Indentation of a rigid sphere into an elastic substrate with surface tension and adhesion

PubMed Central

Hui, Chung-Yuen; Liu, Tianshu; Salez, Thomas; Raphael, Elie; Jagota, Anand

2015-01-01

The surface tension of compliant materials such as gels provides resistance to deformation in addition to and sometimes surpassing that owing to elasticity. This paper studies how surface tension changes the contact mechanics of a small hard sphere indenting a soft elastic substrate. Previous studies have examined the special case where the external load is zero, so contact is driven by adhesion alone. Here, we tackle the much more complicated problem where, in addition to adhesion, deformation is driven by an indentation force. We present an exact solution based on small strain theory. The relation between indentation force (displacement) and contact radius is found to depend on a single dimensionless parameter: ω=σ(μR)−2/3((9π/4)Wad)−1/3, where σ and μ are the surface tension and shear modulus of the substrate, R is the sphere radius and Wad is the interfacial work of adhesion. Our theory reduces to the Johnson–Kendall–Roberts (JKR) theory and Young–Dupre equation in the limits of small and large ω, respectively, and compares well with existing experimental data. Our results show that, although surface tension can significantly affect the indentation force, the magnitude of the pull-off load in the partial wetting liquid-like limit is reduced only by one-third compared with the JKR limit and the pull-off behaviour is completely determined by ω. PMID:25792953

Wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes with surface and nonlocal effects

NASA Astrophysics Data System (ADS)

Zhen, Ya-Xin

2017-02-01

In this paper, the transverse wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes is investigated based on nonlocal elasticity theory with consideration of surface effect. The governing equation is formulated utilizing nonlocal Euler-Bernoulli beam theory and Kelvin-Voigt model. Explicit wave dispersion relation is developed and wave phase velocities and frequencies are obtained. The effect of the fluid flow velocity, structural damping, surface effect, small scale effects and tube diameter on the wave propagation properties are discussed with different wave numbers. The wave frequency increases with the increase of fluid flow velocity, but decreases with the increases of tube diameter and wave number. The effect of surface elasticity and residual surface tension is more significant for small wave number and tube diameter. For larger values of wave number and nonlocal parameters, the real part of frequency ratio raises.

Slip Morphology of Elastic Strips on Frictional Rigid Substrates.

PubMed

Sano, Tomohiko G; Yamaguchi, Tetsuo; Wada, Hirofumi

2017-04-28

The morphology of an elastic strip subject to vertical compressive stress on a frictional rigid substrate is investigated by a combination of theory and experiment. We find a rich variety of morphologies, which-when the bending elasticity dominates over the effect of gravity-are classified into three distinct types of states: pinned, partially slipped, and completely slipped, depending on the magnitude of the vertical strain and the coefficient of static friction. We develop a theory of elastica under mixed clamped-hinged boundary conditions combined with the Coulomb-Amontons friction law and find excellent quantitative agreement with simulations and controlled physical experiments. We also discuss the effect of gravity in order to bridge the difference in the qualitative behaviors of stiff strips and flexible strings or ropes. Our study thus complements recent work on elastic rope coiling and takes a significant step towards establishing a unified understanding of how a thin elastic object interacts vertically with a solid surface.

Closed-form nonlinear frequency of flexoelectric nanobeams with surface and nonlocal effects under closed circuit electric field

NASA Astrophysics Data System (ADS)

Barati, Mohammad Reza

2018-02-01

Nonlocal and surface effects on nonlinear vibration characteristics of a flexoelectric nanobeams under magnetic field are examined. Eringen’s nonlocal elasticity as well as surface elasticity theories are employed to describe the size-dependency of the flexoelectric nanobeam. Also, flexoelectricity is an important size-dependent phenomena for piezoelectric structures at nanoscale, related to the strain gradient-electric polarization coupling. After the derivation of governing equation via Hamilton’s principle, Galerkin method is employed to satisfy boundary conditions. Also, analytical procedures are implemented to obtain the closed-form nonlinear frequency of flexoelectric nanobeam. It is showed that magnetic field intensity, flexoelectric parameter, nonlocal parameter, elastic foundation and applied voltage on the top surface of the nanobeam have great influences on nonlinear vibration frequency.

EXPERIMENTS ON SLIP DAMPING AT ROUNDED CONTACTS

DTIC Science & Technology

SLIDING CONTACTS, *STAINLESS STEEL, DAMPING, ELASTIC PROPERTIES, FRICTION, LABORATORY EQUIPMENT, LOAD DISTRIBUTION , MANAGEMENT ENGINEERING, MEASUREMENT, OSCILLOSCOPES, SHEAR STRESSES, SPHERES, SURFACES, THEORY

Probing mesoscopic crystals with electrons: One-step simultaneous inelastic and elastic scattering theory

NASA Astrophysics Data System (ADS)

Nazarov, Vladimir U.; Silkin, Vyacheslav M.; Krasovskii, Eugene E.

2017-12-01

Inelastic scattering of the medium-energy (˜10 -100 eV) electrons underlies the method of the high-resolution electron energy-loss spectroscopy (HREELS), which has been successfully used for decades to characterize pure and adsorbate-covered surfaces of solids. With the emergence of graphene and other quasi-two-dimensional (Q2D) crystals, HREELS could be expected to become the major experimental tool to study this class of materials. We, however, identify a critical flaw in the theoretical picture of the HREELS of Q2D crystals in the context of the inelastic scattering only ("energy-loss functions" formalism), in contrast to its justifiable use for bulk solids and surfaces. The shortcoming is the neglect of the elastic scattering, which we show is inseparable from the inelastic one, and which, affecting the spectra dramatically, must be taken into account for the meaningful interpretation of the experiment. With this motivation, using the time-dependent density functional theory for excitations, we build a theory of the simultaneous inelastic and elastic electron scattering at Q2D crystals. We apply this theory to HREELS of graphene, revealing an effect of the strongly coupled excitation of the π +σ plasmon and elastic diffraction resonances. Our results open a path to the theoretically interpretable study of the excitation processes in crystalline mesoscopic materials by means of HREELS, with its supreme resolution on the meV energy scale, which is far beyond the capacity of the now overwhelmingly used EELS in transmission electron microscopy.

Dynamics of Geometrically Nonlinear Elastic Nonthin Anisotropic Shells of Variable Thickness

NASA Astrophysics Data System (ADS)

Marchuk, M. V.; Tuchapskii, R. I.

2017-11-01

A theory of dynamic elastic geometrically nonlinear deformation of nonthin anisotropic shells with variable thickness is constructed. Shells are assumed asymmetric about the reference surface. Functions are expanded into Legendre series. The basic equations are written in a coordinate system aligned with the lines of curvature of the reference surface. The equations of motion and appropriate boundary conditions are obtained using the Hamilton-Ostrogradsky variational principle. The change in metric across the thickness is taken into account. The theory assumes that the refinement process is regular and allows deriving equations including products of terms of Legendre series of unknown functions of arbitrary order. The behavior of a square metallic plate acted upon by a pressure pulse distributed over its face is studied.

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.

Dynamic energy release rate in couple-stress elasticity

NASA Astrophysics Data System (ADS)

Morini, L.; Piccolroaz, A.; Mishuris, G.

2013-07-01

This paper is concerned with energy release rate for dynamic steady state crack problems in elastic materials with microstructures. A Mode III semi-infinite crack subject to loading applied on the crack surfaces is considered. The micropolar behaviour of the material is described by the theory of couple-stress elasticity developed by Koiter. A general expression for the dynamic J-integral including both traslational and micro-rotational inertial contributions is derived, and the conservation of this integral on a path surrounding the crack tip is demonstrated.

Nuclear surface diffuseness revealed in nucleon-nucleus diffraction

NASA Astrophysics Data System (ADS)

Hatakeyama, S.; Horiuchi, W.; Kohama, A.

2018-05-01

The nuclear surface provides useful information on nuclear radius, nuclear structure, as well as properties of nuclear matter. We discuss the relationship between the nuclear surface diffuseness and elastic scattering differential cross section at the first diffraction peak of high-energy nucleon-nucleus scattering as an efficient tool in order to extract the nuclear surface information from limited experimental data involving short-lived unstable nuclei. The high-energy reaction is described by a reliable microscopic reaction theory, the Glauber model. Extending the idea of the black sphere model, we find one-to-one correspondence between the nuclear bulk structure information and proton-nucleus elastic scattering diffraction peak. This implies that we can extract both the nuclear radius and diffuseness simultaneously, using the position of the first diffraction peak and its magnitude of the elastic scattering differential cross section. We confirm the reliability of this approach by using realistic density distributions obtained by a mean-field model.

Adhesive contact of a rigid circular cylinder to a soft elastic substrate--the role of surface tension.

