensile loading at 1 K temperature, and model size and strain rate have no obvious effects on tensile behaviors of Ta. Next, from the simulation results at the system temperature from 1 to 1500 K, it can be derived that the elastic modulus of E 100 linearly decrease with the increasing temperature, while the yielding stress decrease with conforming a quadratic polynomial formula. Finally, the pressure dependence of the elastic properties is performed from 0 to 140 GPa and the observations show that the elastic modulus increases with the increasing pressure overall.

Quantitative Estimation of Seismic Velocity Changes Using Time-Lapse Seismic Data and Elastic-Wave Sensitivity Approach

NASA Astrophysics Data System (ADS)

Denli, H.; Huang, L.

2008-12-01

Quantitative monitoring of reservoir property changes is essential for safe geologic carbon sequestration. Time-lapse seismic surveys have the potential to effectively monitor fluid migration in the reservoir that causes geophysical property changes such as density, and P- and S-wave velocities. We introduce a novel method for quantitative estimation of seismic velocity changes using time-lapse seismic data. The method employs elastic sensitivity wavefields, which are the derivatives of elastic wavefield with respect to density, P- and S-wave velocities of a target region. We derive the elastic sensitivity equations from analytical differentiations of the elastic-wave equations with respect to seismic-wave velocities. The sensitivity equations are coupled with the wave equations in a way that elastic waves arriving in a target reservoir behave as a secondary source to sensitivity fields. We use a staggered-grid finite-difference scheme with perfectly-matched layers absorbing boundary conditions to simultaneously solve the elastic-wave equations and the elastic sensitivity equations. By elastic-wave sensitivities, a linear relationship between relative seismic velocity changes in the reservoir and time-lapse seismic data at receiver locations can be derived, which leads to an over-determined system of equations. We solve this system of equations using a least- square method for each receiver to obtain P- and S-wave velocity changes. We validate the method using both surface and VSP synthetic time-lapse seismic data for a multi-layered model and the elastic Marmousi model. Then we apply it to the time-lapse field VSP data acquired at the Aneth oil field in Utah. A total of 10.5K tons of CO2 was injected into the oil reservoir between the two VSP surveys for enhanced oil recovery. The synthetic and field data studies show that our new method can quantitatively estimate changes in seismic velocities within a reservoir due to CO2 injection/migration.

The hybrid mass-spring pendulum model of human leg swinging: stiffness in the control of cycle period.

PubMed

Obusek, J P; Holt, K G; Rosenstein, R M

1995-07-01

Human leg swinging is modeled as the harmonic motion of a hybrid mass-spring pendulum. The cycle period is determined by a gravitational component and an elastic component, which is provided by the attachment of a soft-tissue/muscular spring of variable stiffness. To confirm that the stiffness of the spring changes with alterations in the inertial properties of the oscillator and that stiffness is relevant for the control of cycle period, we conducted this study in which the simple pendulum equivalent length was experimentally manipulated by adding mass to the ankle of a comfortably swinging leg. Twenty-four young, healthy adults were videotaped as they swung their right leg under four conditions: no added mass and with masses of 2.27, 4.55, and 6.82kg added to the ankle. Strong, linear relationships between the acceleration and displacement of the swinging leg within subjects and conditions were found, confirming the motion's harmonic nature. Cycle period significantly increased with the added mass. However, the observed increases were not as large as would be predicted by the induced changes in the gravitational component alone. These differences were interpreted as being due to increases in the active muscular stiffness. Significant linear increases in the elastic component (and hence stiffness) were demonstrated with increases in the simple pendulum equivalent length in 20 of the individual subjects, with r2 values ranging between 0.89 and 0.99. Significant linear relationships were also demonstrated between the elastic and gravitational components in 22 subjects, with individual r2 values between 0.90 and 0.99.(ABSTRACT TRUNCATED AT 250 WORDS)

Static response of coated microbubbles compressed between rigid plates: Simulations and asymptotic analysis including elastic and adhesive forces

NASA Astrophysics Data System (ADS)

Lytra, A.; Pelekasis, N.

2018-03-01

The static response of coated microbubbles is investigated with a novel approach employed for modeling contact between a microbubble and the cantilever of an atomic force microscope. Elastic tensions and moments are described via appropriate constitutive laws. The encapsulated gas is assumed to undergo isothermal variations. Due to the hydrophilic nature of the cantilever, an ultrathin aqueous film is formed, which transfers the force onto the shell. An interaction potential describes the local pressure applied on the shell. The problem is solved in axisymmetric form with the finite element method. The response is governed by the dimensionless bending, k^ b=kb/(χ R02 ), pressure, P^ A=(PAR0 )/χ , and interaction potential, W ^ =w0/χ . Hard polymeric shells have negligible resistance to gas compression, while for the softer lipid shells gas compressibility is comparable with shell elasticity. As the external force increases, numerical simulations reveal that the force versus deformation (f vs d) curve of polymeric shells exhibits a transition from the linear O(d) (Reissner) regime, marked by flattened shapes around the contact region, to a non-linear O(d1/2) (Pogorelov) regime dominated by shapes exhibiting crater formation due to buckling. When lipid shells are tested, buckling is bypassed as the external force increases and flattened shapes prevail in an initially linear f vs d curve. Transition to a curved upwards regime is observed as the force increases, where gas compression and area dilatation form the dominant balance providing a nonlinear regime with an O(d3) dependence. Asymptotic analysis recovers the above patterns and facilitates estimation of the shell mechanical properties.

Slip accumulation and lateral propagation of active normal faults in Afar

NASA Astrophysics Data System (ADS)

Manighetti, I.; King, G. C. P.; Gaudemer, Y.; Scholz, C. H.; Doubre, C.

2001-01-01

We investigate fault growth in Afar, where normal fault systems are known to be currently growing fast and most are propagating to the northwest. Using digital elevation models, we have examined the cumulative slip distribution along 255 faults with lengths ranging from 0.3 to 60 km. Faults exhibiting the elliptical or "bell-shaped" slip profiles predicted by simple linear elastic fracture mechanics or elastic-plastic theories are rare. Most slip profiles are roughly linear for more than half of their length, with overall slopes always <0.035. For the dominant population of NW striking faults and fault systems longer than 2 km, the slip profiles are asymmetric, with slip being maximum near the eastern ends of the profiles where it drops abruptly to zero, whereas slip decreases roughly linearly and tapers in the direction of overall Aden rift propagation. At a more detailed level, most faults appear to be composed of distinct, shorter subfaults or segments, whose slip profiles, while different from one to the next, combine to produce the roughly linear overall slip decrease along the entire fault. On a larger scale, faults cluster into kinematically coupled systems, along which the slip on any scale individual fault or fault system complements that of its neighbors, so that the total slip of the whole system is roughly linearly related to its length, with an average slope again <0.035. We discuss the origin of these quasilinear, asymmetric profiles in terms of "initiation points" where slip starts, and "barriers" where fault propagation is arrested. In the absence of a barrier, slip apparently extends with a roughly linear profile, tapered in the direction of fault propagation.

Internal strain estimation for quantification of human heel pad elastic modulus: A phantom study.

PubMed

Holst, Karen; Liebgott, Hervé; Wilhjelm, Jens E; Nikolov, Svetoslav; Torp-Pedersen, Søren T; Delachartre, Philippe; Jensen, Jørgen A

2013-02-01

Shock absorption is the most important function of the human heel pad. However, changes in heel pad elasticity, as seen in e.g. long-distance runners, diabetes patients, and victims of Falanga torture are affecting this function, often in a painful manner. Assessment of heel pad elasticity is usually based on one or a few strain measurements obtained by an external load-deformation system. The aim of this study was to develop a technique for quantitative measurements of heel pad elastic modulus based on several internal strain measures from within the heel pad by use of ultrasound images. Nine heel phantoms were manufactured featuring a combination of three heel pad stiffnesses and three heel pad thicknesses to model the normal human variation. Each phantom was tested in an indentation system comprising a 7MHz linear array ultrasound transducer, working as the indentor, and a connected load cell. Load-compression data and ultrasound B-mode images were simultaneously acquired in 19 compression steps of 0.1mm each. The internal tissue displacement was for each step calculated by a phase-based cross-correlation technique and internal strain maps were derived from these displacement maps. Elastic moduli were found from the resulting stress-strain curves. The elastic moduli made it possible to distinguish eight of nine phantoms from each other according to the manufactured stiffness and showed very little dependence of the thickness. Mean elastic moduli for the three soft, the three medium, and the three hard phantoms were 89kPa, 153kPa, and 168kPa, respectively. The combination of ultrasound images and force measurements provided an effective way of assessing the elastic properties of the heel pad due to the internal strain estimation. Copyright © 2012 Elsevier B.V. All rights reserved.

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.

Charge-regularized swelling kinetics of polyelectrolyte gels: Elasticity and diffusion

NASA Astrophysics Data System (ADS)

Sen, Swati; Kundagrami, Arindam

2017-11-01

We apply a recently developed method [S. Sen and A. Kundagrami, J. Chem. Phys. 143, 224904 (2015)], using a phenomenological expression of osmotic stress, as a function of polymer and charge densities, hydrophobicity, and network elasticity for the swelling of spherical polyelectrolyte (PE) gels with fixed and variable charges in a salt-free solvent. This expression of stress is used in the equation of motion of swelling kinetics of spherical PE gels to numerically calculate the spatial profiles for the polymer and free ion densities at different time steps and the time evolution of the size of the gel. We compare the profiles of the same variables obtained from the classical linear theory of elasticity and quantitatively estimate the bulk modulus of the PE gel. Further, we obtain an analytical expression of the elastic modulus from the linearized expression of stress (in the small deformation limit). We find that the estimated bulk modulus of the PE gel decreases with the increase of its effective charge for a fixed degree of deformation during swelling. Finally, we match the gel-front locations with the experimental data, taken from the measurements of charged reversible addition-fragmentation chain transfer gels to show an increase in gel-size with charge and also match the same for PNIPAM (uncharged) and imidazolium-based (charged) minigels, which specifically confirms the decrease of the gel modulus value with the increase of the charge. The agreement between experimental and theoretical results confirms general diffusive behaviour for swelling of PE gels with a decreasing bulk modulus with increasing degree of ionization (charge). The new formalism captures large deformations as well with a significant variation of charge content of the gel. It is found that PE gels with large deformation but same initial size swell faster with a higher charge.

Effect of pressure variation on structural, elastic, mechanical, optoelectronic and thermodynamic properties of SrNaF3 fluoroperovskite

NASA Astrophysics Data System (ADS)

Erum, Nazia; Azhar Iqbal, Muhammad

2017-12-01

The effect of pressure variation on structural, electronic, elastic, mechanical, optical and thermodynamic characteristics of cubic SrNaF3 fluoroperovskite have been investigated by employing first-principles method within the framework of gradient approximation (GGA). For the total energy calculations, we have used the full-potential linearized augmented plane wave (FP-LAPW) method. Thermodynamic properties are computed in terms of quasi-harmonic Debye model. The pressure effects are determined in the range of 0-25 GPa, in which mechanical stability of SrNaF3 fluoroperovskite remains valid. A prominent decrease in lattice constant and bonds length is observed with the increase in pressure from 0 to 25 GPa. The effect of increase in pressure on band structure calculations with GGA and GGA plus Tran-Blaha modified Becke-Johnson (TB-mBJ) potential reveals a predominant characteristic associated with widening of bandgap. The influence of pressure on set of isotropic elastic parameters and their related properties are numerically estimated for SrNaF3 polycrystalline aggregate. Apart of linear dependence of elastic coefficients, transition from brittle to ductile behavior is observed as pressure is increased from 0 to 25 GPa. We have successfully obtained variation of lattice constant, volume expansion, bulk modulus, Debye temperature and specific heat capacities with pressure and temperature in the range of 0-25 GPa and 0-600 K. All the calculated optical properties such as the complex dielectric function ɛ(ω), optical conductivity σ(ω), energy loss function L(ω), absorption coefficient α(w), refractive index n(ω), reflectivity R(ω), and effective number of electrons n eff, via sum rules shift towards the higher energies under the application of pressure.

The Role of Network Architecture in Collagen Mechanics.

PubMed

Jansen, Karin A; Licup, Albert J; Sharma, Abhinav; Rens, Robbie; MacKintosh, Fred C; Koenderink, Gijsje H

2018-06-05

Collagen forms fibrous networks that reinforce tissues and provide an extracellular matrix for cells. These networks exhibit remarkable strain-stiffening properties that tailor the mechanical functions of tissues and regulate cell behavior. Recent models explain this nonlinear behavior as an intrinsic feature of disordered networks of stiff fibers. Here, we experimentally validate this theoretical framework by measuring the elastic properties of collagen networks over a wide range of self-assembly conditions. We show that the model allows us to quantitatively relate both the linear and nonlinear elastic behavior of collagen networks to their underlying architecture. Specifically, we identify the local coordination number (or connectivity) 〈z〉 as a key architectural parameter that governs the elastic response of collagen. The network elastic response reveals that 〈z〉 decreases from 3.5 to 3 as the polymerization temperature is raised from 26 to 37°C while being weakly dependent on concentration. We furthermore infer a Young's modulus of 1.1 MPa for the collagen fibrils from the linear modulus. Scanning electron microscopy confirms that 〈z〉 is between three and four but is unable to detect the subtle changes in 〈z〉 with polymerization conditions that rheology is sensitive to. Finally, we show that, consistent with the model, the initial stress-stiffening response of collagen networks is controlled by the negative normal stress that builds up under shear. Our work provides a predictive framework to facilitate future studies of the regulatory effect of extracellular matrix molecules on collagen mechanics. Moreover, our findings can aid mechanobiological studies of wound healing, fibrosis, and cancer metastasis, which require collagen matrices with tunable mechanical properties. Copyright © 2018 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Experimental and numerical study on frost heave of saturated rock under uniform freezing conditions

NASA Astrophysics Data System (ADS)

Lv, Zhitao; Xia, Caichu; Li, Qiang

2018-04-01

A series of freezing experiments are conducted on saturated sandstone and mortar specimens to investigate the frost heave of saturated rock under uniform freezing conditions. The experimental results show that the frost heave of saturated rock is isotropic under uniform freezing conditions. During the freezing process, three stages are observed in the curves of variation of total frost heaving strain versus time: the thermal contraction stage, the frost heaving stage and the steady stage. Moreover, the amount of final stable frost heave first increases and then decreases with decrease in freezing temperature, and the maximum final stable frost heave occurs at different freezing temperature in saturated sandstone and mortar. Furthermore, a coupled thermal-mechanical (TM) model of frost heave of saturated rock is proposed in which a constraint coefficient \\zeta is used to consider the susceptibility of the internal rock grain structure to the expansion of pore ice. Then, numerical simulations are implemented with COMSOL to solve the governing equations of the TM model. Comparisons of the numerical results with the experimental results are performed to demonstrate the reliability of the model. The influences of elastic modulus and porosity on frost heave are also investigated, and the results show that the total frost heaving strain decreases non-linearly with increasing elastic modulus, and the decrease is significant when the elastic modulus is less than 3000 MPa, or approximately five times the elastic modulus of ice. In addition, the total frost heaving strain increases linearly with increasing porosity. Finally, an empirical equation between total frost heaving strain and freezing temperature is proposed and the equation well describes the variation of total frost heaving strain with freezing temperature.