PubMed

Liu, Tianshu; Jagota, Anand; Hui, Chung-Yuen

2015-05-21

This article studies the effects of surface tension on the adhesive contact mechanics of a long rigid cylinder on an infinite half space comprising an incompressible elastic material. We present an exact solution based on small strain theory. The relationship between the indentation force and contact width was found to depend on a single dimensionless parameter ω = σ/[4(μR)(2/3)(W(ad)/2π)(1/3'), where R is the cylinder radius, Wad is the interfacial work of adhesion, and σ and μ are the surface tension and shear modulus of the half space, respectively. For small ω the solution reduces to the classical Johnson-Kendall-Roberts (JKR) theory, whereas for large ω the solution reduces to the small slope version of the Young-Dupre equation. The pull-off phenomenon was carefully examined and it was found that the contact width at pull-off reduces to zero when surface tension is larger than a critical value.

Surface acoustic admittance of highly porous open-cell, elastic foams

NASA Technical Reports Server (NTRS)

Lambert, R. F.

1983-01-01

This work presents a comprehensive study of the surface acoustic admittance properties of graded sizes of open-cell foams that are highly porous and elastic. The intrinsic admittance as well as properties of samples of finite depth were predicted and then measured for sound at normal incidence over a frequency range extending from about 35-3500 Hz. The agreement between theory and experiment for a range of mean pore size and volume porosity is excellent. The implications of fibrous structure on the admittance of open-cell foams is quite evident from the results.

Elasto-dynamic analysis of spinning nanodisks via a surface energy-based model

NASA Astrophysics Data System (ADS)

Kiani, Keivan

2016-07-01

Using the surface elasticity theory of Gurtin and Murdoch, in-plane vibrations of annular nanodisks due to their rotary motion are explored. By the imposition of non-classical boundary conditions on the innermost and outermost surfaces and employing Hamilton’s principle, the unknown elasto-dynamic fields of the bulk zone are determined via the finite element method. The roles of both nanodisk geometry and surface effect on the natural frequencies are addressed. Subsequently, forced vibrations of spinning nanodisks with fixed-free and free-free boundary conditions are comprehensively examined. The obtained results show that the maximum dynamic elastic fields grow in a parabolic manner as the steady angular velocity increases. By increasing the outermost radius, the maximum dynamic elastic field is magnified and the influence of the surface effect on the results reduced. This work can be considered as a pivotal step towards optimal design and dynamic analysis of nanorotors with disk-like parts, which are one of the basic building blocks of the upcoming advanced nanotechnologies.

Computing the Dynamic Response of a Stratified Elastic Half Space Using Diffuse Field Theory

NASA Astrophysics Data System (ADS)

Sanchez-Sesma, F. J.; Perton, M.; Molina Villegas, J. C.

2015-12-01

The analytical solution for the dynamic response of an elastic half-space for a normal point load at the free surface is due to Lamb (1904). For a tangential force, we have Chaós (1960) formulae. For an arbitrary load at any depth within a stratified elastic half space, the resulting elastic field can be given in the same fashion, by using an integral representation in the radial wavenumber domain. Typically, computations use discrete wave number (DWN) formalism and Fourier analysis allows for solution in space and time domain. Experimentally, these elastic Greeńs functions might be retrieved from ambient vibrations correlations when assuming a diffuse field. In fact, the field could not be totally diffuse and only parts of the Green's functions, associated to surface or body waves, are retrieved. In this communication, we explore the computation of Green functions for a layered media on top of a half-space using a set of equipartitioned elastic plane waves. Our formalism includes body and surface waves (Rayleigh and Love waves). These latter waves correspond to the classical representations in terms of normal modes in the asymptotic case of large separation distance between source and receiver. This approach allows computing Green's functions faster than DWN and separating the surface and body wave contributions in order to better represent Green's function experimentally retrieved.

Studying the influence of surface effects on vibration behavior of size-dependent cracked FG Timoshenko nanobeam considering nonlocal elasticity and elastic foundation

NASA Astrophysics Data System (ADS)

Ghadiri, Majid; Soltanpour, Mahdi; Yazdi, Ali; Safi, Mohsen

2016-05-01

Free transverse vibration of a size-dependent cracked functionally graded (FG) Timoshenko nanobeam resting on a polymer elastic foundation is investigated in the present study. Also, all of the surface effects: surface density, surface elasticity and residual surface tension are studied. Moreover, satisfying the balance condition between the nanobeam and its surfaces was discussed. According to the power-law distribution, it is supposed that the material properties of the FG nanobeam are varying continuously across the thickness. Considering the small-scale effect, the Eringen's nonlocal theory is used; accounting the effect of polymer elastic foundation, the Winkler model is proposed. For this purpose, the equations of motion of the FG Timoshenko nanobeam and boundary conditions are obtained using Hamilton's principle. To find the analytical solutions for equations of motion of the FG nanobeam, the separation of variables method is employed. Two cases of boundary conditions, i.e., simply supported-simply supported (SS) and clamped-clamped (CC) are investigated in the present work. Numerical results are demonstrating a good agreement between the results of the present study and some available cases in the literature. The emphasis of the present study is on investigating the effect of various parameters such as crack severity, crack position, gradient index, mode number, nonlocal parameter, elastic foundation parameter and nanobeam length. It is clearly revealed that the vibrational behavior of a FG nanobeam is depending significantly on these effects. Also, these numerical results can be serving as benchmarks for future studies of FG nanobeams.

On the diffusion and self-trapping of surface dimers

NASA Astrophysics Data System (ADS)

Kappus, W.

The theory of elastic interactions between surface atoms which are caused by substrate strains is applied to the interaction of dimers on the (211) surface of tungsten. From the comparison of theoretical and experimental interactions which were derived from the diffusion behaviour of dimers, conclusions are drawn on the nature of the adatom-substrate bond.

On the diffusion and self-trapping of surface dimers

NASA Astrophysics Data System (ADS)

Kappus, W.

1982-03-01

The theory of elastic interactions between surface atoms which are caused by substrate strains is applied to the interaction of dimers on the (211) surface of tungsten. From the comparison of theoretical and experimental interactions which were derived from the diffusion behaviour of dimers, conclusions are drawn on the nature of the adatom-substrate bond.

Elasticity Dominated Surface Segregation of Small Molecules in Polymer Mixtures

NASA Astrophysics Data System (ADS)

Krawczyk, Jarosław; Croce, Salvatore; McLeish, T. C. B.; Chakrabarti, Buddhapriya

2016-05-01

We study the phenomenon of migration of the small molecular weight component of a binary polymer mixture to the free surface using mean field and self-consistent field theories. By proposing a free energy functional that incorporates polymer-matrix elasticity explicitly, we compute the migrant volume fraction and show that it decreases significantly as the sample rigidity is increased. A wetting transition, observed for high values of the miscibility parameter can be prevented by increasing the matrix rigidity. Estimated values of the bulk modulus suggest that the effect should be observable experimentally for rubberlike materials. This provides a simple way of controlling surface migration in polymer mixtures and can play an important role in industrial formulations, where surface migration often leads to decreased product functionality.

Interaction potential for indium phosphide: a molecular dynamics and first-principles study of the elastic constants, generalized stacking fault and surface energies.

PubMed

Branicio, Paulo Sergio; Rino, José Pedro; Gan, Chee Kwan; Tsuzuki, Hélio

2009-03-04

Indium phosphide is investigated using molecular dynamics (MD) simulations and density-functional theory calculations. MD simulations use a proposed effective interaction potential for InP fitted to a selected experimental dataset of properties. The potential consists of two- and three-body terms that represent atomic-size effects, charge-charge, charge-dipole and dipole-dipole interactions as well as covalent bond bending and stretching. Predictions are made for the elastic constants as a function of density and temperature, the generalized stacking fault energy and the low-index surface energies.

Requirements for energy based constitutive modeling in tire mechanics

NASA Technical Reports Server (NTRS)

Luchini, John R.; Peters, Jim M.; Mars, Will V.

1995-01-01

The history, requirements, and theoretical basis of a new energy based constitutive model for (rubber) material elasticity, hysteresis, and failure are presented. Energy based elasticity is handled by many constitutive models, both in one dimension and in three dimensions. Conversion of mechanical energy to heat can be modeled with viscoelasticity or as structural hysteresis. We are seeking unification of elasticity, hysteresis, and failure mechanisms such as fatigue and wear. An energy state characterization for failure criteria of (rubber) materials may provide this unification and also help explain the interaction of temperature effects with failure mechanisms which are described as creation of growth of internal crack surface. Improved structural modeling of tires with FEM should result from such a unified constitutive theory. The theory will also guide experimental work and should enable better interpretation of the results of computational stress analyses.

Wetting and phase separation in soft adhesion

PubMed Central

Jensen, Katharine E.; Sarfati, Raphael; Style, Robert W.; Boltyanskiy, Rostislav; Chakrabarti, Aditi; Chaudhury, Manoj K.; Dufresne, Eric R.

2015-01-01

In the classic theory of solid adhesion, surface energy drives deformation to increase contact area whereas bulk elasticity opposes it. Recently, solid surface stress has been shown also to play an important role in opposing deformation of soft materials. This suggests that the contact line in soft adhesion should mimic that of a liquid droplet, with a contact angle determined by surface tensions. Consistent with this hypothesis, we observe a contact angle of a soft silicone substrate on rigid silica spheres that depends on the surface functionalization but not the sphere size. However, to satisfy this wetting condition without a divergent elastic stress, the gel phase separates from its solvent near the contact line. This creates a four-phase contact zone with two additional contact lines hidden below the surface of the substrate. Whereas the geometries of these contact lines are independent of the size of the sphere, the volume of the phase-separated region is not, but rather depends on the indentation volume. These results indicate that theories of adhesion of soft gels need to account for both the compressibility of the gel network and a nonzero surface stress between the gel and its solvent. PMID:26553989

Propagation of Love waves with surface effects in an electrically-shorted piezoelectric nanofilm on a half-space elastic substrate.

PubMed

Zhang, Sijia; Gu, Bin; Zhang, Hongbin; Feng, Xi-Qiao; Pan, Rongying; Alamusi; Hu, Ning

2016-03-01

The propagation of Love waves in the structure consisting of a nanosized piezoelectric film and a semi-infinite elastic substrate is investigated in the present paper with the consideration of surface effects. In our analysis, surface effects are taken into account in terms of the surface elasticity theory and the electrically-shorted conditions are adopted on the free surface of the piezoelectric film and the interface between the film and the substrate. This work focuses on the new features in the dispersion relations of different modes due to surface effects. It is found that with the existence of surface effects, the frequency dispersion of Love waves shows the distinct dependence on the thickness and the surface constants when the film thickness reduces to nanometers. In general, phase velocities of all dispersion modes increase with the decrease of the film thickness and the increase of the surface constants. However, surface effects play different functions in the frequency dispersions of different modes, especially for the first mode dispersion. Moreover, different forms of Love waves are observed in the first mode dispersion, depending on the presence of the surface effects on the surface and the interface. Copyright © 2015 Elsevier B.V. All rights reserved.

On multiscale moving contact line theory.

PubMed

Li, Shaofan; Fan, Houfu

2015-07-08

In this paper, a multiscale moving contact line (MMCL) theory is presented and employed to simulate liquid droplet spreading and capillary motion. The proposed MMCL theory combines a coarse-grained adhesive contact model with a fluid interface membrane theory, so that it can couple molecular scale adhesive interaction and surface tension with hydrodynamics of microscale flow. By doing so, the intermolecular force, the van der Waals or double layer force, separates and levitates the liquid droplet from the supporting solid substrate, which avoids the shear stress singularity caused by the no-slip condition in conventional hydrodynamics theory of moving contact line. Thus, the MMCL allows the difference of the surface energies and surface stresses to drive droplet spreading naturally. To validate the proposed MMCL theory, we have employed it to simulate droplet spreading over various elastic substrates. The numerical simulation results obtained by using MMCL are in good agreement with the molecular dynamics results reported in the literature.

On actions for (entangling) surfaces and DCFTs

NASA Astrophysics Data System (ADS)

Armas, Jay; Tarrío, Javier

2018-04-01

The dynamics of surfaces and interfaces describe many physical systems, including fluid membranes, entanglement entropy and the coupling of defects to quantum field theories. Based on the formulation of submanifold calculus developed by Carter, we introduce a new variational principle for (entangling) surfaces. This principle captures all diffeomorphism constraints on surface/interface actions and their associated spacetime stress tensor. The different couplings to the geometric tensors appearing in the surface action are interpreted in terms of response coefficients within elasticity theory. An example of a surface action with edges at the two-derivative level is studied, including both the parity-even and parity-odd sectors. Its conformally invariant counterpart restricts the type of conformal anomalies that can appear in two-dimensional submanifolds with boundaries. Analogously to hydrodynamics, it is shown that classification methods can be used to constrain the stress tensor of (entangling) surfaces at a given order in derivatives. This analysis reveals a purely geometric parity-odd contribution to the Young modulus of a thin elastic membrane. Extending this novel variational principle to BCFTs and DCFTs in curved spacetimes allows to obtain the Ward identities for diffeomorphism and Weyl transformations. In this context, we provide a formal derivation of the contact terms in the stress tensor and of the displacement operator for a broad class of actions.

Continuum elastic theory for dynamics of surfaces and interfaces

NASA Astrophysics Data System (ADS)

Pykhtin, Michael V.

This thesis is divided into three parts, different by problems they deal with, but similar by underlying assumptions (crystals are treated as classical elastic anisotropic media) and methods of solving (vibrational Green's functions). (i) In the first part we compute the density of vibrational modes for a vicinal Ni(977) surface. In the spectrum we find new step induced modes which are compared with recently reported experimental data for Ni(977) surface obtained by inelastic atom scattering. (ii) In the second part we study damping of low-frequency adsorbate vibrations via resonant coupling to the substrate phonons. Our theory provides a general expression for the vibrational damping rate which can be applied to widely varying coverages and arbitrary overlayer structures. The damping rates predicted by our theory for CO on Cu(100) are in excellent quantitative agreement with available experimental data. (iii) In the third part we develop a theory for the density of vibrational modes at the surface of a thin film of one anisotropic solid an on top of the other. We compute the density of modes for a GaN film on a sapphire substrate for a wide range of wavevector and frequency, and obtain dispersion maps which contain waves trapped between the surface of the film and the interface. Two families of the trapped modes were observed: Love waves and generalized Lamb waves. We also study the effect of threading edge dislocations (majority of defects in the GaN film) on the trapped modes. At the experimental dislocation density the effect is negligible.

The contact sport of rough surfaces

NASA Astrophysics Data System (ADS)

Carpick, Robert W.

2018-01-01

Describing the way two surfaces touch and make contact may seem simple, but it is not. Fully describing the elastic deformation of ideally smooth contacting bodies, under even low applied pressure, involves second-order partial differential equations and fourth-rank elastic constant tensors. For more realistic rough surfaces, the problem becomes a multiscale exercise in surface-height statistics, even before including complex phenomena such as adhesion, plasticity, and fracture. A recent research competition, the “Contact Mechanics Challenge” (1), was designed to test various approximate methods for solving this problem. A hypothetical rough surface was generated, and the community was invited to model contact with this surface with competing theories for the calculation of properties, including contact area and pressure. A supercomputer-generated numerical solution was kept secret until competition entries were received. The comparison of results (2) provides insights into the relative merits of competing models and even experimental approaches to the problem.

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

Contribution to the theory of tidal oscillations of an elastic earth. External tidal potential

NASA Technical Reports Server (NTRS)

Musen, P.

1974-01-01

The differential equations of the tidal oscillations of the earth were established under the assumption that the interior of the earth is laterally inhomogeneous. The theory was developed using vectorial and dyadic symbolism to shorten the exposition and to reduce the differential equations to a symmetric form convenient for programming and for numerical integration. The formation of tidal buldges on the surfaces of discontinuity and the changes in the internal density produce small periodic variations in the exterior geopotential which are reflected in the motion of artificial satellites. The analoques of Love elastic parameters in the expansion of exterior tidal potential reflect the asymmetric and inhomogeneous structure of the interior of the earth.

An Experimental Study of Incremental Surface Loading of an Elastic Plate: Application to Volcano Tectonics

NASA Technical Reports Server (NTRS)

Williams, K. K.; Zuber, M. T.

1995-01-01

Models of surface fractures due to volcanic loading an elastic plate are commonly used to constrain thickness of planetary lithospheres, but discrepancies exist in predictions of the style of initial failure and in the nature of subsequent fracture evolution. In this study, we perform an experiment to determine the mode of initial failure due to the incremental addition of a conical load to the surface of an elastic plate and compare the location of initial failure with that predicted by elastic theory. In all experiments, the mode of initial failure was tension cracking at the surface of the plate, with cracks oriented circumferential to the load. The cracks nucleated at a distance from load center that corresponds the maximum radial stress predicted by analytical solutions, so a tensile failure criterion is appropriate for predictions of initial failure. With continued loading of the plate, migration of tensional cracks was observed. In the same azimuthal direction as the initial crack, subsequent cracks formed at a smaller radial distance than the initial crack. When forming in a different azimuthal direction, the subsequent cracks formed at a distance greater than the radial distance of the initial crack. The observed fracture pattern may explain the distribution of extensional structures in annular bands around many large scale, circular volcanic features.

Finsler geometry of nonlinear elastic solids with internal structure

NASA Astrophysics Data System (ADS)

Clayton, J. D.