Certification of a hybrid parameter model of the fully flexible Shuttle Remote Manipulator System

NASA Technical Reports Server (NTRS)

Barhorst, Alan A.

1995-01-01

The development of high fidelity models of mechanical systems with flexible components is in flux. Many working models of these devices assume the elastic motion is small and can be superimposed on the overall rigid body motion. A drawback associated with this type of modeling technique is that it is required to regenerate the linear modal model of the device if the elastic motion is sufficiently far from the base rigid motion. An advantage to this type of modeling is that it uses NASTRAN modal data which is the NASA standard means of modal information exchange. A disadvantage to the linear modeling is that it fails to accurately represent large motion of the system, unless constant modal updates are performed. In this study, which is a continuation of a project started last year, the drawback of the currently used modal snapshot modeling technique is addressed in a rigorous fashion by novel and easily applied means.

Fluid-structure interaction of turbulent boundary layer over a compliant surface

NASA Astrophysics Data System (ADS)

Anantharamu, Sreevatsa; Mahesh, Krishnan

2016-11-01

Turbulent flows induce unsteady loads on surfaces in contact with them, which affect material stresses, surface vibrations and far-field acoustics. We are developing a numerical methodology to study the coupled interaction of a turbulent boundary layer with the underlying surface. The surface is modeled as a linear elastic solid, while the fluid follows the spatially filtered incompressible Navier-Stokes equations. An incompressible Large Eddy Simulation finite volume flow approach based on the algorithm of Mahesh et al. is used in the fluid domain. The discrete kinetic energy conserving property of the method ensures robustness at high Reynolds number. The linear elastic model in the solid domain is integrated in space using finite element method and in time using the Newmark time integration method. The fluid and solid domain solvers are coupled using both weak and strong coupling methods. Details of the algorithm, validation, and relevant results will be presented. This work is supported by NSWCCD, ONR.

Transport properties of elastically coupled fractional Brownian motors

NASA Astrophysics Data System (ADS)

Lv, Wangyong; Wang, Huiqi; Lin, Lifeng; Wang, Fei; Zhong, Suchuan

2015-11-01

Under the background of anomalous diffusion, which is characterized by the sub-linear or super-linear mean-square displacement in time, we proposed the coupled fractional Brownian motors, in which the asymmetrical periodic potential as ratchet is coupled mutually with elastic springs, and the driving source is the external harmonic force and internal thermal fluctuations. The transport mechanism of coupled particles in the overdamped limit is investigated as the function of the temperature of baths, coupling constant and natural length of the spring, the amplitude and frequency of driving force, and the asymmetry of ratchet potential by numerical stimulations. The results indicate that the damping force involving the information of historical velocity leads to the nonlocal memory property and blocks the traditional dissipative motion behaviors, and it even plays a cooperative role of driving force in drift motion of the coupled particles. Thus, we observe various non-monotonic resonance-like behaviors of collective directed transport in the mediums with different diffusion exponents.

Demand for prescription drugs under non-linear pricing in Medicare Part D.

PubMed

Jung, Kyoungrae; Feldman, Roger; McBean, A Marshall

2014-03-01

We estimate the price elasticity of prescription drug use in Medicare Part D, which features a non-linear price schedule due to a coverage gap. We analyze patterns of drug utilization prior to the coverage gap, where the "effective price" is higher than the actual copayment for drugs because consumers anticipate that more spending will make them more likely to reach the gap. We find that enrollees' total pre-gap drug spending is sensitive to their effective prices: the estimated price elasticity of drug spending ranges between [Formula: see text]0.14 and [Formula: see text]0.36. This finding suggests that filling in the coverage gap, as mandated by the health care reform legislation passed in 2010, will influence drug utilization prior to the gap. A simulation analysis indicates that closing the gap could increase Part D spending by a larger amount than projected, with additional pre-gap costs among those who do not hit the gap.

Active control of panel vibrations induced by boundary-layer flow

NASA Technical Reports Server (NTRS)

Chow, Pao-Liu

1991-01-01

Some problems in active control of panel vibration excited by a boundary layer flow over a flat plate are studied. In the first phase of the study, the optimal control problem of vibrating elastic panel induced by a fluid dynamical loading was studied. For a simply supported rectangular plate, the vibration control problem can be analyzed by a modal analysis. The control objective is to minimize the total cost functional, which is the sum of a vibrational energy and the control cost. By means of the modal expansion, the dynamical equation for the plate and the cost functional are reduced to a system of ordinary differential equations and the cost functions for the modes. For the linear elastic plate, the modes become uncoupled. The control of each modal amplitude reduces to the so-called linear regulator problem in control theory. Such problems can then be solved by the method of adjoint state. The optimality system of equations was solved numerically by a shooting method. The results are summarized.

Inverse dynamics of a 3 degree of freedom spatial flexible manipulator

NASA Technical Reports Server (NTRS)

Bayo, Eduardo; Serna, M.

1989-01-01

A technique is presented for solving the inverse dynamics and kinematics of 3 degree of freedom spatial flexible manipulator. The proposed method finds the joint torques necessary to produce a specified end effector motion. Since the inverse dynamic problem in elastic manipulators is closely coupled to the inverse kinematic problem, the solution of the first also renders the displacements and rotations at any point of the manipulator, including the joints. Furthermore the formulation is complete in the sense that it includes all the nonlinear terms due to the large rotation of the links. The Timoshenko beam theory is used to model the elastic characteristics, and the resulting equations of motion are discretized using the finite element method. An iterative solution scheme is proposed that relies on local linearization of the problem. The solution of each linearization is carried out in the frequency domain. The performance and capabilities of this technique are tested through simulation analysis. Results show the potential use of this method for the smooth motion control of space telerobots.

Elastic properties of graphene: A pseudo-beam model with modified internal bending moment and its application

NASA Astrophysics Data System (ADS)

Xia, Z. M.; Wang, C. G.; Tan, H. F.

2018-04-01

A pseudo-beam model with modified internal bending moment is presented to predict elastic properties of graphene, including the Young's modulus and Poisson's ratio. In order to overcome a drawback in existing molecular structural mechanics models, which only account for pure bending (constant bending moment), the presented model accounts for linear bending moments deduced from the balance equations. Based on this pseudo-beam model, an analytical prediction is accomplished to predict the Young's modulus and Poisson's ratio of graphene based on the equation of the strain energies by using Castigliano second theorem. Then, the elastic properties of graphene are calculated compared with results available in literature, which verifies the feasibility of the pseudo-beam model. Finally, the pseudo-beam model is utilized to study the twisting wrinkling characteristics of annular graphene. Due to modifications of the internal bending moment, the wrinkling behaviors of graphene sheet are predicted accurately. The obtained results show that the pseudo-beam model has a good ability to predict the elastic properties of graphene accurately, especially the out-of-plane deformation behavior.

Flexible multibody simulation of automotive systems with non-modal model reduction techniques

NASA Astrophysics Data System (ADS)

Shiiba, Taichi; Fehr, Jörg; Eberhard, Peter

2012-12-01

The stiffness of the body structure of an automobile has a strong relationship with its noise, vibration, and harshness (NVH) characteristics. In this paper, the effect of the stiffness of the body structure upon ride quality is discussed with flexible multibody dynamics. In flexible multibody simulation, the local elastic deformation of the vehicle has been described traditionally with modal shape functions. Recently, linear model reduction techniques from system dynamics and mathematics came into the focus to find more sophisticated elastic shape functions. In this work, the NVH-relevant states of a racing kart are simulated, whereas the elastic shape functions are calculated with modern model reduction techniques like moment matching by projection on Krylov-subspaces, singular value decomposition-based reduction techniques, and combinations of those. The whole elastic multibody vehicle model consisting of tyres, steering, axle, etc. is considered, and an excitation with a vibration characteristics in a wide frequency range is evaluated in this paper. The accuracy and the calculation performance of those modern model reduction techniques is investigated including a comparison of the modal reduction approach.

Approximate nonlinear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-07-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-wave scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform. After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic nonlinear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P- and S-wave information.

Inelastic effects in molecular transport junctions: The probe technique at high bias

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

Kilgour, Michael; Segal, Dvira, E-mail: dsegal@chem.utoronto.ca

2016-03-28

We extend the Landauer-Büttiker probe formalism for conductances to the high bias regime and study the effects of environmentally induced elastic and inelastic scattering on charge current in single molecule junctions, focusing on high-bias effects. The probe technique phenomenologically incorporates incoherent elastic and inelastic effects to the fully coherent case, mimicking a rich physical environment at trivial cost. We further identify environmentally induced mechanisms which generate an asymmetry in the current, manifested as a weak diode behavior. This rectifying behavior, found in two types of molecular junction models, is absent in the coherent-elastic limit and is only active in themore » case with incoherent-inelastic scattering. Our work illustrates that in the low bias-linear response regime, the commonly used “dephasing probe” (mimicking only elastic decoherence effects) operates nearly indistinguishably from a “voltage probe” (admitting inelastic-dissipative effects). However, these probes realize fundamentally distinct I-V characteristics at high biases, reflecting the central roles of dissipation and inelastic scattering processes on molecular electronic transport far-from-equilibrium.« less

Non-linear optical measurement of the twist elastic constant in thermotropic and DNA lyotropic chiral nematics.

PubMed

Lucchetti, Liana; Fraccia, Tommaso P; Ciciulla, Fabrizio; Bellini, Tommaso

2017-07-10

Throughout the whole history of liquid crystals science, the balancing of intrinsic elasticity with coupling to external forces has been the key strategy for most application and investigation. While the coupling of the optical field to the nematic director is at the base of a wealth of thoroughly described optical effects, a significant variety of geometries and materials have not been considered yet. Here we show that by adopting a simple cell geometry and measuring the optically induced birefringence, we can readily extract the twist elastic coefficient K 22 of thermotropic and lyotropic chiral nematics (N*). The value of K 22 we obtain for chiral doped 5CB thermotropic N* well matches those reported in the literature. With this same strategy, we could determine for the first time K 22 of the N* phase of concentrated aqueous solutions of DNA oligomers, bypassing the limitations that so far prevented measuring the elastic constants of this class of liquid crystalline materials. The present study also enlightens the significant nonlinear optical response of DNA liquid crystals.

Nanoindentation studies of full and empty viral capsids and the effects of capsid protein mutations on elasticity and strength

PubMed Central

Michel, J. P.; Ivanovska, I. L.; Gibbons, M. M.; Klug, W. S.; Knobler, C. M.; Wuite, G. J. L.; Schmidt, C. F.

2006-01-01

The elastic properties of capsids of the cowpea chlorotic mottle virus have been examined at pH 4.8 by nanoindentation measurements with an atomic force microscope. Studies have been carried out on WT capsids, both empty and containing the RNA genome, and on full capsids of a salt-stable mutant and empty capsids of the subE mutant. Full capsids resisted indentation more than empty capsids, but all of the capsids were highly elastic. There was an initial reversible linear regime that persisted up to indentations varying between 20% and 30% of the diameter and applied forces of 0.6–1.0 nN; it was followed by a steep drop in force that is associated with irreversible deformation. A single point mutation in the capsid protein increased the capsid stiffness. The experiments are compared with calculations by finite element analysis of the deformation of a homogeneous elastic thick shell. These calculations capture the features of the reversible indentation region and allow Young's moduli and relative strengths to be estimated for the empty capsids. PMID:16606825

Stresses and deformations in cross-ply composite tubes subjected to a uniform temperature change: Elasticity and Approximate Solutions

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Cooper, D. E.; Cohen, D.

1985-01-01

The effects of a uniform temperature change on the stresses and deformations of composite tubes are investigated. The accuracy of an approximate solution based on the principle of complementary virtual work is determined. Interest centers on tube response away from the ends and so a planar elasticity approach is used. For the approximate solution a piecewise linear variation of stresses with the radial coordinate is assumed. The results from the approximate solution are compared with the elasticity solution. The stress predictions agree well, particularly peak interlaminar stresses. Surprisingly, the axial deformations also agree well. This, despite the fact that the deformations predicted by the approximate solution do not satisfy the interface displacement continuity conditions required by the elasticity solution. The study shows that the axial thermal expansion coefficient of tubes with a specific number of axial and circumferential layers depends on the stacking sequence. This is in contrast to classical lamination theory which predicts the expansion to be independent of the stacking arrangement. As expected, the sign and magnitude of the peak interlaminar stresses depends on stacking sequence.

Gurtin-Murdoch surface elasticity theory revisit: An orbital-free density functional theory perspective

NASA Astrophysics Data System (ADS)

Zhu, Yichao; Wei, Yihai; Guo, Xu

2017-12-01

In the present paper, the well-established Gurtin-Murdoch theory of surface elasticity (Gurtin and Murdoch, 1975, 1978) is revisited from an orbital-free density functional theory (OFDFT) perspective by taking the boundary layer into consideration. Our analysis indicates that firstly, the quantities introduced in the Gurtin-Murdoch theory of surface elasticity can all find their explicit expressions in the derived OFDFT-based theoretical model. Secondly, the derived expression for surface energy density captures a competition between the surface normal derivatives of the electron density and the electrostatic potential, which well rationalises the onset of signed elastic constants that are observed both experimentally and computationally. Thirdly, the established model naturally yields an inversely linear relationship between the materials surface stiffness and its size, which conforms to relevant findings in literature. Since the proposed OFDFT-based model is established under arbitrarily imposed boundary condition of electron density, electrostatic potential and external load, it also has the potential of being used to investigate the electro-mechanical behaviour of nanoscale materials manifesting surface effect.

Vascular mechanics of the coronary artery

NASA Technical Reports Server (NTRS)

Veress, A. I.; Vince, D. G.; Anderson, P. M.; Cornhill, J. F.; Herderick, E. E.; Klingensmith, J. D.; Kuban, B. D.; Greenberg, N. L.; Thomas, J. D.