2017-02-01

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

Elasticity dominated surface segregation of small molecules in polymer mixtures

NASA Astrophysics Data System (ADS)

Croce, Salvatore; Krawczyk, Jaroslaw; McLeish, Tom; Chakrabarti, Buddhapriya

When a binary polymer mixture with mobile components is left to equilibrate, the low molecular weight component migrates to the free surface. A balance between loss of translational entropy and gain in surface energy dictates the equilibrium partitioning ratio and the migrant fraction. Despite its ubiquity and several theoretical and experimental investigations, the phenomenon is not fully understood. Further, methods by which migration can be controlled are in its nascent stage of development. We propose a new phenomenological free energy functional that incorporates the elasticity of bulk polymer mixtures (reticulated networks and gels) and show (using mean field and self-consistent field theories) that the migrant fraction decreases with increasing the bulk modulus of the system. Further, a wetting transition observed otherwise for large values of miscibility parameter and polymerization index can be avoided by increasing the elastic modulus of the system. Estimated values of moduli (for the effect to be observable) are akin to those of rubbery polymers. Our work paves the way for controlling surface migration in complex industrial formulations with polymeric ingredients where this effect leads to decreased product stability and performance.

Optimum Design of a Helicopter Rotor for Low Vibration Using Aeroelastic Analysis and Response Surface Methods

NASA Astrophysics Data System (ADS)

Ganguli, R.

2002-11-01

An aeroelastic analysis based on finite elements in space and time is used to model the helicopter rotor in forward flight. The rotor blade is represented as an elastic cantilever beam undergoing flap and lag bending, elastic torsion and axial deformations. The objective of the improved design is to reduce vibratory loads at the rotor hub that are the main source of helicopter vibration. Constraints are imposed on aeroelastic stability, and move limits are imposed on the blade elastic stiffness design variables. Using the aeroelastic analysis, response surface approximations are constructed for the objective function (vibratory hub loads). It is found that second order polynomial response surfaces constructed using the central composite design of the theory of design of experiments adequately represents the aeroelastic model in the vicinity of the baseline design. Optimization results show a reduction in the objective function of about 30 per cent. A key accomplishment of this paper is the decoupling of the analysis problem and the optimization problems using response surface methods, which should encourage the use of optimization methods by the helicopter industry.

Mesoscale studies of ionic closed membranes with polyhedral geometries

DOE PAGES

Olvera de la Cruz, Monica

2016-06-01

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

New theory for Mode I crack-tip dislocation emission

NASA Astrophysics Data System (ADS)

Andric, Predrag; Curtin, W. A.

2017-09-01

A material is intrinsically ductile under Mode I loading when the critical stress intensity KIe for dislocation emission is lower than the critical stress intensity KIc for cleavage. KIe is usually evaluated using the approximate Rice theory, which predicts a dependence on the elastic constants and the unstable stacking fault energy γusf for slip along the plane of dislocation emission. Here, atomistic simulations across a wide range of fcc metals show that KIe is systematically larger (10-30%) than predicted. However, the critical (crack tip) shear displacement is up to 40% smaller than predicted. The discrepancy arises because Mode I emission is accompanied by the formation of a surface step that is not considered in the Rice theory. A new theory for Mode I emission is presented based on the ideas that (i) the stress resisting step formation at the crack tip creates "lattice trapping" against dislocation emission such that (ii) emission is due to a mechanical instability at the crack tip. The new theory is formulated using a Peierls-type model, naturally includes the energy to form the step, and reduces to the Rice theory (no trapping) when the step energy is small. The new theory predicts a higher KIe at a smaller critical shear displacement, rationalizing deviations of simulations from the Rice theory. Specific predictions of KIe for the simulated materials, usually requiring use of the measured critical crack tip shear displacement due to complex material non-linearity, show very good agreement with simulations. An analytic model involving only γusf, the surface energy γs, and anisotropic elastic constants is shown to be quite accurate, serves as a replacement for the analytical Rice theory, and is used to understand differences between Rice theory and simulation in recent literature. The new theory highlights the role of surface steps created by dislocation emission in Mode I, which has implications not only for intrinsic ductility but also for crack tip twinning and fracture due to chemical interactions at the crack tip.

Nonlinear fractional waves at elastic interfaces

NASA Astrophysics Data System (ADS)

Kappler, Julian; Shrivastava, Shamit; Schneider, Matthias F.; Netz, Roland R.

2017-11-01

We derive the nonlinear fractional surface wave equation that governs compression waves at an elastic interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective thickness of the bulk layer that is coupled to the interface is frequency dependent. The nonlinearity arises from the nonlinear dependence of the interface compressibility on the local compression, which is obtained from experimental measurements and reflects a phase transition at the interface. Numerical solutions of our nonlinear fractional theory reproduce several experimental key features of surface waves in phospholipid monolayers at the air-water interface without freely adjustable fitting parameters. In particular, the propagation distance of the surface wave abruptly increases at a threshold excitation amplitude. The wave velocity is found to be of the order of 40 cm/s in both experiments and theory and slightly increases as a function of the excitation amplitude. Nonlinear acoustic switching effects in membranes are thus shown to arise purely based on intrinsic membrane properties, namely, the presence of compressibility nonlinearities that accompany phase transitions at the interface.

Roughening of surfaces under intense and rapid heating

NASA Astrophysics Data System (ADS)

Andersen, Michael Louis

The High Average Power Laser (HAPL) project is aimed at a chamber design with a solid first wall in pursuit of sustained Laser Inertial Confinement Fusion. The wall must be able to withstand cyclic high temperatures and the corresponding thermal stresses. Tungsten was proposed as a suitable armor for the wall, because as a refractory metal, it has a high melting temperature and can act as a stress dampener. The nature of the surface loading consists of x-rays, ions, and neutrons, which through mainly thermal loading, create a biaxial surface stress. This condition causes the surface to roughen as ridges and valleys form to relieve the elastic energy. As the valleys deepen they eventually become cracks and traditional fracture mechanics can be used to determine the life of the first wall. Beginning from the Asaro-Tiller-Grinfeld instability, sharp interface calculations can be performed to determine the surface profile as a result of the interplay between surface stress energy and mass transport mechanisms. One successful approach to determine interface evolution is phase field theory and its embodiment in the numerical level-set method. Applications of the method included problems of solid/liquid and solid/vapor interfaces. In the present method, however, we develop a numerical procedure for surface profile tracking directly without the need to develop partial differential equations for the phase field, which typically smooth out sharp interfaces. Surface roughening instabilities, which are driven by a competition between elastic and surface energy contributions, are shown to be significantly controlled by plastic energy dissipation. We consider here a general parametric description of the surface of a stressed solid and through a mechanical kinetic transport mechanism, follow the temporal evolution of the surface morphology. It is found that once a groove reaches a certain depth and curvature, an instability is created that cannot be followed through elasticity alone. It is shown in this thesis that these morphological instabilities do not experience unbounded growth, as predicted by consideration of elastic energy alone, and that their growth will be severely limited by dislocation emission from high curvature grooves. Comparisons between perturbation theory and the present numerical approach are given along with comparisons to results from laser, ion, and x-ray experiments. Finally, the model is applied to the conditions of Inertial Confinement Fusion chamber walls to determine the number of cycles for crack nucleation.

Nematic elastomers: from a microscopic model to macroscopic elasticity theory.

PubMed

Xing, Xiangjun; Pfahl, Stephan; Mukhopadhyay, Swagatam; Goldbart, Paul M; Zippelius, Annette

2008-05-01

A Landau theory is constructed for the gelation transition in cross-linked polymer systems possessing spontaneous nematic ordering, based on symmetry principles and the concept of an order parameter for the amorphous solid state. This theory is substantiated with help of a simple microscopic model of cross-linked dimers. Minimization of the Landau free energy in the presence of nematic order yields the neoclassical theory of the elasticity of nematic elastomers and, in the isotropic limit, the classical theory of isotropic elasticity. These phenomenological theories of elasticity are thereby derived from a microscopic model, and it is furthermore demonstrated that they are universal mean-field descriptions of the elasticity for all chemical gels and vulcanized media.

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.

Magnetorheological elastic super-smooth finishing for high-efficiency manufacturing of ultraviolet laser resistant optics

NASA Astrophysics Data System (ADS)

Shi, Feng; Shu, Yong; Dai, Yifan; Peng, Xiaoqiang; Li, Shengyi

2013-07-01

Based on the elastic-plastic deformation theory, status between abrasives and workpiece in magnetorheological finishing (MRF) process and the feasibility of elastic polishing are analyzed. The relationship among material removal mechanism and particle force, removal efficiency, and surface topography are revealed through a set of experiments. The chemical dominant elastic super-smooth polishing can be fulfilled by changing the components of magnetorheological (MR) fluid and optimizing polishing parameters. The MR elastic super-smooth finishing technology can be applied in polishing high-power laser-irradiated components with high efficiency, high accuracy, low damage, and high laser-induced damage threshold (LIDT). A 430×430×10 mm fused silica (FS) optic window is polished and surface error is improved from 538.241 nm [peak to valley (PV)], 96.376 nm (rms) to 76.372 nm (PV), 8.295 nm (rms) after 51.6 h rough polishing, 42.6 h fine polishing, and 54.6 h super-smooth polishing. A 50×50×10 mm sample is polished with exactly the same parameters. The roughness is improved from 1.793 nm [roughness average (Ra)] to 0.167 nm (Ra) and LIDT is improved from 9.77 to 19.2 J/cm2 after MRF elastic polishing.

Development of a nonlinear unsteady transonic flow theory

NASA Technical Reports Server (NTRS)

Stahara, S. S.; Spreiter, J. R.

1973-01-01

A nonlinear, unsteady, small-disturbance theory capable of predicting inviscid transonic flows about aerodynamic configurations undergoing both rigid body and elastic oscillations was developed. The theory is based on the concept of dividing the flow into steady and unsteady components and then solving, by method of local linearization, the coupled differential equation for unsteady surface pressure distribution. The equations, valid at all frequencies, were derived for two-dimensional flows, numerical results, were obtained for two classses of airfoils and two types of oscillatory motions.

An IBEM solution to the scattering of plane SH-waves by a lined tunnel in elastic wedge space

NASA Astrophysics Data System (ADS)

Liu, Zhongxian; Liu, Lei

2015-02-01

The indirect boundary element method (IBEM) is developed to solve the scattering of plane SH-waves by a lined tunnel in elastic wedge space. According to the theory of single-layer potential, the scattered-wave field can be constructed by applying virtual uniform loads on the surface of lined tunnel and the nearby wedge surface. The densities of virtual loads can be solved by establishing equations through the continuity conditions on the interface and zero-traction conditions on free surfaces. The total wave field is obtained by the superposition of free field and scattered-wave field in elastic wedge space. Numerical results indicate that the IBEM can solve the diffraction of elastic wave in elastic wedge space accurately and efficiently. The wave motion feature strongly depends on the wedge angle, the angle of incidence, incident frequency, the location of lined tunnel, and material parameters. The waves interference and amplification effect around the tunnel in wedge space is more significant, causing the dynamic stress concentration factor on rigid tunnel and the displacement amplitude of flexible tunnel up to 50.0 and 17.0, respectively, more than double that of the case of half-space. Hence, considerable attention should be paid to seismic resistant or anti-explosion design of the tunnel built on a slope or hillside.

Comparison of the Modified Biot-Gassmann Theory and the Kuster-Toksoz Theory in Predicting Elastic Velocities of Sediments

USGS Publications Warehouse

Lee, Myung W.

2008-01-01

Elastic velocities of water-saturated sandstones depend primarily on porosity, effective pressure, and the degree of consolidation. If the dry-frame moduli are known, from either measurements or theoretical calculations, the effect of pore water on velocities can be modeled using the Gassmann theory. Kuster and Toksoz developed a theory based on wave-scattering theory for a variety of inclusion shapes, which provides a means for calculating dry- or wet-frame moduli. In the Kuster-Toksoz theory, elastic wave velocities through different sediments can be predicted by using different aspect ratios of the sediment's pore space. Elastic velocities increase as the pore aspect ratio increases (larger pore aspect ratio describes a more spherical pore). On the basis of the velocity ratio, which is assumed to be a function of (1-0)n, and the Biot-Gassmann theory, Lee developed a semi-empirical equation for predicting elastic velocities, which is referred to as the modified Biot-Gassmann theory of Lee. In this formulation, the exponent n, which depends on the effective pressure and the degree of consolidation, controls elastic velocities; as n increases, elastic velocities decrease. Computationally, the role of exponent n in the modified Biot-Gassmann theory by Lee is similar to the role of pore aspect ratios in the Kuster-Toksoz theory. For consolidated sediments, either theory predicts accurate velocities. However, for unconsolidated sediments, the modified Biot-Gassmann theory by Lee performs better than the Kuster-Toksoz theory, particularly in predicting S-wave velocities.

Nonlinear softening of unconsolidated granular earth materials

NASA Astrophysics Data System (ADS)

Lieou, Charles K. C.; Daub, Eric G.; Guyer, Robert A.; Johnson, Paul A.

2017-09-01

Unconsolidated granular earth materials exhibit softening behavior due to external perturbations such as seismic waves, namely, the wave speed and elastic modulus decrease upon increasing the strain amplitude above dynamics strains of about 10-6 under near-surface conditions. In this letter, we describe a theoretical model for such behavior. The model is based on the idea that shear transformation zones—clusters of grains that are loose and susceptible to contact changes, particle displacement, and rearrangement—are responsible for plastic deformation and softening of the material. We apply the theory to experiments on simulated fault gouge composed of glass beads and demonstrate that the theory predicts nonlinear resonance shifts, reduction of the P wave modulus, and attenuation, in agreement with experiments. The theory thus offers insights on the nature of nonlinear elastic properties of a granular medium and potentially into phenomena such as triggering on earthquake faults.

Spatial buckling analysis of current-carrying nanowires in the presence of a longitudinal magnetic field accounting for both surface and nonlocal effects

NASA Astrophysics Data System (ADS)

Foroutan, Shahin; Haghshenas, Amin; Hashemian, Mohammad; Eftekhari, S. Ali; Toghraie, Davood

2018-03-01

In this paper, three-dimensional buckling behavior of nanowires was investigated based on Eringen's Nonlocal Elasticity Theory. The electric current-carrying nanowires were affected by a longitudinal magnetic field based upon the Lorentz force. The nanowires (NWs) were modeled based on Timoshenko beam theory and the Gurtin-Murdoch's surface elasticity theory. Generalized Differential Quadrature (GDQ) method was used to solve the governing equations of the NWs. Two sets of boundary conditions namely simple-simple and clamped-clamped were applied and the obtained results were discussed. Results demonstrated the effect of electric current, magnetic field, small-scale parameter, slenderness ratio, and nanowires diameter on the critical compressive buckling load of nanowires. As a key result, increasing the small-scale parameter decreased the critical load. By the same token, increasing the electric current, magnetic field, and slenderness ratio resulted in a decrease in the critical load. As the slenderness ratio increased, the effect of nonlocal theory decreased. In contrast, by expanding the NWs diameter, the nonlocal effect increased. Moreover, in the present article, the critical values of the magnetic field of strength and slenderness ratio were revealed, and the roles of the magnetic field, slenderness ratio, and NWs diameter on higher buckling loads were discussed.

Alignment of nematic liquid crystals by inhomogeneous surfaces

NASA Astrophysics Data System (ADS)

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

1985-01-01

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

Characterizing crustal and uppermost mantle anisotropy with a depth-dependent tilted hexagonally symmetric elastic tensor: theory and examples

NASA Astrophysics Data System (ADS)

Feng, L.; Xie, J.; Ritzwoller, M. H.

2017-12-01

Two major types of surface wave anisotropy are commonly observed by seismologists but are only rarely interpreted jointly: apparent radial anisotropy, which is the difference in propagation speed between horizontally and vertically polarized waves inferred from Love and Rayleigh waves, and apparent azimuthal anisotropy, which is the directional dependence of surface wave speeds (usually Rayleigh waves). We describe a method of inversion that interprets simultaneous observations of radial and azimuthal anisotropy under the assumption of a hexagonally symmetric elastic tensor with a tilted symmetry axis defined by dip and strike angles. With a full-waveform numerical solver based on the spectral element method (SEM), we verify the validity of the forward theory used for the inversion. We also present two examples, in the US and Tibet, in which we have successfully applied the tomographic method to demonstrate that the two types of apparent anisotropy can be interpreted jointly as a tilted hexagonally symmetric medium.

Elastic thickness determination based on Vening Meinesz-Moritz and flexural theories of isostasy

NASA Astrophysics Data System (ADS)

Eshagh, Mehdi

2018-06-01

Elastic thickness (Te) is one of mechanical properties of the Earth's lithosphere. The lithosphere is assumed to be a thin elastic shell, which is bended under the topographic, bathymetric and sediment loads on. The flexure of this elastic shell depends on its thickness or Te. Those shells having larger Te flex less. In this paper, a forward computational method is presented based on the Vening Meinesz-Moritz (VMM) and flexural theories of isostasy. Two Moho flexure models are determined using these theories, considering effects of surface and subsurface loads. Different values are selected for Te in the flexural method to see by which one, the closest Moho flexure to that of the VMM is achieved. The effects of topographic/bathymetric, sediments and crustal crystalline masses, and laterally variable upper mantle density, Young's modulus and Poisson's ratio are considered in whole computational process. Our mathematical derivations are based on spherical harmonics, which can be used to estimate Te at any single point, meaning that there is no edge effect in the method. However, the Te map needs to be filtered to remove noise at some points. A median filter with a window size of 5° × 5° and overlap of 4° works well for this purpose. The method is applied to estimate Te over South America using the data of CRUST1.0 and a global gravity model.