2000-01-01

This paper describes our research into the vascular mechanics of the coronary artery and plaque. The three sections describe the determination of arterial mechanical properties using intravascular ultrasound (IVUS), a constitutive relation for the arterial wall, and finite element method (FEM) models of the arterial wall and atheroma. METHODS: Inflation testing of porcine left anterior descending coronary arteries was conducted. The changes in the vessel geometry were monitored using IVUS, and intracoronary pressure was recorded using a pressure transducer. The creep and quasistatic stress/strain responses were determined. A Standard Linear Solid (SLS) was modified to reproduce the non-linear elastic behavior of the arterial wall. This Standard Non-linear Solid (SNS) was implemented into an axisymetric thick-walled cylinder numerical model. Finite element analysis models were created for five age groups and four levels of stenosis using the Pathobiological Determinants of Atherosclerosis Youth (PDAY) database. RESULTS: The arteries exhibited non-linear elastic behavior. The total tissue creep strain was epsilon creep = 0.082 +/- 0.018 mm/mm. The numerical model could reproduce both the non-linearity of the porcine data and time dependent behavior of the arterial wall found in the literature with a correlation coefficient of 0.985. Increasing age had a strong positive correlation with the shoulder stress level, (r = 0.95). The 30% stenosis had the highest shoulder stress due to the combination of a fully formed lipid pool and a thin cap. CONCLUSIONS: Studying the solid mechanics of the arterial wall and the atheroma provide important insights into the mechanisms involved in plaque rupture.

An integrated structural and geochemical study of fracture aperture growth in the Campito Formation of eastern California

NASA Astrophysics Data System (ADS)

Doungkaew, N.; Eichhubl, P.

2015-12-01

Processes of fracture formation control flow of fluid in the subsurface and the mechanical properties of the brittle crust. Understanding of fundamental fracture growth mechanisms is essential for understanding fracture formation and cementation in chemically reactive systems with implications for seismic and aseismic fault and fracture processes, migration of hydrocarbons, long-term CO2 storage, and geothermal energy production. A recent study on crack-seal veins in deeply buried sandstone of east Texas provided evidence for non-linear fracture growth, which is indicated by non-elliptical kinematic fracture aperture profiles. We hypothesize that similar non-linear fracture growth also occurs in other geologic settings, including under higher temperature where solution-precipitation reactions are kinetically favored. To test this hypothesis, we investigate processes of fracture growth in quartzitic sandstone of the Campito Formation, eastern California, by combining field structural observations, thin section petrography, and fluid inclusion microthermometry. Fracture aperture profile measurements of cemented opening-mode fractures show both elliptical and non-elliptical kinematic aperture profiles. In general, fractures that contain fibrous crack-seal cement have elliptical aperture profiles. Fractures filled with blocky cement have linear aperture profiles. Elliptical fracture aperture profiles are consistent with linear-elastic or plastic fracture mechanics. Linear aperture profiles may reflect aperture growth controlled by solution-precipitation creep, with the aperture distribution controlled by solution-precipitation kinetics. We hypothesize that synkinematic crack-seal cement preserves the elliptical aperture profiles of elastic fracture opening increments. Blocky cement, on the other hand, may form postkinematically relative to fracture opening, with fracture opening accommodated by continuous solution-precipitation creep.

High Pressure Elastic Constants of High-Pressure Iron Analog Osmium

NASA Astrophysics Data System (ADS)

Godwal, B. K.; Geballe, Z.; Jeanloz, R.

2011-12-01

Understanding the elasticity of hcp iron is important both for ascertaining the stable phase and for explaining the observed seismic anomalies of Earth's inner core. A systematic experimental study of analog materials is warranted because experiments at inner-core conditions remain exceptionally challenging and theory has yielded conflicting results for iron. The deformation of hexagonal close-packed (hcp) Os, an analog for the high-pressure hcp form of Fe, has been characterized under non-hydrostatic stresses using synchrotron-based angular-dispersive radial x-ray diffraction to pressures of 60 GPa at room temperature. Starting with published ultrasonic values of elastic constants and previous measurements of linear and volume compressibilities, we estimate the single-crystal elasticity tensor of osmium to 60 GPa and find that the crystal orientation with the largest shear modulus, (002), accommodates the largest shear stress (10 GPa) and a differential strain surpassing the Voigt iso-strain limit. We find the conventional elastic model, bounded by Reuss (iso-stress) and Voigt limits, inadequate for explaining our measurements. Instead, we infer that plastic deformation limits the amount of shear stress supported by the crystal planes near the a-axis, causing the more elastically strong c-axis to support the majority of the differential strain. This conclusion is consistent with the elasto-plastic self-consistent approach used to model the effect of plasticity on the high-pressure deformation of hcp-Co (Merkel et al, PRB 79, 064110 (2009)). Importantly, we document a strength anisotropy so large that the Voigt (elastic) limit is clearly surpassed.

Determination of elastic moduli from measured acoustic velocities.

PubMed

Brown, J Michael

2018-06-01

Methods are evaluated in solution of the inverse problem associated with determination of elastic moduli for crystals of arbitrary symmetry from elastic wave velocities measured in many crystallographic directions. A package of MATLAB functions provides a robust and flexible environment for analysis of ultrasonic, Brillouin, or Impulsive Stimulated Light Scattering datasets. Three inverse algorithms are considered: the gradient-based methods of Levenberg-Marquardt and Backus-Gilbert, and a non-gradient-based (Nelder-Mead) simplex approach. Several data types are considered: body wave velocities alone, surface wave velocities plus a side constraint on X-ray-diffraction-based axes compressibilities, or joint body and surface wave velocities. The numerical algorithms are validated through comparisons with prior published results and through analysis of synthetic datasets. Although all approaches succeed in finding low-misfit solutions, the Levenberg-Marquardt method consistently demonstrates effectiveness and computational efficiency. However, linearized gradient-based methods, when applied to a strongly non-linear problem, may not adequately converge to the global minimum. The simplex method, while slower, is less susceptible to being trapped in local misfit minima. A "multi-start" strategy (initiate searches from more than one initial guess) provides better assurance that global minima have been located. Numerical estimates of parameter uncertainties based on Monte Carlo simulations are compared to formal uncertainties based on covariance calculations. Copyright © 2018 Elsevier B.V. All rights reserved.

An Effective Reservoir Parameter for Seismic Characterization of Organic Shale Reservoir

NASA Astrophysics Data System (ADS)

Zhao, Luanxiao; Qin, Xuan; Zhang, Jinqiang; Liu, Xiwu; Han, De-hua; Geng, Jianhua; Xiong, Yineng

2017-12-01

Sweet spots identification for unconventional shale reservoirs involves detection of organic-rich zones with abundant porosity. However, commonly used elastic attributes, such as P- and S-impedances, often show poor correlations with porosity and organic matter content separately and thus make the seismic characterization of sweet spots challenging. Based on an extensive analysis of worldwide laboratory database of core measurements, we find that P- and S-impedances exhibit much improved linear correlations with the sum of volume fraction of organic matter and porosity than the single parameter of organic matter volume fraction or porosity. Importantly, from the geological perspective, porosity in conjunction with organic matter content is also directly indicative of the total hydrocarbon content of shale resources plays. Consequently, we propose an effective reservoir parameter (ERP), the sum of volume fraction of organic matter and porosity, to bridge the gap between hydrocarbon accumulation and seismic measurements in organic shale reservoirs. ERP acts as the first-order factor in controlling the elastic properties as well as characterizing the hydrocarbon storage capacity of organic shale reservoirs. We also use rock physics modeling to demonstrate why there exists an improved linear correlation between elastic impedances and ERP. A case study in a shale gas reservoir illustrates that seismic-derived ERP can be effectively used to characterize the total gas content in place, which is also confirmed by the production well.

A 3/D finite element approach for metal matrix composites based on micromechanical models

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

Svobodnik, A.J.; Boehm, H.J.; Rammerstorfer, F.G.

Based on analytical considerations by Dvorak and Bahel-El-Din, a 3/D finite element material law has been developed for the elastic-plastic analysis of unidirectional fiber-reinforced metal matrix composites. The material law described in this paper has been implemented in the finite element code ABAQUS via the user subroutine UMAT. A constitutive law is described under the assumption that the fibers are linear-elastic and the matrix is of a von Mises-type with a Prager-Ziegler kinematic hardening rule. The uniaxial effective stress-strain relationship of the matrix in the plastic range is approximated by a Ramberg-Osgood law, a linear hardening rule or a nonhardeningmore » rule. Initial yield surface of the matrix material and for the fiber reinforced composite are compared to show the effect of reinforcement. Implementation of this material law in a finite element program is shown. Furthermore, the efficiency of substepping schemes and stress corrections for the numerical integration of the elastic-plastic stress-strain relations for anisotropic materials are investigated. The results of uniaxial monotonic tests of a boron/aluminum composite are compared to some finite element analyses based on micromechanical considerations. Furthermore a complete 3/D analysis of a tensile test specimen made of a silicon-carbide/aluminum MMC and the analysis of an MMC inlet inserted in a homogenous material are shown. 12 refs.« less

Determining Tension-Compression Nonlinear Mechanical Properties of Articular Cartilage from Indentation Testing.

PubMed

Chen, Xingyu; Zhou, Yilu; Wang, Liyun; Santare, Michael H; Wan, Leo Q; Lu, X Lucas

2016-04-01

The indentation test is widely used to determine the in situ biomechanical properties of articular cartilage. The mechanical parameters estimated from the test depend on the constitutive model adopted to analyze the data. Similar to most connective tissues, the solid matrix of cartilage displays different mechanical properties under tension and compression, termed tension-compression nonlinearity (TCN). In this study, cartilage was modeled as a porous elastic material with either a conewise linear elastic matrix with cubic symmetry or a solid matrix reinforced by a continuous fiber distribution. Both models are commonly used to describe the TCN of cartilage. The roles of each mechanical property in determining the indentation response of cartilage were identified by finite element simulation. Under constant loading, the equilibrium deformation of cartilage is mainly dependent on the compressive modulus, while the initial transient creep behavior is largely regulated by the tensile stiffness. More importantly, altering the permeability does not change the shape of the indentation creep curves, but introduces a parallel shift along the horizontal direction on a logarithmic time scale. Based on these findings, a highly efficient curve-fitting algorithm was designed, which can uniquely determine the three major mechanical properties of cartilage (compressive modulus, tensile modulus, and permeability) from a single indentation test. The new technique was tested on adult bovine knee cartilage and compared with results from the classic biphasic linear elastic curve-fitting program.

Enhanced dewaterability of sludge during anaerobic digestion with thermal hydrolysis pretreatment: New insights through structure evolution.

PubMed

Zhang, Jingsi; Li, Ning; Dai, Xiaohu; Tao, Wenquan; Jenkinson, Ian R; Li, Zhuo

2017-12-19

Comprehensive insights into the sludge digestate dewaterability were gained through porous network structure of sludge. We measured the evolution of digestate dewaterability, represented by the solid content of centrifugally dewatered cake, in high-solids sequencing batch digesters with and without thermal hydrolysis pretreatment (THP). The results show that the dewaterability of the sludge after digestion was improved by 3.5% (±0.5%) for unpretreated sludge and 5.1% (±0.4%) for thermally hydrolyzed sludge. Compared to the unpretreated sludge digestate, thermal hydrolysis pretreatment eventually resulted in an improvement of dewaterability by 4.6% (±0.5%). Smaller particle size and larger surface area of sludge were induced by thermal hydrolysis and anaerobic digestion treatments. The structure strength and compactness of sludge, represented by elastic modulus and fractal dimension respectively, decreased with increase of digestion time. The porous network structure was broken up by thermal hydrolysis pretreatment and was further weakened during anaerobic digestion, which correspondingly improved the dewaterability of digestates. The logarithm of elastic modulus increased linearly with fractal dimension regardless of the pretreatment. Both fractal dimension and elastic modulus showed linear relationship with dewaterability. The rheological characterization combined with the analysis of fractal dimension of sewage sludge porous network structure was found applicable in quantitative evaluation of sludge dewaterability, which depended positively on both thermal hydrolysis and anaerobic digestion. Copyright © 2017 Elsevier Ltd. All rights reserved.

A Comparison of Curing Process-Induced Residual Stresses and Cure Shrinkage in Micro-Scale Composite Structures with Different Constitutive Laws

NASA Astrophysics Data System (ADS)

Li, Dongna; Li, Xudong; Dai, Jianfeng; Xi, Shangbin

2018-02-01

In this paper, three kinds of constitutive laws, elastic, "cure hardening instantaneously linear elastic (CHILE)" and viscoelastic law, are used to predict curing process-induced residual stress for the thermoset polymer composites. A multi-physics coupling finite element analysis (FEA) model implementing the proposed three approaches is established in COMSOL Multiphysics-Version 4.3b. The evolution of thermo-physical properties with temperature and degree of cure (DOC), which improved the accuracy of numerical simulations, and cure shrinkage are taken into account for the three models. Subsequently, these three proposed constitutive models are implemented respectively in a 3D micro-scale composite laminate structure. Compared the differences between these three numerical results, it indicates that big error in residual stress and cure shrinkage generates by elastic model, but the results calculated by the modified CHILE model are in excellent agreement with those estimated by the viscoelastic model.

Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

Effects of biaxial strains on electronic and elastic properties of hexagonal XSi2 (X = Cr, Mo, W) from first-principles

NASA Astrophysics Data System (ADS)

Zhu, Haiyan; Shi, Liwei; Li, Shuaiqi; Zhang, Shaobo; Xia, Wangsuo

2018-02-01

Structural, electronic properties and elastic anisotropy of hexagonal C40 XSi2 (X = Cr, Mo, W) under equibiaxial in-plane strains are systematically studied using first-principle calculations. The energy gaps show significant changes with biaxial strains, whereas they are always indirect band-gap materials for -6% <ɛxx < 6%. All elastic constants, bulk modulus, shear modulus, Young's modulus increase (decrease) almost linearly with increasing compressive (tensile) strains. The evolutions of BH /GH ratio and Poisson's ratio indicate that these compounds have a better (worse) ductile behaviour under compressive (tensile) strains. A set of 3D plots show a larger directional variability in the Young's modulus E and shear modulus G at different strains for the three compounds, which is consist with the values of anisotropy factors. Moreover, the evolution of Debye temperature and anisotropy of sound velocities with biaxial strains are discussed.