Elastic strain relaxation in interfacial dislocation patterns: I. A parametric energy-based framework

NASA Astrophysics Data System (ADS)

Vattré, A.

2017-08-01

A parametric energy-based framework is developed to describe the elastic strain relaxation of interface dislocations. By means of the Stroh sextic formalism with a Fourier series technique, the proposed approach couples the classical anisotropic elasticity theory with surface/interface stress and elasticity properties in heterogeneous interface-dominated materials. For any semicoherent interface of interest, the strain energy landscape is computed using the persistent elastic fields produced by infinitely periodic hexagonal-shaped dislocation configurations with planar three-fold nodes. A finite element based procedure combined with the conjugate gradient and nudged elastic band methods is applied to determine the minimum-energy paths for which the pre-computed energy landscapes yield to elastically favorable dislocation reactions. Several applications on the Au/Cu heterosystems are given. The simple and limiting case of a single set of infinitely periodic dislocations is introduced to determine exact closed-form expressions for stresses. The second limiting case of the pure (010) Au/Cu heterophase interfaces containing two crossing sets of straight dislocations investigates the effects due to the non-classical boundary conditions on the stress distributions, including separate and appropriate constitutive relations at semicoherent interfaces and free surfaces. Using the quantized Frank-Bilby equation, it is shown that the elastic strain landscape exhibits intrinsic dislocation configurations for which the junction formation is energetically unfavorable. On the other hand, the mismatched (111) Au/Cu system gives rise to the existence of a minimum-energy path where the fully strain-relaxed equilibrium and non-regular intrinsic hexagonal-shaped dislocation rearrangement is accompanied by a significant removal of the short-range elastic energy.

A predictive theory for elastic scattering and recoil of protons from 4He

DOE PAGES

Hupin, Guillaume; Quaglioni, Sofia; Navratil, Petr

2014-12-08

Low-energy cross sections for elastic scattering and recoil of protons from 4He nuclei (also known as α particles) are calculated directly by solving the Schrodinger equation for five nucleons interacting through accurate two- and three-nucleon forces derived within the framework of chiral effective field theory. Precise knowledge of these processes at various proton backscattering/recoil angles and energies is needed for the ion-beam analysis of numerous materials, from the surface layers of solids, to thin films, to fusion-reactor materials. Indeed, the same elastic scattering process, in two different kinematic configurations, can be used to probe the concentrations and depth profiles ofmore » either hydrogen or helium. Furthermore, we compare our results to available experimental data and show that direct calculations with modern nuclear potentials can help to resolve remaining inconsistencies among data sets and can be used to predict these cross sections when measurements are not available.« less

Size effects and strain localization in atomic-scale cleavage modeling

NASA Astrophysics Data System (ADS)

Elsner, B. A. M.; Müller, S.

2015-09-01

In this work, we study the adhesion and decohesion of Cu(1 0 0) surfaces using density functional theory (DFT) calculations. An upper stress to surface decohesion is obtained via the universal binding energy relation (UBER), but the model is limited to rigid separation of bulk-terminated surfaces. When structural relaxations are included, an unphysical size effect arises if decohesion is considered to occur as soon as the strain energy equals the energy of the newly formed surfaces. We employ the nudged elastic band (NEB) method to show that this size effect is opposed by a size-dependency of the energy barriers involved in the transition. Further, we find that the transition occurs via a localization of bond strain in the vicinity of the cleavage plane, which resembles the strain localization at the tip of a sharp crack that is predicted by linear elastic fracture mechanics.

Size effects and strain localization in atomic-scale cleavage modeling.

PubMed

Elsner, B A M; Müller, S

2015-09-04

In this work, we study the adhesion and decohesion of Cu(1 0 0) surfaces using density functional theory (DFT) calculations. An upper stress to surface decohesion is obtained via the universal binding energy relation (UBER), but the model is limited to rigid separation of bulk-terminated surfaces. When structural relaxations are included, an unphysical size effect arises if decohesion is considered to occur as soon as the strain energy equals the energy of the newly formed surfaces. We employ the nudged elastic band (NEB) method to show that this size effect is opposed by a size-dependency of the energy barriers involved in the transition. Further, we find that the transition occurs via a localization of bond strain in the vicinity of the cleavage plane, which resembles the strain localization at the tip of a sharp crack that is predicted by linear elastic fracture mechanics.

PREFACE: Festschrift to mark the sixtieth birthday of Professor Jens Lothe

NASA Astrophysics Data System (ADS)

Jøssang, Torstein; Barnett, David M.

1992-01-01

The collection of papers in this Festschrift represents the proceedings of a symposium held at the Norwegian Academy of Science and Letters on November 25-26, 1991, marking the occasion of the sixtieth birthday of Professor Jens Lothe. The symposium organizers attempted to invite contributors, either written, oral, or both, from a group of international scientists who have either collaborated with Jens in the past or whose work has had a significant impact in one of three areas in which Jens has focussed his own research interests, namely, statistical physics, elasticity and elastic waves, and the theory of dislocations in crystalline solids. The extent to which we have succeeded in obtaining a proper spectrum of contributors and contributions must be judged by the readers of this volume. It is rather rare in modern times to encounter a physicist such as Jens who has made seminal contributions in fields as diverse as the three included in this Festschrift. For this reason it is both historically interesting and instructive to follow the path that Jens Lothe's research career has taken him, since doing so clearly points out the international nature of the scientific endeavor and the fact that the search for scientific truth transcends national borders and governmental ideologies. Jens' postdoctoral studies at the University of Bristol in the late 1950s brought him in contact with an American postdoctoral student, John Hirth, who had worked on nucleation theory and condensation under the late Professor G M Pound at Carnegie-Mellon University. (Alex Maradudin, one of the contributors to the surface wave session of this symposium was also a postdoctoral fellow at Bristol at this time.) Both Lothe and Hirth had come to Bristol to acquaint themselves with dislocation theory; their first joint paper on double-kink nucleation theory was followed by numerous joint efforts, including their now-classic book Theory of Dislocations. Clearly, their interaction jelled. As legend has it, Hirth, recognizing Jens' interests and talents in statistical physics, brought Lothe to Pound's attention. Jens accepted an invitation to spend time at Carnegie-Mellon as a visiting faculty member, a stay which ultimately resulted in a series of penetrating papers on nucleation theory with Pound, Ken Russell (a student of Pound's, later a postdoctoral fellow with Jens, and a contributor to this symposium), and Jens Feder (a former student of Jens' and co-author of the opening lecture). When Pound later moved to Stanford University, he was fond of saying how at that time nucleation theory needed the strong hand of a good statistical physicist, and that "Jens Lothe showed us how to do it right". Meanwhile, a part of the "Bristol Connection" had moved to Ohio State University, where John Hirth had joined the faculty, and where one of us (TJ, who is also a former student of Jens') had come for postdoctoral work with Hirth on dislocation theory. When Jøssang returned to Oslo, Lothe rejoined Hirth for a year, to continue the preparations for production of the dislocation text several years later. A glance at Jens' publication list shows that upon his return to the physics group in Oslo in the mid 1960s his research interests were turning to the effects of elastic anisotropy in dislocation theory. His 1967 paper "Dislocation Bends in Anisotropic Media" appears immediately before L M Brown's "A Proof of Lothe's Theorem" in the same issue of Philosophical Magazine, the latter paper being stimulated by the former. Together these two articles form the basis for what might be termed the modern geometrical theory of planar dislocation loops. Within a year V L Indenbom and S S Orlov in the Soviet Union would publish the fully three-dimensional version of the theory; Jens was instrumental in bringing to the attention of western scientists the correctness and importance of the Indenbom-Orlov work at the 1969 National Bureau of Standards Conference on Fundamental Aspects of Dislocation Theory (Gaithersburg, Maryland, USA). This familiarity with and appreciation for contemporary Russian work in dislocation theory and (later) in elastic waves, as well as his knowledge of the Russian language, was to become a trademark of Jens during the next 20 years, a point to which we shall return. Kazumi Nishioka, a student of Pound's from Stanford (and a contributor to this symposium) joined Jens for post- doctoral studies in statistical physics in 1970, but soon found himself engaged in anisotropic elasticity and the connection between dislocations in uniform motion and the theory of surface waves (as pointed out by the late A N Stroh in 1962). Lothe and Nishioka wrote to one of us (DMB), who was now at Stanford and pursuing the use of an integral formalism rather than the Stroh sextic formalism for anisotropic elasticity, about the possibility of collaborating on certain aspects of subsonic Rayleigh wave theory. By 1974 Jens and DMB had not only virtually settled the issue of the existence of subsonic surface waves in anisotropic elastic half-spaces, but had embarked on a collaboration which still exists, having produced 24 joint publications. Oddly enough, a key ingredient in resolving the Rayleigh wave problem was somewhat fortuitously recalled by Barnett from a paper he requested from Jens ("Some Unifying Relations for Moving Dislocations", by R J Beltz, T L Davis and K Malen, three of Jens' postdoctoral students in 1967-68) four years prior to their collaboration. Professor Peter Chadwick, FRS (a contributor to the surface wave session), of the School of Mathematics at the University of East Anglia, UK, and his student, G D Smith, placed the Lothe-Barnett theory of subsonic surface waves on a much firmer and comprehensive basis in their beautiful 1977 monograph "Foundations of the Theory of Surface Waves in Anisotropic Elastic Materials"; this work clearly delineated the important notions of limiting speed, first transonic state, and exceptional limiting waves, notions which in a sense lead to what can be called the "Russian Connection" with V L Indenbom, V I Alshits (a contributor to the surface wave session), and their colleagues, as well as the broadening of Jens' interests in elastic waves. Jens' much earlier work on radiation forces on moving dislocations was known and well-appreciated by Indenbom. Following a stay in Oslo as a visiting scientist, Alshits collaborated with Lothe to produce a remarkable series of three papers which clearly showed that degeneracies between slowness branches (acoustic axes) are usually the rule and not the exception in any crystal symmetry class, and that acoustic axes are the anchoring points for lines of exceptional waves on the unit sphere. Later, Professor Per Holm (Mathematics Department, University of Oslo, and a contributor of this volume) and Jens co-authored a deep mathematical study of the topology of bulk wave polarization fields on the unit sphere. In 1981 Alshits and Lothe provided the link between surface wave theory and the theory of bulk wave reflection, which have essentially paved the way for a clearer and more unified view of supersonic surface wave theory. More recent work by Steinar A Gundersen (Jens' most recent doctoral graduate and author of the introductory surface wave paper in this volume), Litian Wang (Jens' present graduate student and a contributor to this volume), and Jens on secluded surface waves and by Chadwick, Lothe and Barnett on one-component surface waves have roots in the 1981 Alshits-Lothe paper. We now eagerly await the appearance of the book Elastic Strain Fields and Dislocation Mobility, co-edited by Jens and V L Indenbom, currently in press through North-Holland, Amsterdam. A glance at the last 30 publications in Jens' vita shows the extent to which his Russian connection has broadened. He has taken great efforts to maintain familiarity with the relevant Russian scientific literature and to nurture and encourage western acquaintance with their work. No doubt his warm personality, natural curiosity and willingness to promote and seize opportunities for collaboration across national boundaries is what has allowed great intellect stationed in a somewhat remote part of the scientific community to engender such a large international following, when other gifted men might have chosen to work in isolation under similar circumstances. Vladimir Alshits may have said it best during his visit to Oslo last April, namely, "There are three Norwegian names known to every Russian—Henrik Ibsen, Fridtjof Nansen and Jens Lothe". None of this is meant to imply that Jens has neglected or ignored his colleagues in Norway. Indeed, quite the contrary is true, but we believe the exposition on the development within the Solid State Group and the Cooperative Phenomena Program at the University of Oslo and at NTH in Trondheim in this symposium and its proceedings, presented by the local staff and present close associates addresses Jens Lothe's contribution on the home front far better than this preface would allow. We believe we speak for all the symposium attendees by extending to Jens the happiest greetings and our best wishes for continued health and happiness.

Friction measurements on InAs NWs by AFM manipulation

NASA Astrophysics Data System (ADS)

Pettersson, Hakan; Conache, Gabriela; Gray, Struan; Bordag, Michael; Ribayrol, Aline; Froberg, Linus; Samuelson, Lars; Montelius, Lars

2008-03-01

We discuss a new approach to measure the friction force between elastically deformed nanowires and a surface. The wires are bent, using an AFM, into an equilibrium shape determined by elastic restoring forces within the wire and friction between the wire and the surface. From measurements of the radius of curvature of the bent wires, elasticity theory allows the friction force per unit length to be calculated. We have studied friction properties of InAs nanowires deposited on SiO2, silanized SiO2 and Si3N4 substrates. The wires were typically from 0.5 to a few microns long, with diameters varying between 20 and 80 nm. Manipulation is done in a `Retrace Lift' mode, where feedback is turned off for the reverse scan and the tip follows a nominal path. The effective manipulation force during the reverse scan can be changed by varying an offset in the height of the tip over the surface. We will report on interesting static- and sliding friction experiments with nanowires on the different substrates, including how the friction force per unit length varies with the diameter of the wires.

Elastically frustrated rehybridization: Origin of chemical order and compositional limits in InGaN quantum wells

NASA Astrophysics Data System (ADS)

Lymperakis, L.; Schulz, T.; Freysoldt, C.; Anikeeva, M.; Chen, Z.; Zheng, X.; Shen, B.; Chèze, C.; Siekacz, M.; Wang, X. Q.; Albrecht, M.; Neugebauer, J.

2018-01-01

Nominal InN monolayers grown by molecular beam epitaxy on GaN(0001) are investigated combining in situ reflection high-energy electron diffraction (RHEED), transmission electron microscopy (TEM), and density functional theory (DFT). TEM reveals a chemical intraplane ordering never observed before. Employing DFT, we identify a novel surface stabilization mechanism elastically frustrated rehybridization, which is responsible for the observed chemical ordering. The mechanism also sets an incorporation barrier for indium concentrations above 25% and thus fundamentally limits the indium content in coherently strained layers.

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.

Rayleigh-Taylor instability in soft elastic layers

NASA Astrophysics Data System (ADS)

Riccobelli, D.; Ciarletta, P.

2017-04-01

This work investigates the morphological stability of a soft body composed of two heavy elastic layers attached to a rigid surface and subjected only to the bulk gravity force. Using theoretical and computational tools, we characterize the selection of different patterns as well as their nonlinear evolution, unveiling the interplay between elastic and geometric effects for their formation. Unlike similar gravity-induced shape transitions in fluids, such as the Rayleigh-Taylor instability, we prove that the nonlinear elastic effects saturate the dynamic instability of the bifurcated solutions, displaying a rich morphological diagram where both digitations and stable wrinkling can emerge. The results of this work provide important guidelines for the design of novel soft systems with tunable shapes, with several applications in engineering sciences. This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

Elastic Reverse Time Migration (RTM) From Surface Topography

NASA Astrophysics Data System (ADS)

Akram, Naveed; Chen, Xiaofei

2017-04-01

Seismic Migration is a promising data processing technique to construct subsurface images by projecting the recorded seismic data at surface back to their origins. There are numerous Migration methods. Among them, Reverse Time Migration (RTM) is considered a robust and standard imaging technology in present day exploration industry as well as in academic research field because of its superior performance compared to traditional migration methods. Although RTM is extensive computing and time consuming but it can efficiently handle the complex geology, highly dipping reflectors and strong lateral velocity variation all together. RTM takes data recorded at the surface as a boundary condition and propagates the data backwards in time until the imaging condition is met. It can use the same modeling algorithm that we use for forward modeling. The classical seismic exploration theory assumes flat surface which is almost impossible in practice for land data. So irregular surface topography has to be considered in simulation of seismic wave propagation, which is not always a straightforward undertaking. In this study, Curved grid finite difference method (CG-FDM) is adapted to model elastic seismic wave propagation to investigate the effect of surface topography on RTM results and explore its advantages and limitations with synthetic data experiments by using Foothill model with topography as the true model. We focus on elastic wave propagation rather than acoustic wave because earth actually behaves as an elastic body. Our results strongly emphasize on the fact that irregular surface topography must be considered for modeling of seismic wave propagation to get better subsurface images specially in mountainous scenario and suggest practitioners to properly handled the geometry of data acquired on irregular topographic surface in their imaging algorithms.

Elastic Reverse Time Migration (RTM) From Surface Topography

NASA Astrophysics Data System (ADS)

Naveed, A.; Chen, X.