BEST3D user's manual: Boundary Element Solution Technology, 3-Dimensional Version 3.0

NASA Technical Reports Server (NTRS)

1991-01-01

The theoretical basis and programming strategy utilized in the construction of the computer program BEST3D (boundary element solution technology - three dimensional) and detailed input instructions are provided for the use of the program. An extensive set of test cases and sample problems is included in the manual and is also available for distribution with the program. The BEST3D program was developed under the 3-D Inelastic Analysis Methods for Hot Section Components contract (NAS3-23697). The overall objective of this program was the development of new computer programs allowing more accurate and efficient three-dimensional thermal and stress analysis of hot section components, i.e., combustor liners, turbine blades, and turbine vanes. The BEST3D program allows both linear and nonlinear analysis of static and quasi-static elastic problems and transient dynamic analysis for elastic problems. Calculation of elastic natural frequencies and mode shapes is also provided.

Feedback equilibrium control during human standing

PubMed Central

Alexandrov, Alexei V.; AA, Frolov; FB, Horak; P, Carlson-Kuhta; S, Park

2006-01-01

Equilibrium maintenance during standing in humans was investigated with a 3-joint (ankle, knee and hip) sagittal model of body movement. The experimental paradigm consisted of sudden perturbations of humans in quiet stance by backward displacements of the support platform. Data analysis was performed using eigenvectors of motion equation. The results supported three conclusions. First, independent feedback control of movements along eigenvectors (eigenmovements) can adequately describe human postural responses to stance perturbations. This conclusion is consistent with previous observations (Alexandrov et al., 2001b) that these same eigenmovements are also independently controlled in a feed-forward manner during voluntary upper-trunk bending. Second, independent feedback control of each eigenmovement is sufficient to provide its stability. Third, the feedback loop in each eigenmovement can be modeled as a linear visco-elastic spring with delay. Visco-elastic parameters and time-delay values result from the combined contribution of passive visco-elastic mechanisms and sensory systems of different modalities. PMID:16228222

Equilibrium stability of a cylindrical body subject to the internal structure of the material and inelastic behaviour of the completely compressed matrix

NASA Astrophysics Data System (ADS)

Gotsev, D. V.; Perunov, N. S.; Sviridova, E. N.

2018-03-01

The mathematical model describing the stress-strain state of a cylindrical body under the uniform radial compression effect is constructed. The model of the material is the porous medium model. The compressed skeleton of the porous medium possesses hardening elastic-plastic properties. Deforming of the porous medium under the specified compressive loads is divided into two stages: elastic deforming of the porous medium and further elastic-plastic deforming of the material with completely compressed matrix. The analytical relations that define the fields of stress and displacement at each stage of the deforming are obtained. The influence of the porosity and other physical, mechanical and geometric parameters of the construction on the size of the plastic zone is evaluated. The question of the ground state equilibrium instability is investigated within the framework of the three-dimensional linearized relationships of the stability theory of deformed bodies.

The Single-Crystal Elasticity of Yttria (Y2O3) to High Temperature

NASA Technical Reports Server (NTRS)

Kriven, Waltraud M.; Palko, James W.; Sinogeikin, Stanislav V.; Bass, Jay D.; Sayir, Ali; Levine, Stanley R. (Technical Monitor)

2000-01-01

The single-crystal elastic moduli of yttria have been measured by Brillouin spectroscopy up to 1200 C. The room temperature values obtained are C11 = 223.6 +/- 0.6 GPa, C44 = 74.6 +/- 0.5 GPa, and C12 = 112.4 +/- 1.0 GPa. The resulting bulk and (Voigt-Reuss-Hill) shear moduli are K = 149.5 +/- 1.0 GPa and G(sub VRH) = 66.3 +/- 0.8 GPa, respectively. These agree much more closely with experimental values reported for polycrystalline samples than do previous single-crystal measurements. Linear least squares regressions to the variation of bulk and shear moduli with temperature result in derivatives of dK/dT = -17 +/- 2 MPa/degC and dG(sub VRH)/dT = -8 +/- 2 MPa/degC. Elastic anisotropy was found to remain essentially constant over the temperature range studied.

Analysis of Mode II Crack in Bilayered Composite Beam

NASA Astrophysics Data System (ADS)

Rizov, Victor I.; Mladensky, Angel S.

2012-06-01

Mode II crack problem in cantilever bilayered composite beams is considered. Two configurations are analyzed. In the first configuration the crack arms have equal heights while in the second one the arms have different heights. The modulus of elasticity and the shear modulus of the beam un-cracked part in the former case and the moment of inertia in the latter are derived as functions of the two layers characteristics. The expressions for the strain energy release rate, G are obtained on the basis of the simple beam theory according to the hypotheses of linear elastic fracture mechanics. The validity of these expressions is established by comparison with a known solution. Parametrical investigations for the influence of the moduli of elasticity ratio as well as the moments of inertia ratio on the strain energy release rate are also performed. The present article is a part of comprehensive investigation in Fracture mechanics of composite beams.

Levitation of YBa2Cu3O(7-x) superconductor in a variable magnetic field

NASA Technical Reports Server (NTRS)

Terentiev, Alexander N.; Kuznetsov, Anatoliy A.

1992-01-01

The influence of both a linear alternating and rotational magnetic field component on the levitation behavior of a YBa2Cu3O(7-x) superconductor was examined. The transition from a plastic regime of levitation to an elastic one, induced by an alternating field component, was observed. An elastic regime in contrast to a plastic one is characterized by the unique position of stable levitation and field frequency dependence of relaxation time to this position. It was concluded that the vibrations of a magnet levitated above the superconductor can induce a transition from a plastic regime of levitation to an elastic one. It was found that a rotational magnetic field component induced rotations of a levitated superconductor. Rotational frictional motion of flux lines is likely to be an origin of torque developed. A prototype of a motor based on a levitated superconductor rotor is proposed.

Comparative analysis of strain fields in layers of step-graded metamorphic buffers of various designs

NASA Astrophysics Data System (ADS)

Aleshin, A. N.; Bugaev, A. S.; Ruban, O. A.; Tabachkova, N. Yu.; Shchetinin, I. V.

2017-10-01

Spatial distribution of residual elastic strain in the layers of two step-graded metamophic buffers of various designs, grown by molecular beam epitaxy from ternary InxAl1-xAs solutions on GaAs(001) substrates, is obtained using reciprocal space mapping by three-axis X-ray diffractometry and the linear theory of elasticity. The difference in the design of the buffers enabled the formation of a dislocation-free layer with different thickness in each of the heterostructures, which was the main basis of this study. It is shown that, in spite of the different design of graded metamorphic buffers, the nature of strain fields in them is the same, and the residual elastic strains in the final elements of both buffers adjusted for the effect of work hardening subject to the same phenomenological law, which describes the strain relief process in single-layer heterostructures.

A multilayer model of time dependent deformation following an earthquake on a strike-slip fault

NASA Technical Reports Server (NTRS)

Cohen, S. C.

1981-01-01

A multilayer model of the Earth to calculate finite element of time dependent deformation and stress following an earthquake on a strike slip fault is discussed. The model involves shear properties of an elastic upper lithosphere, a standard viscoelastic linear solid lower lithosphere, a Maxwell viscoelastic asthenosphere and an elastic mesosphere. Systematic variations of fault and layer depths and comparisons with simpler elastic lithosphere over viscoelastic asthenosphere calculations are analyzed. Both the creep of the lower lithosphere and astenosphere contribute to the postseismic deformation. The magnitude of the deformation is enhanced by a short distance between the bottom of the fault (slip zone) and the top of the creep region but is less sensitive to the thickness of the creeping layer. Postseismic restressing is increased as the lower lithosphere becomes more viscoelastic, but the tendency for the width of the restressed zone to growth with time is retarded.

The effect of waiting times on demand and supply for elective surgery: Evidence from Italy.

PubMed

Riganti, Andrea; Siciliani, Luigi; Fiorio, Carlo V

2017-09-01

Waiting times are a major policy concern in publicly funded health systems across OECD countries. Economists have argued that, in the presence of excess demand, waiting times act as nonmonetary prices to bring demand for and supply of health care in equilibrium. Using administrative data disaggregated by region and surgical procedure over 2010-2014 in Italy, we estimate demand and supply elasticities with respect to waiting times. We employ linear regression models with first differences and instrumental variables to deal with endogeneity of waiting times. We find that demand is inelastic to waiting times while supply is more elastic. Estimates of demand elasticity are between -0.15 to -0.24. Our results have implications on the effectiveness of policies aimed at increasing supply and their ability to reduce waiting times. Copyright © 2017 John Wiley & Sons, Ltd.

Fracture toughness of Kevlar 29/poly(methyl methacrylate) composite materials for surgical implantations.

PubMed

Pourdeyhimi, B; Robinson, H H; Schwartz, P; Wagner, H D

1986-01-01

A study of the fracture behaviour of Kevlar 29 reinforced dental cement is undertaken using both linear elastic and nonlinear elastic fracture mechanics techniques. Results from both approaches--of which the nonlinear elastic is believed to be more appropriate--indicate that a reinforcing effect is obtained for the fracture toughness even at very low fibre content. The flexural strength and modulus are apparently not improved, however, by the incorporation of Kevlar 29 fibres in the PMMA cement, probably because of the presence of voids, the poor fibre/matrix interfacial bonding and unsatisfying cement mixing practice. When compared to other PMMA composite cements, the present system appears to be probably more effective than carbon/PMMA, for example, in terms of fracture toughness. More experimental and analytical work is needed so as to optimize the mechanical properties with respect to structural parameters and cement preparation technique.

Refractive index of r-cut sapphire under shock pressure range 5 to 65 GPa

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

Cao, Xiuxia; Li, Jiabo; Li, Jun

2014-09-07

High-pressure refractive index of optical window materials not only can provide information on electronic polarizability and band-gap structure, but also is important for velocity correction in particle-velocity measurement with laser interferometers. In this work, the refractive index of r-cut sapphire window at 1550 nm wavelength was measured under shock pressures of 5–65 GPa. The refractive index (n) decreases linearly with increasing shock density (ρ) for shock stress above the Hugoniot elastic limit (HEL): n = 2.0485 (± 0.0197) − 0.0729 (± 0.0043)ρ, while n remains nearly a constant for elastic shocks. This behavior is attributed to the transition from elastic (below HEL) to heterogeneous plastic deformationmore » (above HEL). Based on the obtained refractive index-density relationship, polarizability of the shocked sapphire was also obtained.« less

Nonlinear effects in thermal stress analysis of a solid propellant rocket motor

NASA Technical Reports Server (NTRS)

Francis, E. C.; Peeters, R. L.; Murch, S. A.

1976-01-01

Direct characterization procedures were used to determine the relaxation modulus as a function of time, temperature, and state of strain. Using the quasi-elastic method of linearviscoelasticity, these properties were employed in a finite element computer code to analyze a thick-walled, nonlinear viscoelastic cylinder in the state of plane strain bonded to a thin (but stiff) elastic casing and subjected to slow thermal cooling. The viscoelastic solution is then expressed as a sequence of elastic finite element solutions. The strain-dependent character of the relaxation modulus is included by replacing the single relaxation curve used in the linear viscoelastic theory by a family of relaxation functions obtained at various strain levels. These functions may be regarded as a collection of stress histories or responses to specific loads (in this case, step strains) with which the cooldown solution is made to agree by iterations on the modulus and strain level.

Nearly metastable rhombohedral phases of bcc metals

NASA Astrophysics Data System (ADS)

Mehl, Michael J.; Finkenstadt, Daniel

2008-02-01

The energy E(c/a) for a bcc element stretched along its [001] axis (the Bain path) has a minimum at c/a=1 , a maximum at c/a=2 , and an elastically unstable local minimum at c/a>2 . An alternative path connecting the bcc and fcc structures is the rhombohedral lattice. The primitive lattice has R3¯m symmetry, with the angle α changing from 109.4° (bcc), to 90° (simple cubic), to 60 ° (fcc). We study this path for the non-magnetic bcc transition metals (V, Nb, Mo, Ta, and W) using both all-electron linearized augmented plane wave and projector augmented wave VASP codes. Except for Ta, the energy E(α) has a local maximum at α=60° , with local minima near 55° and 70° , the latter having lower energy, suggesting the possibility of a metastable rhombohedral state for these materials. We first examine the elastic stability of the 70° minimum structure, and determine that only W is elastically stable in this structure, with the smallest eigenvalue of the elastic tensor at 4GPa . We then consider the possibility that tungsten is actually metastable in this structure by looking at its vibrational and third-order elastic stability.

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope

PubMed Central

Nitzan, Sarah H.; Zega, Valentina; Li, Mo; Ahn, Chae H.; Corigliano, Alberto; Kenny, Thomas W.; Horsley, David A.

2015-01-01

Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes. PMID:25762243

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope.

PubMed

Nitzan, Sarah H; Zega, Valentina; Li, Mo; Ahn, Chae H; Corigliano, Alberto; Kenny, Thomas W; Horsley, David A

2015-03-12

Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.

A cell-centered Lagrangian finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries

NASA Astrophysics Data System (ADS)

Sambasivan, Shiv Kumar; Shashkov, Mikhail J.; Burton, Donald E.

2013-03-01

A finite volume cell-centered Lagrangian formulation is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor-corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke's law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the J2 von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative Eulerian and Lagrangian hydrocodes in addition to analytical and experimental results are made to validate the current approach.

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

Elastic-plastic fracture mechanics of compact bone

NASA Astrophysics Data System (ADS)

Yan, Jiahau

Bone is a composite composed mainly of organics, minerals and water. Most studies on the fracture toughness of bone have been conducted at room temperature. Considering that the body temperature of animals is higher than room temperature, and that bone has a high volumetric percentage of organics (generally, 35--50%), the effect of temperature on fracture toughness of bone should be studied. Single-edged V-shaped notched (SEVN) specimens were prepared to measure the fracture toughness of bovine femur and manatee rib in water at 0, 10, 23, 37 and 50°C. The fracture toughness of bovine femur and manatee rib were found to decrease from 7.0 to 4.3 MPa·m1/2 and from 5.5 to 4.1 MPa·m1/2, respectively, over a temperature range of 50°C. The decreases were attributed to inability of the organics to sustain greater stresses at higher temperatures. We studied the effects of water and organics on fracture toughness of bone using water-free and organics-free SEVN specimens at 23°C. Water-free and organics-free specimens were obtained by placing fresh bone specimen in a furnace at different temperatures. Water and organics significantly affected the fracture toughness of bone. Fracture toughness of the water-free specimens was 44.7% (bovine femur) and 32.4% (manatee rib) less than that of fresh-bone specimens. Fracture toughness of the organics-free specimens was 92.7% (bovine femur) and 91.5% (manatee rib) less than that of fresh bone specimens. Linear Elastic Fracture Mechanics (LEFM) is widely used to study bone. However, bone often has small to moderate scale yielding during testing. We used J integral, an elastic-plastic fracture-mechanics parameter, to study the fracture process of bone. The J integral of bovine femur increased from 6.3 KJ/mm2 at 23°C to 6.7 KJ/mm2 at 37°C. Although the fracture toughness of bovine bone decreases as the temperature increases, the J integral results show a contrary trend. The energy spent in advancing the crack beyond the linear-elastic deformation was much greater than the energy spent in linear-elastic deformation. This could be because bone has at least four toughening mechanisms and a high volumetric percentage of organics (approximately 42% for bovine femur). The J integral is shown to better describe the fracture process of bovine femur and manatee rib.

Viscoelastic Earthquake Cycle Simulation with Memory Variable Method

NASA Astrophysics Data System (ADS)

Hirahara, K.; Ohtani, M.

2017-12-01

There have so far been no EQ (earthquake) cycle simulations, based on RSF (rate and state friction) laws, in viscoelastic media, except for Kato (2002), who simulated cycles on a 2-D vertical strike-slip fault, and showed nearly the same cycles as those in elastic cases. The viscoelasticity could, however, give more effects on large dip-slip EQ cycles. In a boundary element approach, stress is calculated using a hereditary integral of stress relaxation function and slip deficit rate, where we need the past slip rates, leading to huge computational costs. This is a cause for almost no simulations in viscoelastic media. We have investigated the memory variable method utilized in numerical computation of wave propagation in dissipative media (e.g., Moczo and Kristek, 2005). In this method, introducing memory variables satisfying 1st order differential equations, we need no hereditary integrals in stress calculation and the computational costs are the same order of those in elastic cases. Further, Hirahara et al. (2012) developed the iterative memory variable method, referring to Taylor et al. (1970), in EQ cycle simulations in linear viscoelastic media. In this presentation, first, we introduce our method in EQ cycle simulations and show the effect of the linear viscoelasticity on stick-slip cycles in a 1-DOF block-SLS (standard linear solid) model, where the elastic spring of the traditional block-spring model is replaced by SLS element and we pull, in a constant rate, the block obeying RSF law. In this model, the memory variable stands for the displacement of the dash-pot in SLS element. The use of smaller viscosity reduces the recurrence time to a minimum value. The smaller viscosity means the smaller relaxation time, which makes the stress recovery quicker, leading to the smaller recurrence time. Second, we show EQ cycles on a 2-D dip-slip fault with the dip angel of 20 degrees in an elastic layer with thickness of 40 km overriding a Maxwell viscoelastic half layer with the relaxation time of 5 yrs. In a test model where we set the fault at 30-40 km depths, the recurrence time of the EQ cycle is reduced by 1 yr from 27.92 in elastic case to 26.85 yrs. This smaller recurrence time is the same as in Kato (2002), but the effect of the viscoelasticity on the cycles would be larger in the dip-slip fault case than that in the strike-slip one.

A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media

NASA Technical Reports Server (NTRS)

Martin, C. J.; Lee, Y. M.

1972-01-01

A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

Characteristics of the First Longitudinal-Fourth Bending Mode Linear Ultrasonic Motors

NASA Astrophysics Data System (ADS)

Park, Taegone; Kim, Beomjin; Kim, Myong-Ho; Uchino, Kenji

2002-11-01

Linear ultrasonic motors using a combination of the first longitudinal mode and the fourth bending mode were designed and fabricated. The driving characteristics of the motors, which were composed of a straight metal bar bonded with piezoelectric ceramic vibrators as a driving element, were measured. Unimorph and bimorph ceramic vibrators were attached on three kinds of metal bars for constructing the stators of the linear motors. As results, motors made with the bimorph ceramic vibrators had higher velocity than motors of the unimorph vibrators. As a metal bar for stator, magnesium alloy, which has lower elastic coefficient than aluminum alloy, was better for the motors.

Development, calibration, and validation of performance prediction models for the Texas M-E flexible pavement design system.

DOT National Transportation Integrated Search

2010-08-01

This study was intended to recommend future directions for the development of TxDOTs Mechanistic-Empirical : (TexME) design system. For stress predictions, a multi-layer linear elastic system was evaluated and its validity was : verified by compar...

Temperature Dependence of Irradiation Damage to Polythene

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

TODD, G.; WILD, G. A.

1963-07-13

Comparison of measurements of radiation damage to polythene exposed to a 4.3-Mev linear accelerator and in a reactor led to the conclusion that radiation damage of polythene is temperature dependent. Applications of radiation in raising or lowering the elastic modulus of polythene are suggested. (C.H.)

Effect of rock rheology on fluid leak- off during hydraulic fracturing

NASA Astrophysics Data System (ADS)

Yarushina, V. M.; Bercovici, D.; Oristaglio, M. L.

2012-04-01

In this communication, we evaluate the effect of rock rheology on fluid leak­off during hydraulic fracturing of reservoirs. Fluid leak-off in hydraulic fracturing is often nonlinear. The simple linear model developed by Carter (1957) for flow of fracturing fluid into a reservoir has three different regions in the fractured zone: a filter cake on the fracture face, formed by solid additives from the fracturing fluid; a filtrate zone affected by invasion of the fracturing fluid; and a reservoir zone with the original formation fluid. The width of each zone, as well as its permeability and pressure drop, is assumed to remain constant. Physical intuition suggests some straightforward corrections to this classical theory to take into account the pressure dependence of permeability, the compressibility or non-Newtonian rheology of fracturing fluid, and the radial (versus linear) geometry of fluid leak­off from the borehole. All of these refinements, however, still assume that the reservoir rock adjacent to the fracture face is non­deformable. Although the effect of poroelastic stress changes on leak-off is usually thought to be negligible, at the very high fluid pressures used in hydraulic fracturing, where the stresses exceed the rock strength, elastic rheology may not be the best choice. For example, calculations show that perfectly elastic rock formations do not undergo the degree of compaction typically seen in sedimentary basins. Therefore, pseudo-elastic or elastoplastic models are used to fit observed porosity profiles with depth. Starting from balance equations for mass and momentum for fluid and rock, we derive a hydraulic flow equation coupled with a porosity equation describing rock compaction. The result resembles a pressure diffusion equation with the total compressibility being a sum of fluid, rock and pore-space compressibilities. With linear elastic rheology, the bulk formation compressibility is dominated by fluid compressibility. But the possibility of permanent, time-independent (plastic) rock deformation significantly increases the pore space compressibility (compaction), which becomes a leading term in the total compressibility. Inclusion of rock and fluid compressibilities in the model can explain both linear and nonlinear leak­off. In particular, inclusion of rock compaction and decompaction may be important for description of naturally fractured and tight gas reservoirs for which very strong dependence of permeability on porosity has been reported. Carter R.D. Derivation of the general equation for estimating the extent of the fractured area. Appendix I of "Optimum fluid characteristics for fracture extension", Drilling and Production Practice, G.C. Howard and C.R.Fast, New York, New York, USA, American Petroleum Institute (1957), 261-269.

Long-wave dynamics of an elastic sheet lubricated by a thin liquid film on a wetting substrate

NASA Astrophysics Data System (ADS)

Young, Y.-N.; Stone, H. A.

2017-06-01

The dynamics of an elastic sheet lubricated by a thin liquid film on a wetting solid substrate is examined using both numerical simulations of a long-wave lubrication equation and a quasistatic model. Interactions between the liquid and the wetting substrate are modeled by a disjoining pressure that gives rise to an ultrathin (precursor) film. For a fluid interface without elastic bending stiffness, a flat precursor film may be linearly unstable and evolve towards an equilibrium of a single "drop" connected to a flat ultrathin film. Similar behavior is found when the thin film is covered by an elastic sheet: The sheet deforms, rearranging the thin liquid film, and contributes regulating surface forces such as a bending resistance and/or a tensile force, which may arise from interactions between the sheet and liquid or inextensibility of the sheet. Glasner's quasistatic model [Phys. Fluids 15, 1837 (2003), 10.1063/1.1578076], developed for a liquid film, is adopted to investigate the combined effects of elastic and tensile forces in the sheet on the thin film dynamics. The equilibrium height of the drop is found to vary inversely with the bending rigidity. When the elastic sheet is inextensible (such as a lipid bilayer membrane), a compressive tensile force may occur and the equilibrium film height is dependent less on the bending rigidity and more on the excess area of the membrane. Analyses of the lubrication equation also show that the precursor film transitions monotonically to the core film for tension-dominated dynamics. In contrast, for elasticity-dominated dynamics, a spatial oscillation of film height in the contact line region is found. In addition, elasticity in the sheet causes a sliding motion of the thin film: the contact angle is rendered zero by elasticity, and the contact line moves at a finite speed.

Characterization of the mechanical properties of resected porcine organ tissue using optical fiber photoelastic polarimetry.

PubMed

Hudnut, Alexa W; Babaei, Behzad; Liu, Sonya; Larson, Brent K; Mumenthaler, Shannon M; Armani, Andrea M

2017-10-01

Characterizing the mechanical behavior of living tissue presents an interesting challenge because the elasticity varies by eight orders of magnitude, from 50Pa to 5GPa. In the present work, a non-destructive optical fiber photoelastic polarimetry system is used to analyze the mechanical properties of resected samples from porcine liver, kidney, and pancreas. Using a quasi-linear viscoelastic fit, the elastic modulus values of the different organ systems are determined. They are in agreement with previous work. In addition, a histological assessment of compressed and uncompressed tissues confirms that the tissue is not damaged during testing.

On the theory of hysteretic magnetostriction of soft ferrogels

NASA Astrophysics Data System (ADS)

Zubarev, Andrey; Chirikov, Dmitry; Stepanov, Gennady; Borin, Dmitry; Lopez-Lopez, M. T.

2018-05-01

The paper deals with theoretical study of hysteretic magnetostriction of soft ferrogels - composite materials, consisting of the micron-sized magnetizable particles embedded into gel matrices. It is supposed that initially, before application of an external magnetic field, the particles are homogeneously and isotropically distributed in an elastic matrix. The theoretical explanation of the hysteresis phenomena is based on the conception that, under the field action, the particles rearrange into the linear chain-like aggregates. The typical length of the chains is determined by the competition between the force of magnetic attraction of the particles and the force of elastic deformation of the matrix.

On the strain energy of laminated composite plates

NASA Technical Reports Server (NTRS)

Atilgan, Ali R.; Hodges, Dewey H.

1991-01-01

The present effort to obtain the asymptotically correct form of the strain energy in inhomogeneous laminated composite plates proceeds from the geometrically nonlinear elastic theory-based three-dimensional strain energy by decomposing the nonlinear three-dimensional problem into a linear, through-the-thickness analysis and a nonlinear, two-dimensional analysis analyzing plate formation. Attention is given to the case in which each lamina exhibits material symmetry about its middle surface, deriving closed-form analytical expressions for the plate elastic constants and the displacement and strain distributions through the plate's thickness. Despite the simplicity of the plate strain energy's form, there are no restrictions on the magnitudes of displacement and rotation measures.

Active Vibration Control of Elastic Beam by Means of Shape Memory Alloy Layers

NASA Technical Reports Server (NTRS)

Chen, Q.; Levy, C.

1996-01-01

The mathematical model of a flexible beam covered with shape memory alloy (SMA) layers is presented. The SMA layers are used as actuators, which are capable of changing their elastic modulus and recovery stress, thus changing the natural frequency of, and adjusting the excitation to, the vibrating beam. The frequency factor variation as a function of SMA Young's modulus, SMA layer thickness and beam thickness is discussed. Also control of the beam employing an optimal linear control law is evaluated. The control results indicate how the system reacts to various levels of excitation input through the non-homogeneous recovery shear term of the governing differential equation.

Viscoelastic/damage modeling of filament-wound spherical pressure vessels

NASA Technical Reports Server (NTRS)

Hackett, Robert M.; Dozier, Jan D.

1987-01-01

A model of the viscoelastic/damage response of a filament-wound spherical vessel used for long-term pressure containment is developed. The matrix material of the composite system is assumed to be linearly viscoelastic. Internal accumulated damage based upon a quadratic relationship between transverse modulus and maximum circumferential strain is postulated. The resulting nonlinear problem is solved by an iterative routine. The elastic-viscoelastic correspondence is employed to produce, in the Laplace domain, the associated elastic solution for the maximum circumferential strain which is inverted by the method of collocation to yield the time-dependent solution. Results obtained with the model are compared to experimental 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.

A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures

PubMed Central

Colli Franzone, Piero; Pavarino, Luca F.; Scacchi, Simone

2018-01-01

We introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing) architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1) the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2) the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3) the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4) the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks. PMID:29674971

Molecular dynamics for near melting temperatures simulations of metals using modified embedded-atom method

NASA Astrophysics Data System (ADS)

Etesami, S. Alireza; Asadi, Ebrahim

2018-01-01

Availability of a reliable interatomic potential is one of the major challenges in utilizing molecular dynamics (MD) for simulations of metals at near the melting temperatures and melting point (MP). Here, we propose a novel approach to address this challenge in the concept of modified-embedded-atom (MEAM) interatomic potential; also, we apply the approach on iron, nickel, copper, and aluminum as case studies. We propose adding experimentally available high temperature elastic constants and MP of the element to the list of typical low temperature properties used for the development of MD interatomic potential parameters. We show that the proposed approach results in a reasonable agreement between the MD calculations of melting properties such as latent heat, expansion in melting, liquid structure factor, and solid-liquid interface stiffness and their experimental/computational counterparts. Then, we present the physical properties of mentioned elements near melting temperatures using the new MEAM parameters. We observe that the behavior of elastic constants, heat capacity and thermal linear expansion coefficient at room temperature compared to MP follows an empirical linear relation (α±β × MP) for transition metals. Furthermore, a linear relation between the tetragonal shear modulus and the enthalpy change from room temperature to MP is observed for face-centered cubic materials.

Mathematical modeling of the crack growth in linear elastic isotropic materials by conventional fracture mechanics approaches and by molecular dynamics method: crack propagation direction angle under mixed mode loading

NASA Astrophysics Data System (ADS)

Stepanova, Larisa; Bronnikov, Sergej

2018-03-01

The crack growth directional angles in the isotropic linear elastic plane with the central crack under mixed-mode loading conditions for the full range of the mixity parameter are found. Two fracture criteria of traditional linear fracture mechanics (maximum tangential stress and minimum strain energy density criteria) are used. Atomistic simulations of the central crack growth process in an infinite plane medium under mixed-mode loading using Large-scale Molecular Massively Parallel Simulator (LAMMPS), a classical molecular dynamics code, are performed. The inter-atomic potential used in this investigation is Embedded Atom Method (EAM) potential. The plane specimens with initial central crack were subjected to Mixed-Mode loadings. The simulation cell contains 400000 atoms. The crack propagation direction angles under different values of the mixity parameter in a wide range of values from pure tensile loading to pure shear loading in a wide diapason of temperatures (from 0.1 К to 800 К) are obtained and analyzed. It is shown that the crack propagation direction angles obtained by molecular dynamics method coincide with the crack propagation direction angles given by the multi-parameter fracture criteria based on the strain energy density and the multi-parameter description of the crack-tip fields.

Update to the conventional model for rotational deformation

NASA Astrophysics Data System (ADS)

Ries, J. C.; Desai, S.

2017-12-01

Rotational deformation (also called the "pole tide") is the deformation resulting from the centrifugal effect of polar motion on the solid earth and ocean, which manifests itself as variations in ocean heights, in the gravity field and in surface displacements. The model for rotational deformation assumes a primarily elastic response of the Earth to the centrifugal potential at the annual and Chandler periods and applies body tide Love numbers to the polar motion after removing the mean pole. The original model was conceived when the mean pole was moving (more or less) linearly, largely in response to glacial isostatic adjustment. In light of the significant variations in the mean pole due to present-day ice mass losses, an `appropriately' filtered mean pole was adopted for the conventional model, so that the longer period variations in the mean pole were not included in the rotational deformation model. However, the elastic Love numbers should be applicable to longer period variations as well, and only the secular (i.e. linear) mean pole should be removed. A model for the linear mean pole is recommended based on a linear fit to the IERS C01 time series spanning 1900 to 2015: in milliarcsec, Xp = 55.0+1.677*dt and Yp = 320.5+3.460*dt where dt=(t-t0), t0=2000.0 and assuming a year=365.25 days. The consequences of an updated model for rotational deformation for site motion and the gravity field are illustrated.

A First Step towards Variational Methods in Engineering

ERIC Educational Resources Information Center

Periago, Francisco

2003-01-01

In this paper, a didactical proposal is presented to introduce the variational methods for solving boundary value problems to engineering students. Starting from a couple of simple models arising in linear elasticity and heat diffusion, the concept of weak solution for these models is motivated and the existence, uniqueness and continuous…

Effect of non-linearity in predicting doppler waveforms through a novel model

PubMed Central

Gayasen, Aman; Dua, Sunil Kumar; Sengupta, Amit; Nagchoudhuri, D

2003-01-01

Background In pregnancy, the uteroplacental vascular system develops de novo locally in utero and a systemic haemodynamic & bio-rheological alteration accompany it. Any abnormality in the non-linear vascular system is believed to trigger the onset of serious morbid conditions like pre-eclampsia and/or intrauterine growth restriction (IUGR). Exact Aetiopathogenesis is unknown. Advancement in the field of non-invasive doppler image analysis and simulation incorporating non-linearities may unfold the complexities associated with the inaccessible uteroplacental vessels. Earlier modeling approaches approximate it as a linear system. Method We proposed a novel electrical model for the uteroplacental system that uses MOSFETs as non-linear elements in place of traditional linear transmission line (TL) model. The model to simulate doppler FVW's was designed by including the inputs from our non-linear mathematical model. While using the MOSFETs as voltage-controlled switches, a fair degree of controlled-non-linearity has been introduced in the model. Comparative analysis was done between the simulated data and the actual doppler FVW's waveforms. Results & Discussion Normal pregnancy has been successfully modeled and the doppler output waveforms are simulated for different gestation time using the model. It is observed that the dicrotic notch disappears and the S/D ratio decreases as the pregnancy matures. Both these results are established clinical facts. Effects of blood density, viscosity and the arterial wall elasticity on the blood flow velocity profile were also studied. Spectral analysis on the output of the model (blood flow velocity) indicated that the Total Harmonic Distortion (THD) falls during the mid-gestation. Conclusion Total harmonic distortion (THD) is found to be informative in determining the Feto-maternal health. Effects of the blood density, the viscosity and the elasticity changes on the blood FVW are simulated. Future works are expected to concentrate mainly on improving the load with respect to varying non-linear parameters in the model. Heart rate variability, which accounts for the vascular tone, should also be included. We also expect the model to initiate extensive clinical or experimental studies in the near future. PMID:14561227

A fundamental reconsideration of the CRASH3 damage analysis algorithm: the case against uniform ubiquitous linearity between BEV, peak collision force magnitude, and residual damage depth.

PubMed

Singh, Jai

2013-01-01

The objective of this study was a thorough reconsideration, within the framework of Newtonian mechanics and work-energy relationships, of the empirically interpreted relationships employed within the CRASH3 damage analysis algorithm in regards to linearity between barrier equivalent velocity (BEV) or peak collision force magnitude and residual damage depth. The CRASH3 damage analysis algorithm was considered, first in terms of the cases of collisions that produced no residual damage, in order to properly explain the damage onset speed and crush resistance terms. Under the modeling constraints of the collision partners representing a closed system and the a priori assumption of linearity between BEV or peak collision force magnitude and residual damage depth, the equations for the sole realistic model were derived. Evaluation of the work-energy relationships for collisions at or below the elastic limit revealed that the BEV or peak collision force magnitude relationships are bifurcated based upon the residual damage depth. Rather than being additive terms from the linear curve fits employed in the CRASH3 damage analysis algorithm, the Campbell b 0 and CRASH3 AL terms represent the maximum values that can be ascribed to the BEV or peak collision force magnitude, respectively, for collisions that produce zero residual damage. Collisions resulting in the production of non-zero residual damage depth already account for the surpassing of the elastic limit during closure and therefore the secondary addition of the elastic limit terms represents a double accounting of the same. This evaluation shows that the current energy absorbed formulation utilized in the CRASH3 damage analysis algorithm extraneously includes terms associated with the A and G stiffness coefficients. This sole realistic model, however, is limited, secondary to reducing the coefficient of restitution to a constant value for all cases in which the residual damage depth is nonzero. Linearity between BEV or peak collision force magnitude and residual damage depth may be applicable for particular ranges of residual damage depth for any given region of any given vehicle. Within the modeling construct employed by the CRASH3 damage algorithm, the case of uniform and ubiquitous linearity cannot be supported. Considerations regarding the inclusion of internal work recovered and restitution for modeling the separation phase change in velocity magnitude should account for not only the effects present during the evaluation of a vehicle-to-vehicle collision of interest but also to the approach taken for modeling the force-deflection response for each collision partner.

Covariant balance laws in continua with microstructure

NASA Astrophysics Data System (ADS)

Yavari, Arash; Marsden, Jerrold E.

2009-02-01

The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the group of diffeomorphisms of the ambient space. A key advantage is that one obtains in a natural way all the needed balance laws on both the macro and micro levels along with two Doyle-Erickson formulas. We model a structured continuum as a triplet of Riemannian manifolds: a material manifold, the ambient space manifold of material particles and a director field manifold. The Green-Naghdi-Rivlin theorem and its extensions for structured continua are critically reviewed. We show that when the ambient space is Euclidean and when the microstructure manifold is the tangent space of the ambient space manifold, postulating a single balance of energy law and its invariance under time-dependent isometries of the ambient space, one obtains conservation of mass, balances of linear and angular momenta but not a separate balance of linear momentum. We develop a covariant elasticity theory for structured continua by postulating that energy balance is invariant under time-dependent spatial diffeomorphisms of the ambient space, which in this case is the product of two Riemannian manifolds. We then introduce two types of constrained continua in which microstructure manifold is linked to the reference and ambient space manifolds. In the case when at every material point, the microstructure manifold is the tangent space of the ambient space manifold at the image of the material point, we show that the assumption of covariance leads to balances of linear and angular momenta with contributions from both forces and micro-forces along with two Doyle-Ericksen formulas. We show that generalized covariance leads to two balances of linear momentum and a single coupled balance of angular momentum. Using this theory, we covariantly obtain the balance laws for two specific examples, namely elastic solids with distributed voids and mixtures. Finally, the Lagrangian field theory of structured elasticity is revisited and a connection is made between covariance and Noether's theorem.

Single-Crystal Elastic Constants of Yttria (Y2O3) Measured to High Temperatures

NASA Technical Reports Server (NTRS)

Sayir, Ali; Palko, James W.; Kriven, Waltraud M.; Sinogeikin, Sergey V.; Bass, Jay D.

2001-01-01

Yttria, or yttrium sesquioxide (Y2O3), has been considered for use in nuclear applications and has gained interest relatively recently for use in infrared optics. Single crystals of yttria have been grown successfully at the NASA Glenn Research Center using a laser-heated float zone technique in a fiber and rod. Such samples allow measurement of the single-crystal elastic properties, and these measurements provide useful property data for the design of components using single crystals. They also yield information as to what degree the elastic properties of yttria ceramics are a result of the intrinsic properties of the yttria crystal in comparison to characteristics that may depend on processing, such as microstructure and intergranular phases, which are common in sintered yttria. The single-crystal elastic moduli are valuable for designing such optical components. In particular, the temperature derivatives of elastic moduli allow the dimensional changes due to heating under physical constraints, as well as acoustic excitation, to be determined. The single-crystal elastic moduli of yttria were measured by Brillouin spectroscopy up to 1200 C. The room-temperature values obtained were C(sub 11) = 223.6 + 0.6 GPa, C(sub 44) = 74.6 + 0.5 GPa, and C(sub 12) = 112.4 + 1.0 GPa. The resulting bulk and (Voigt-Reuss-Hill) shear moduli were K = 149.5 + 1.0 GPa and G(sub VRH) = 66.3 + 0.8 GPa, respectively. Linear least-squares regressions to the variation of bulk and shear moduli with temperature resulted in derivatives of dK/dT = -17 + 2 MPa/C and dG(sub VRH)/dT = -8 + 2 MPa/ C. Elastic anisotropy was found to remain essentially constant over the temperature range studied.

Determination of Spearman Correlation Coefficient (r) to Evaluate the Linear Association of Dermal Collagen and Elastic Fibers in the Perspectives of Skin Injury.

PubMed

Kumar, Naveen; Kumar, Pramod; Badagabettu, Satheesha Nayak; Lewis, Melissa Glenda; Adiga, Murali; Padur, Ashwini Aithal

2018-01-01

Difference in scar formation at different sites, in different directions at the same site, but with changes in the elasticity of skin with age, sex, and race or in some pathological conditions, is well known to clinicians. The inappropriate collagen syntheses and delayed or lack of epithelialization are known to induce scar formation with negligible elasticity at the site of damage. Changes in the elasticity of scars may be due to an unequal distribution of dermal collagen (C) and elastic (E) fibers. Spearman correlation coefficients ( r ) of collagen and elastic fibers in horizontal (H) and in vertical (V) directions (variables CV, CH, EV, and EH) were measured from the respective quantitative fraction data in 320 skin samples from 32 human cadavers collected at five selected sites over extremities. Spearman's correlation analysis revealed the statistically significant ( p < 0.01) strong positive correlation between C H and C V in all the areas, that is, shoulder joint area ( r = 0.66), wrist ( r = 0.75), forearm ( r = 0.75), and thigh ( r = 0.80), except at the ankle ( r = 0.26, p = 0.14) region. Similarly, positive correlation between E H and E V has been observed at the forearm ( r = 0.65, moderate) and thigh ( r = 0.42, low) regions. However, a significant moderate negative correlation was observed between C V and E V at the forearm ( r = -0.51) and between C H and E H at the thigh region ( r = -0.65). Significant differences of correlations of collagen and elastic fibers in different directions from different areas of extremities were noted. This may be one of the possible anatomical reasons of scar behavior in different areas and different directions of the same area.

Quasi-static incremental behavior of granular materials: Elastic-plastic coupling and micro-scale dissipation

NASA Astrophysics Data System (ADS)

Kuhn, Matthew R.; Daouadji, Ali

2018-05-01

The paper addresses a common assumption of elastoplastic modeling: that the recoverable, elastic strain increment is unaffected by alterations of the elastic moduli that accompany loading. This assumption is found to be false for a granular material, and discrete element (DEM) simulations demonstrate that granular materials are coupled materials at both micro- and macro-scales. Elasto-plastic coupling at the macro-scale is placed in the context of thermomechanics framework of Tomasz Hueckel and Hans Ziegler, in which the elastic moduli are altered by irreversible processes during loading. This complex behavior is explored for multi-directional loading probes that follow an initial monotonic loading. An advanced DEM model is used in the study, with non-convex non-spherical particles and two different contact models: a conventional linear-frictional model and an exact implementation of the Hertz-like Cattaneo-Mindlin model. Orthotropic true-triaxial probes were used in the study (i.e., no direct shear strain), with tiny strain increments of 2 ×10-6 . At the micro-scale, contact movements were monitored during small increments of loading and load-reversal, and results show that these movements are not reversed by a reversal of strain direction, and some contacts that were sliding during a loading increment continue to slide during reversal. The probes show that the coupled part of a strain increment, the difference between the recoverable (elastic) increment and its reversible part, must be considered when partitioning strain increments into elastic and plastic parts. Small increments of irreversible (and plastic) strain and contact slipping and frictional dissipation occur for all directions of loading, and an elastic domain, if it exists at all, is smaller than the strain increment used in the simulations.

Effects of elastic bed on hydrodynamic forces for a submerged sphere in an ocean of finite depth

NASA Astrophysics Data System (ADS)

Mohapatra, Smrutiranjan

2017-08-01

In this paper, we consider a hydroelastic model to examine the radiation of waves by a submerged sphere for both heave and sway motions in a single-layer fluid flowing over an infinitely extended elastic bottom surface in an ocean of finite depth. The elastic bottom is modeled as a thin elastic plate and is based on the Euler-Bernoulli beam equation. The effect of the presence of surface tension at the free-surface is neglected. In such situation, there exist two modes of time-harmonic waves: the one with a lower wavenumber (surface mode) propagates along the free-surface and the other with higher wavenumber (flexural mode) propagates along the elastic bottom surface. Based on the small amplitude wave theory and by using the multipole expansion method, we find the particular solution for the problem of wave radiation by a submerged sphere of finite depth. Furthermore, this method eliminates the need to use large and cumbersome numerical packages for the solution of such problem and leads to an infinite system of linear algebraic equations which are easily solved numerically by any standard technique. The added-mass and damping coefficients for both heave and sway motions are derived and plotted for different submersion depths of the sphere and flexural rigidity of the elastic bottom surface. It is observed that, whenever the sphere nearer to the elastic bed, the added-mass move toward to a constant value of 1, which is approximately twice of the value of added-mass of a moving sphere in a single-layer fluid flowing over a rigid and flat bottom surface.

Design and performance testing of an ultrasonic linear motor with dual piezoelectric actuators.

PubMed

Smithmaitrie, Pruittikorn; Suybangdum, Panumas; Laoratanakul, Pitak; Muensit, Nantakan

2012-05-01

In this work, design and performance testing of an ultrasonic linear motor with dual piezoelectric actuator patches are studied. The motor system consists of a linear stator, a pre-load weight, and two piezoelectric actuator patches. The piezoelectric actuators are bonded with the linear elastic stator at specific locations. The stator generates propagating waves when the piezoelectric actuators are subjected to harmonic excitations. Vibration characteristics of the linear stator are analyzed and compared with finite element and experimental results. The analytical, finite element, and experimental results show agreement. In the experiments, performance of the ultrasonic linear motor is tested. Relationships between velocity and pre-load weight, velocity and applied voltage, driving force and applied voltage, and velocity and driving force are reported. The design of the dual piezoelectric actuators yields a simpler structure with a smaller number of actuators and lower stator stiffness compared with a conventional design of an ultrasonic linear motor with fully laminated piezoelectric actuators.

Influence of a Levelness Defect in a Thrust Bearing on the Dynamic Behaviour of AN Elastic Shaft

NASA Astrophysics Data System (ADS)

BERGER, S.; BONNEAU, O.; FRÊNE, J.

2002-01-01

This paper examines the non-linear dynamic behaviour of a flexible shaft. The shaft is mounted on two journal bearings and the axial load is supported by a defective hydrodynamic thrust bearing at one end. The defect is a levelness defect of the rotor. The thrust bearing behaviour must be considered to be non-linear because of the effects of the defect. The shaft is modelled with typical beam finite elements including effects such as the gyroscopic effects. A modal technique is used to reduce the number of degrees of freedom. Results show that the thrust bearing defects introduce supplementary critical speeds. The linear approach is unable to show the supplementary critical speeds which are obtained only by using non-linear analysis.

Linear and Nonlinear Finite Elements.

DTIC Science & Technology

1983-12-01

Metzler. Con/ ugte rapdent solution of a finite element elastic problem with high Poson rato without scaling and once with the global stiffness matrix K...nonzero c, that makes u(0) = 1. According to the linear, small deflection theory of the membrane the central displacement given to the membrane is not... theory is possible based on the approximations (l-y 2 )t = +y’ 2 +y𔃾 , (1-y𔃼)’ 1-y’ 2 - y" (6) that change eq. (5) to V𔃺) = , [yŖ(1 + y") - Qy𔃼

Estimation of parameters of constant elasticity of substitution production functional model

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Sankar, J. Ravi

2017-11-01

Nonlinear model building has become an increasing important powerful tool in mathematical economics. In recent years the popularity of applications of nonlinear models has dramatically been rising up. Several researchers in econometrics are very often interested in the inferential aspects of nonlinear regression models [6]. The present research study gives a distinct method of estimation of more complicated and highly nonlinear model viz Constant Elasticity of Substitution (CES) production functional model. Henningen et.al [5] proposed three solutions to avoid serious problems when estimating CES functions in 2012 and they are i) removing discontinuities by using the limits of the CES function and its derivative. ii) Circumventing large rounding errors by local linear approximations iii) Handling ill-behaved objective functions by a multi-dimensional grid search. Joel Chongeh et.al [7] discussed the estimation of the impact of capital and labour inputs to the gris output agri-food products using constant elasticity of substitution production function in Tanzanian context. Pol Antras [8] presented new estimates of the elasticity of substitution between capital and labour using data from the private sector of the U.S. economy for the period 1948-1998.

Dissecting the Impact of Matrix Anchorage and Elasticity in Cell Adhesion

PubMed Central

Pompe, Tilo; Glorius, Stefan; Bischoff, Thomas; Uhlmann, Ina; Kaufmann, Martin; Brenner, Sebastian; Werner, Carsten

2009-01-01

Abstract Extracellular matrices determine cellular fate decisions through the regulation of intracellular force and stress. Previous studies suggest that matrix stiffness and ligand anchorage cause distinct signaling effects. We show herein how defined noncovalent anchorage of adhesion ligands to elastic substrates allows for dissection of intracellular adhesion signaling pathways related to matrix stiffness and receptor forces. Quantitative analysis of the mechanical balance in cell adhesion using traction force microscopy revealed distinct scalings of the strain energy imparted by the cells on the substrates dependent either on matrix stiffness or on receptor force. Those scalings suggested the applicability of a linear elastic theoretical framework for the description of cell adhesion in a certain parameter range, which is cell-type-dependent. Besides the deconvolution of biophysical adhesion signaling, site-specific phosphorylation of focal adhesion kinase, dependent either on matrix stiffness or on receptor force, also demonstrated the dissection of biochemical signaling events in our approach. Moreover, the net contractile moment of the adherent cells and their strain energy exerted on the elastic substrate was found to be a robust measure of cell adhesion with a unifying power-law scaling exponent of 1.5 independent of matrix stiffness. PMID:19843448

The energy of naturally curved elastic rods with an application to the stretching and contraction of a free helical spring as a model for DNA.

PubMed

Manning, Gerald S

2015-09-14

We give a contemporary and direct derivation of a classical, but insufficiently familiar, result in the theory of linear elasticity-a representation for the energy of a stressed elastic rod with central axis that intrinsically takes the shape of a general space curve. We show that the geometric torsion of the space curve, while playing a crucial role in the bending energy, is physically unrelated to the elastic twist. We prove that the twist energy vanishes in the lowest-energy states of a rod subject to constraints that do not restrict the twist. The stretching and contraction energies of a free helical spring are computed. There are local high-energy minima. We show the possibility of using the spring to model the chirality of DNA. We then compare our results with an available atomic level energy simulation that was performed on DNA unconstrained in the same sense as the free spring. We find some possible reflections of springlike behavior in the mechanics of DNA, but, unsurprisingly, the base pairs lend a material substance to the core of DNA that a spring does not capture.

Nanoindentation studies of full and empty viral capsids and the effects of capsid protein mutations on elasticity and strength

NASA Astrophysics Data System (ADS)

Michel, J. P.; Ivanovska, I. L.; Gibbons, M. M.; Klug, W. S.; Knobler, C. M.; Wuite, G. J. L.; Schmidt, C. F.

2006-04-01

The elastic properties of capsids of the cowpea chlorotic mottle virus have been examined at pH 4.8 by nanoindentation measurements with an atomic force microscope. Studies have been carried out on WT capsids, both empty and containing the RNA genome, and on full capsids of a salt-stable mutant and empty capsids of the subE mutant. Full capsids resisted indentation more than empty capsids, but all of the capsids were highly elastic. There was an initial reversible linear regime that persisted up to indentations varying between 20% and 30% of the diameter and applied forces of 0.6-1.0 nN; it was followed by a steep drop in force that is associated with irreversible deformation. A single point mutation in the capsid protein increased the capsid stiffness. The experiments are compared with calculations by finite element analysis of the deformation of a homogeneous elastic thick shell. These calculations capture the features of the reversible indentation region and allow Young's moduli and relative strengths to be estimated for the empty capsids. atomic force microscopy | cowpea chlorotic mottle virus | finite element analysis | biomechanics

Buckling of an Elastic Ridge: Competition between Wrinkles and Creases

NASA Astrophysics Data System (ADS)

Lestringant, C.; Maurini, C.; Lazarus, A.; Audoly, B.

2017-04-01

We investigate the elastic buckling of a triangular prism made of a soft elastomer. A face of the prism is bonded to a stiff slab that imposes an average axial compression. We observe two possible buckling modes which are localized along the free ridge. For ridge angles ϕ below a critical value ϕ⋆≈9 0 ° , experiments reveal an extended sinusoidal mode, while for ϕ above ϕ⋆, we observe a series of creases progressively invading the lateral faces starting from the ridge. A numerical linear stability analysis is set up using the finite-element method and correctly predicts the sinusoidal mode for ϕ ≤ϕ⋆, as well as the associated critical strain ɛc(ϕ ). The experimental transition at ϕ⋆ is found to occur when this critical strain ɛc(ϕ ) attains the value ɛc(ϕ⋆)=0.44 corresponding to the threshold of the subcritical surface creasing instability. Previous analyses have focused on elastic crease patterns appearing on planar surfaces, where the role of scale invariance has been emphasized; our analysis of the elastic ridge provides a different perspective, and reveals that scale invariance is not a sufficient condition for localization.

Turbofan Volume Dynamics Model for Investigations of Aero-Propulso-Servo-Elastic Effects in a Supersonic Commercial Transport

NASA Technical Reports Server (NTRS)

Connolly, Joseph W.; Kopasakis, George; Lemon, Kimberly A.

2010-01-01

A turbofan simulation has been developed for use in aero-propulso-servo-elastic coupling studies, on supersonic vehicles. A one-dimensional lumped volume approach is used whereby each component (fan, high-pressure compressor, combustor, etc.) is represented as a single volume using characteristic performance maps and conservation equations for continuity, momentum and energy. The simulation is developed in the MATLAB/SIMULINK (The MathWorks, Inc.) environment in order to facilitate controls development, and ease of integration with a future aero-servo-elastic vehicle model being developed at NASA Langley. The complete simulation demonstrated steady state results that closely match a proposed engine suitable for a supersonic business jet at the cruise condition. Preliminary investigation of the transient simulation revealed expected trends for fuel flow disturbances as well as upstream pressure disturbances. A framework for system identification enables development of linear models for controller design. Utilizing this framework, a transfer function modeling an upstream pressure disturbance s impacts on the engine speed is developed as an illustrative case of the system identification. This work will eventually enable an overall vehicle aero-propulso-servo-elastic model

Pore cross-section area on predicting elastic properties of trabecular bovine bone for human implants.

PubMed

Maciel, Alfredo; Presbítero, Gerardo; Piña, Cristina; del Pilar Gutiérrez, María; Guzmán, José; Munguía, Nadia

2015-01-01

A clear understanding of the dependence of mechanical properties of bone remains a task not fully achieved. In order to estimate the mechanical properties in bones for implants, pore cross-section area, calcium content, and apparent density were measured in trabecular bone samples for human implants. Samples of fresh and defatted bone tissue, extracted from one year old bovines, were cut in longitudinal and transversal orientation of the trabeculae. Pore cross-section area was measured with an image analyzer. Compression tests were conducted into rectangular prisms. Elastic modulus presents a linear tendency as a function of pore cross-section area, calcium content and apparent density regardless of the trabecular orientation. The best variable to estimate elastic modulus of trabecular bone for implants was pore cross-section area, and affirmations to consider Nukbone process appropriated for marrow extraction in trabecular bone for implantation purposes are proposed, according to bone mechanical properties. Considering stress-strain curves, defatted bone is stiffer than fresh bone. Number of pores against pore cross-section area present an exponential decay, consistent for all the samples. These graphs also are useful to predict elastic properties of trabecular samples of young bovines for implants.

An elastic-plastic fracture mechanics analysis of weld-toe surface cracks in fillet welded T-butt joint

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

Fu, B.

1994-12-31

This paper describes an elastic-plastic fracture mechanics (EPFM) study of shallow weld-toe cracks. Two limiting crack configurations, plane strain edge crack and semi-circular surface crack in fillet welded T-butt plate joint, were analyzed using the finite element method. Crack depth ranging from 2 to 40% of plate thickness were considered. The elastic-plastic analysis, assuming power-law hardening relationship and Mises yield criterion, was based on incremental plasticity theory. Tension and bending loads applied were monotonically increased to a level causing relatively large scale yielding at the crack tip. Effects of weld-notch geometry and ductile material modeling on prediction of fracture mechanicsmore » characterizing parameter were assessed. It was found that the weld-notch effect reduces and the effect of material modeling increases as crack depth increases. Material modeling is less important than geometric modeling in analysis of very shallow cracks but is more important for relatively deeper cracks, e.g. crack depth more than 20% of thickness. The effect of material modeling can be assessed using a simplified structural model. Weld magnification factors derived assuming linear elastic conditions can be applied to EPFM characterization.« less

A symplectic integration method for elastic filaments

NASA Astrophysics Data System (ADS)

Ladd, Tony; Misra, Gaurav

2009-03-01

Elastic rods are a ubiquitous coarse-grained model of semi-flexible biopolymers such as DNA, actin, and microtubules. The Worm-Like Chain (WLC) is the standard numerical model for semi-flexible polymers, but it is only a linearized approximation to the dynamics of an elastic rod, valid for small deflections; typically the torsional motion is neglected as well. In the standard finite-difference and finite-element formulations of an elastic rod, the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integral over the contour of the filament. This discrete representation of the continuum filament can then be integrated by one of the explicit symplectic integrators frequently used in molecular dynamics. The model systematically approximates the continuum partial differential equations, but has the same level of computational complexity as molecular dynamics and is constraint free. Numerical tests show that the algorithm is much more stable than a finite-difference formulation and can be used for high aspect ratio filaments, such as actin. We present numerical results for the deterministic and stochastic motion of single filaments.

Development of New Elastomers and Elastic Nanocomposites from Plant Oils

NASA Astrophysics Data System (ADS)

Zhu, Lin; Wool, Richard

2006-03-01

Economic and environmental concerns lead to the development of new polymers from renewable resources. In this research, new elastomers were synthesized from plant oil based resins. Acrylated oleic methyl ester (AOME), synthesized from high oleic triglycerides, can readily undergo free radical polymerization and form a linear polymer. To achieve the elastic properties, different strategies have been developed to generate an elastic network and control the crosslink density. The elastomers are reinforced by nanoclays. The intercalated state has a network structure similar to thermoplastic elastomers in which the hard segments aggregate to give ordered crystalline domains. The selected organically modified clay and AOME matrix have similar solubility parameters, therefore intercalation of the monomer/polymer into the clay layers occurs and the nano-scale multilayered structure is stable. In situ intercalation and solution intercalation were used to prepare the elastic nanocomposites. Dramatic improvement in mechanical properties was observed. Changes of tensile strength, strain, Young's modulus and fracture energy were related to the clay concentration. The fracture surface was studied to further understand clay effects on the mechanical properties. Self-Healing of the intercalated nanobeams, thermal stability, biocompatibility and biodegradability of this new elastomer were also explored.

Analytic Intermodel Consistent Modeling of Volumetric Human Lung Dynamics.

PubMed

Ilegbusi, Olusegun; Seyfi, Behnaz; Neylon, John; Santhanam, Anand P

2015-10-01

Human lung undergoes breathing-induced deformation in the form of inhalation and exhalation. Modeling the dynamics is numerically complicated by the lack of information on lung elastic behavior and fluid-structure interactions between air and the tissue. A mathematical method is developed to integrate deformation results from a deformable image registration (DIR) and physics-based modeling approaches in order to represent consistent volumetric lung dynamics. The computational fluid dynamics (CFD) simulation assumes the lung is a poro-elastic medium with spatially distributed elastic property. Simulation is performed on a 3D lung geometry reconstructed from four-dimensional computed tomography (4DCT) dataset of a human subject. The heterogeneous Young's modulus (YM) is estimated from a linear elastic deformation model with the same lung geometry and 4D lung DIR. The deformation obtained from the CFD is then coupled with the displacement obtained from the 4D lung DIR by means of the Tikhonov regularization (TR) algorithm. The numerical results include 4DCT registration, CFD, and optimal displacement data which collectively provide consistent estimate of the volumetric lung dynamics. The fusion method is validated by comparing the optimal displacement with the results obtained from the 4DCT registration.

Analytical Solution for the Aeroelastic Response of a Two-Dimensional Elastic Plate in Axial Flow

NASA Astrophysics Data System (ADS)

Medina, Cory; Kang, Chang-Kwon

2017-11-01

The aeroelastic response of an elastic plate in an unsteady flow describes many engineering problems from bio-locomotion, deforming airfoils, to energy harvesting. However, the analysis is challenging because the shape of the plate is a priori unknown. This study presents an analytical model that can predict the two-way tightly coupled aeroelastic response of a two-dimensional elastic plate including the effects of plate curvature along the flow direction. The plate deforms due to the dynamic balance of wing inertia, elastic restoring force, and aerodynamic force. The coupled model utilizes the linearized Euler-Bernoulli beam theory for the structural model and thin airfoil theory as presented by Theodorsen, which assumes incompressible potential flow, for the aerodynamic model. The coupled equations of motion are solved via Galerkin's method, where closed form solutions for the plate deformation are obtained by deriving the unsteady aerodynamic pressure with respect to the plate normal functions, expressed in a Chebyshev polynomial expansion. Stability analysis is performed for a range of mass ratios obtaining the flutter velocities and corresponding frequencies and the results agree well with the results reported in the literature.

Stress relaxation study of fillers for directly compressed tablets

PubMed Central

Rehula, M.; Adamek, R.; Spacek, V.

2012-01-01

It is possible to assess viscoelastic properties of materials by means of the stress relaxation test. This method records the decrease in pressing power in a tablet at its constant height. The cited method was used to evaluate the time-dependent deformation for six various materials: microcrystalline cellulose, cellulose powder, hydroxypropyl methylcellulose, mannitol, lactose monohydrate, and hydrogen phosphate monohydrate. The decrease in pressing powering of a tablet during a 180 s period was described mathematically by the parameters of three exponential equations, where the whole course of the stress relaxation is divided into three individual processes (instant elastic deformation, retarded elastic deformation and permanent plastic deformation). Three values of the moduli of plasticity and elasticity were calculated for each compound. The values of elastic parameters ATi have a strong relationship with bulk density. The plastic parameters PTi represent particle tendency to form bonds. The values of plasticity in the third process PT3 ranged from 400 to 600 MPas. Mannitol had higher plasticity and lactose monohydrate on the contrary reduced plasticity. A linear relation exists between AT3 and PT3 for the third process. No similar interpretation of moduli calculated on the basis of three exponential equations has been realized yet. PMID:24850972

Wrinkles and creases in the bending, unbending and eversion of soft sectors

NASA Astrophysics Data System (ADS)

Sigaeva, Taisiya; Mangan, Robert; Vergori, Luigi; Destrade, Michel; Sudak, Les

2018-04-01

We study what is clearly one of the most common modes of deformation found in nature, science and engineering, namely the large elastic bending of curved structures, as well as its inverse, unbending, which can be brought beyond complete straightening to turn into eversion. We find that the suggested mathematical solution to these problems always exists and is unique when the solid is modelled as a homogeneous, isotropic, incompressible hyperelastic material with a strain-energy satisfying the strong ellipticity condition. We also provide explicit asymptotic solutions for thin sectors. When the deformations are severe enough, the compressed side of the elastic material may buckle and wrinkles could then develop. We analyse, in detail, the onset of this instability for the Mooney-Rivlin strain energy, which covers the cases of the neo-Hookean model in exact nonlinear elasticity and of third-order elastic materials in weakly nonlinear elasticity. In particular, the associated theoretical and numerical treatment allows us to predict the number and wavelength of the wrinkles. Guided by experimental observations, we finally look at the development of creases, which we simulate through advanced finite-element computations. In some cases, the linearized analysis allows us to predict correctly the number and the wavelength of the creases, which turn out to occur only a few per cent of strain earlier than the wrinkles.

Loss tangent and complex modulus estimated by acoustic radiation force creep and shear wave dispersion

PubMed Central

Amador, Carolina; Urban, Matthew W; Chen, Shigao; Greenleaf, James F

2012-01-01

Elasticity imaging methods have been used to study tissue mechanical properties and have demonstrated that tissue elasticity changes with disease state. In current shear wave elasticity imaging methods typically only shear wave speed is measured and rheological models, e.g., Kelvin-Voigt, Maxwell and Standard Linear Solid, are used to solve for tissue mechanical properties such as the shear viscoelastic complex modulus. This paper presents a method to quantify viscoelastic material properties in a model-independent way by estimating the complex shear elastic modulus over a wide frequency range using time-dependent creep response induced by acoustic radiation force. This radiation force induced creep (RFIC) method uses a conversion formula that is the analytic solution of a constitutive equation. The proposed method in combination with Shearwave Dispersion Ultrasound Vibrometry (SDUV) is used to measure the complex modulus so that knowledge of the applied radiation force magnitude is not necessary. The conversion formula is shown to be sensitive to sampling frequency and the first reliable measure in time according to numerical simulations using the Kelvin-Voigt model creep strain and compliance. Representative model-free shear complex moduli from homogeneous tissue mimicking phantoms and one excised swine kidney were obtained. This work proposes a novel model-free ultrasound-based elasticity method that does not require a rheological model with associated fitting requirements. PMID:22345425

Large-deformation electrohydrodynamics of an elastic capsule in a DC electric field

NASA Astrophysics Data System (ADS)

Das, Sudip; Thaokar, Rochish M.

2018-04-01

The dynamics of a spherical elastic capsule, containing a Newtonian fluid bounded by an elastic membrane and immersed in another Newtonian fluid, in a uniform DC electric field is investigated. Discontinuity of electrical properties such as conductivities of the internal and external fluid media as well as capacitance and conductance of the membrane lead to a net interfacial Maxwell stress which can cause the deformation of such an elastic capsule. We investigate this problem considering well established membrane laws for a thin elastic membrane, with fully resolved hydrodynamics in the Stokes flow limit and describe the electrostatics using the capacitor model. In the limit of small deformation, the analytical theory predicts the dynamics fairly satisfactorily. Large deformations at high capillary number though necessitate a numerical approach (Boundary element method in the present case) to solve this highly non-linear problem. Akin to vesicles, at intermediate times, highly nonlinear biconcave shapes along with squaring and hexagon like shapes are observed when the outer medium is more conducting. The study identifies the essentiality of parameters such as high membrane capacitance, low membrane conductance, low hydrodynamic time scales and high capillary number for observation of these shape transitions. The transition is due to large compressive Maxwell stress at the poles at intermediate times. Thus such shape transition can be seen in spherical globules admitting electrical capacitance, possibly, irrespective of the nature of the interfacial restoring force.

A combined application of boundary-element and Runge-Kutta methods in three-dimensional elasticity and poroelasticity

NASA Astrophysics Data System (ADS)

Igumnov, Leonid; Ipatov, Aleksandr; Belov, Aleksandr; Petrov, Andrey

2015-09-01

The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach boundary integral equations of 3-D isotropic linear theories of elasticity and poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four and five base functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods. The boundary-element method is used in combination with the collocation method, local element-by-element approximation based on the matched interpolation model. The results of analyzing wave problems of the effect of a non-stationary force on elastic and poroelastic finite bodies, a poroelastic half-space (also with a fictitious boundary) and a layered half-space weakened by a cavity, and a half-space with a trench are presented. Excitation of a slow wave in a poroelastic medium is studied, using the stepped BEM-scheme on the nodes of Runge-Kutta methods.

Serum cystatin C level is associated with carotid arterial wall elasticity in subjects with type 2 diabetes mellitus: A potential marker of early-stage atherosclerosis.

PubMed

Kaneko, Rei; Sawada, Shojiro; Tokita, Ai; Honkura, Rieko; Tamura, Noriko; Kodama, Shinjiro; Izumi, Tomohito; Takahashi, Kei; Uno, Kenji; Imai, Junta; Yamada, Tetsuya; Miyachi, Yukiya; Hasegawa, Hideyuki; Kanai, Hiroshi; Ishigaki, Yasushi; Katagiri, Hideki

2018-05-01

Detection of early-stage atherosclerosis in type 2 diabetes mellitus (T2DM) patients is important for preventing cardiovascular disease. A phased tracking method for evaluating arterial wall elasticity sensitively detects early-stage atherosclerosis. However, biochemical markers for early-stage atherosclerosis have yet to be established. This cross-sectional study enrolled 180 T2DM patients, who were classified as not having atherosclerosis according to the carotid intima-media thickness (IMT) criteria. We measured serum cystatin C, the estimated glomerular filtration rate (eGFR) and urinary albumin-to-creatinine ratio (ACR), and analyzed the associations between these markers and arterial wall elasticity (Eθ), IMT and the cardio-ankle velocity index. Multiple linear regression analyses revealed that cystatin C was significantly associated with Eθ, while neither eGFR nor ACR showed an association. Furthermore, among the examined atherosclerotic markers, Eθ was most reliably associated with cystatin C. Additionally, the association between cystatin C and Eθ disappeared in the low elasticity subgroup, which included subjects in whom no atherosclerotic changes had yet been initiated. In T2DM patients without apparent arterial wall thickening, cystatin C is strongly and independently associated with arterial wall elasticity, which reflects the degree of subclinical atherosclerosis. Thus, cystatin C is a potentially useful marker of early-stage atherosclerosis. Copyright © 2018 Elsevier B.V. All rights reserved.

Loss tangent and complex modulus estimated by acoustic radiation force creep and shear wave dispersion.

PubMed

Amador, Carolina; Urban, Matthew W; Chen, Shigao; Greenleaf, James F

2012-03-07

Elasticity imaging methods have been used to study tissue mechanical properties and have demonstrated that tissue elasticity changes with disease state. In current shear wave elasticity imaging methods typically only shear wave speed is measured and rheological models, e.g. Kelvin-Voigt, Maxwell and Standard Linear Solid, are used to solve for tissue mechanical properties such as the shear viscoelastic complex modulus. This paper presents a method to quantify viscoelastic material properties in a model-independent way by estimating the complex shear elastic modulus over a wide frequency range using time-dependent creep response induced by acoustic radiation force. This radiation force induced creep method uses a conversion formula that is the analytic solution of a constitutive equation. The proposed method in combination with shearwave dispersion ultrasound vibrometry is used to measure the complex modulus so that knowledge of the applied radiation force magnitude is not necessary. The conversion formula is shown to be sensitive to sampling frequency and the first reliable measure in time according to numerical simulations using the Kelvin-Voigt model creep strain and compliance. Representative model-free shear complex moduli from homogeneous tissue mimicking phantoms and one excised swine kidney were obtained. This work proposes a novel model-free ultrasound-based elasticity method that does not require a rheological model with associated fitting requirements.

Structural, electronic, elastic, and thermal properties of CaNiH3 perovskite obtained from first-principles calculations

NASA Astrophysics Data System (ADS)

Benlamari, S.; Bendjeddou, H.; Boulechfar, R.; Amara Korba, S.; Meradji, H.; Ahmed, R.; Ghemid, S.; Khenata, R.; Omran, S. Bin

2018-03-01

A theoretical study of the structural, elastic, electronic, mechanical, and thermal properties of the perovskite-type hydride CaNiH3 is presented. This study is carried out via first-principles full potential (FP) linearized augmented plane wave plus local orbital (LAPW+lo) method designed within the density functional theory (DFT). To treat the exchange–correlation energy/potential for the total energy calculations, the local density approximation (LDA) of Perdew–Wang (PW) and the generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) are used. The three independent elastic constants (C 11, C 12, and C 44) are calculated from the direct computation of the stresses generated by small strains. Besides, we report the variation of the elastic constants as a function of pressure as well. From the calculated elastic constants, the mechanical character of CaNiH3 is predicted. Pertaining to the thermal properties, the Debye temperature is estimated from the average sound velocity. To further comprehend this compound, the quasi-harmonic Debye model is used to analyze the thermal properties. From the calculations, we find that the obtained results of the lattice constant (a 0), bulk modulus (B 0), and its pressure derivative ({B}0^{\\prime }) are in good agreement with the available theoretical as well as experimental results. Similarly, the obtained electronic band structure demonstrates the metallic character of this perovskite-type hydride.

Hydrogen diffusion in the elastic fields of dislocations in iron

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

Sivak, A. B., E-mail: Sivak-AB@nrcki.ru; Sivak, P. A.; Romanov, V. A.

2016-12-15

The effect of dislocation stress fields on the sink efficiency thereof is studied for hydrogen interstitial atoms at temperatures of 293 and 600 K and at a dislocation density of 3 × 10{sup 14} m{sup –2} in bcc iron crystal. Rectilinear full screw and edge dislocations in basic slip systems 〈111〉(110), 〈111〉(112), 〈100〉(100), and 〈100〉(110) are considered. Diffusion of defects is simulated by means of the object kinetic Monte Carlo method. The energy of interaction between defects and dislocations is calculated using the anisotropic theory of elasticity. The elastic fields of dislocations result in a less than 25% change ofmore » the sink efficiency as compared to the noninteracting linear sink efficiency at a room temperature. The elastic fields of edge dislocations increase the dislocation sink efficiency, whereas the elastic fields of screw dislocations either decrease this parameter (in the case of dislocations with the Burgers vector being 1/2〈111〉) or do not affect it (in the case of dislocations with the Burgers vector being 〈100〉). At temperatures above 600 K, the dislocations affect the behavior of hydrogen in bcc iron mainly owing to a high binding energy between the hydrogen atom and dislocation cores.« less