2016-12-01

Seismic Migration is a promising data processing technique to construct subsurface images by projecting the recorded seismic data at surface back to their origins. There are numerous Migration methods. Among them, Reverse Time Migration (RTM) is considered a robust and standard imaging technology in present day exploration industry as well as in academic research field because of its superior performance compared to traditional migration methods. Although RTM is extensive computing and time consuming but it can efficiently handle the complex geology, highly dipping reflectors and strong lateral velocity variation all together. RTM takes data recorded at the surface as a boundary condition and propagates the data backwards in time until the imaging condition is met. It can use the same modeling algorithm that we use for forward modeling. The classical seismic exploration theory assumes flat surface which is almost impossible in practice for land data. So irregular surface topography has to be considered in simulation of seismic wave propagation, which is not always a straightforward undertaking. In this study, Curved grid finite difference method (CG-FDM) is adapted to model elastic seismic wave propagation to investigate the effect of surface topography on RTM results and explore its advantages and limitations with synthetic data experiments by using Foothill model with topography as the true model. We focus on elastic wave propagation rather than acoustic wave because earth actually behaves as an elastic body. Our results strongly emphasize on the fact that irregular surface topography must be considered for modeling of seismic wave propagation to get better subsurface images specially in mountainous scenario and suggest practitioners to properly handled the geometry of data acquired on irregular topographic surface in their imaging algorithms.

Compressive buckling of a rectangular nanoplate

NASA Astrophysics Data System (ADS)

Bochkarev, A. O.

2018-05-01

This paper considers the constitutive relations of the nanoplate theory with surface stresses taken into account according to the original or complete Gurtin-Murdoch (GM) model and according to the simplified strain-consistent GM model (which does not include any non-strain terms in the surface stress-strain relation). It is shown that the potential energy of a deformed nanoplate according to both GM models preserves the classical structure using the redefined elastic moduli (effective tangential and flexural elastic properties, which contain the characteristics of bulk phase and a surface). This allows to apply the known solutions and methods from macroplates to nanoplates. As example, it is shown that the critical load of the compressive buckling of a nanoplate according to the complete and strain-consistent GM models has the difference between two solutions no more than 1.5%.

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

NASA Astrophysics Data System (ADS)

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

2010-11-01

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

Elastic moduli in nano-size samples of amorphous solids: System size dependence

NASA Astrophysics Data System (ADS)

Cohen, Yossi; Procaccia, Itamar

2012-08-01

This letter is motivated by some recent experiments on pan-cake-shaped nano-samples of metallic glass that indicate a decline in the measured shear modulus upon decreasing the sample radius. Similar measurements on crystalline samples of the same dimensions showed a much more modest change. In this letter we offer a theory of this phenomenon; we argue that such results are generically expected for any amorphous solid, with the main effect being related to the increased contribution of surfaces with respect to the bulk when the samples get smaller. We employ exact relations between the shear modulus and the eigenvalues of the system's Hessian matrix to explore the role of surface modes in affecting the elastic moduli.

Flexural models of trench/outer rise topography of coronae on Venus with axisymmetric spherical shell elastic plates

NASA Technical Reports Server (NTRS)

Moore, W.; Schubert, Gerald; Sandwell, David T.

1992-01-01

Magellan altimetry has revealed that many coronae on Venus have trenches or moats around their peripheries and rises outboard of the trenches. This trench/outer rise topographic signature is generally associated with the tectonic annulus of the corona. Sandwell and Schubert have interpreted the trench/outer rise topography and the associated tectonic annulus around coronae to be the result of elastic bending of the Venus lithosphere (though the tectonic structures are consequences of inelastic deformation of the lithosphere). They used two-dimensional elastic plate flexure theory to fit topographic profiles across a number of large coronae and inferred elastic lithosphere thicknesses between about 15 and 40 km, similar to inferred values of elastic thickness for the Earth's lithosphere at subduction zones around the Pacific Ocean. Here, we report the results of using axisymmetric elastic flexure theory for the deformation of thin spherical shell plates to interpret the trench/outer rise topography of the large coronae modeled by Sandwell and Schubert and of coronae as small as 250 km in diameter. In the case of a corona only a few hundred kilometers in diameter, the model accounts for the small planform radius of the moat and the nonradial orientation of altimetric traces across the corona. By fitting the flexural topography of coronae we determine the elastic thickness and loading necessary to account for the observed flexure. We calculate the associated bending moment and determine whether the corona interior topographic load can provide the required moment. We also calculate surface stresses and compare the stress distribution with the location of annular tectonic features.

Fracton-Elasticity Duality

NASA Astrophysics Data System (ADS)

Pretko, Michael; Radzihovsky, Leo

2018-05-01

Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid. The topological defects of elasticity theory map onto charges of the tensor gauge theory, with disclinations and dislocations corresponding to fractons and dipoles, respectively. The transverse and longitudinal phonons of crystals map onto the two gapless gauge modes of the gauge theory. The restricted dynamics of fractons matches with constraints on the mobility of lattice defects. The duality leads to numerous predictions for phases and phase transitions of the fracton system, such as the existence of gauge theory counterparts to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory. Extensions of this duality to generalized elasticity theories provide a route to the discovery of new fracton models. As a further consequence, the duality implies that fracton phases are relevant to the study of interacting topological crystalline insulators.

Modelling the Size Effects on the Mechanical Properties of Micro/Nano Structures.

PubMed

Abazari, Amir Musa; Safavi, Seyed Mohsen; Rezazadeh, Ghader; Villanueva, Luis Guillermo

2015-11-11

Experiments on micro- and nano-mechanical systems (M/NEMS) have shown that their behavior under bending loads departs in many cases from the classical predictions using Euler-Bernoulli theory and Hooke's law. This anomalous response has usually been seen as a dependence of the material properties on the size of the structure, in particular thickness. A theoretical model that allows for quantitative understanding and prediction of this size effect is important for the design of M/NEMS. In this paper, we summarize and analyze the five theories that can be found in the literature: Grain Boundary Theory (GBT), Surface Stress Theory (SST), Residual Stress Theory (RST), Couple Stress Theory (CST) and Surface Elasticity Theory (SET). By comparing these theories with experimental data we propose a simplified model combination of CST and SET that properly fits all considered cases, therefore delivering a simple (two parameters) model that can be used to predict the mechanical properties at the nanoscale.

Modelling the Size Effects on the Mechanical Properties of Micro/Nano Structures

PubMed Central

Abazari, Amir Musa; Safavi, Seyed Mohsen; Rezazadeh, Ghader; Villanueva, Luis Guillermo

2015-01-01

Experiments on micro- and nano-mechanical systems (M/NEMS) have shown that their behavior under bending loads departs in many cases from the classical predictions using Euler-Bernoulli theory and Hooke’s law. This anomalous response has usually been seen as a dependence of the material properties on the size of the structure, in particular thickness. A theoretical model that allows for quantitative understanding and prediction of this size effect is important for the design of M/NEMS. In this paper, we summarize and analyze the five theories that can be found in the literature: Grain Boundary Theory (GBT), Surface Stress Theory (SST), Residual Stress Theory (RST), Couple Stress Theory (CST) and Surface Elasticity Theory (SET). By comparing these theories with experimental data we propose a simplified model combination of CST and SET that properly fits all considered cases, therefore delivering a simple (two parameters) model that can be used to predict the mechanical properties at the nanoscale. PMID:26569256

Grain size effect on Lcr elastic wave for surface stress measurement of carbon steel

NASA Astrophysics Data System (ADS)

Liu, Bin; Miao, Wenbing; Dong, Shiyun; He, Peng

2018-04-01

Based on critical refraction longitudinal wave (Lcr wave) acoustoelastic theory, correction method for grain size effect on surface stress measurement was discussed in this paper. Two fixed distance Lcr wave transducers were used to collect Lcr wave, and difference in time of flight between Lcr waves was calculated with cross-correlation coefficient function, at last relationship of Lcr wave acoustoelastic coefficient and grain size was obtained. Results show that as grain size increases, propagation velocity of Lcr wave decreases, one cycle is optimal step length for calculating difference in time of flight between Lcr wave. When stress value is within stress turning point, relationship of difference in time of flight between Lcr wave and stress is basically consistent with Lcr wave acoustoelastic theory, while there is a deviation and it is higher gradually as stress increasing. Inhomogeneous elastic plastic deformation because of inhomogeneous microstructure and average value of surface stress in a fixed distance measured with Lcr wave were considered as the two main reasons for above results. As grain size increasing, Lcr wave acoustoelastic coefficient decreases in the form of power function, then correction method for grain size effect on surface stress measurement was proposed. Finally, theoretical discussion was verified by fracture morphology observation.

Optimization of ceramic strength using elastic gradients

PubMed Central

Zhang, Yu; Ma, Li

2009-01-01

We present a new concept for strengthening ceamics by utilizing a graded structure with a low elastic modulus at both top and bottom surfaces sandwiching a high-modulus interior. Closed-form equations have been developed for stress analysis of simply supported graded sandwich beams subject to transverse center loads. Theory predicts that suitable modulus gradients at the ceramic surface can effectively reduce and spread the maximum bending stress from the surface into the interior. The magnitude of such stress dissipation is governed by the thickness ratio of the beam to the graded layers. We test our concept by infiltrating both top and bottom surfaces of a strong class of zirconia ceramic with an in-house prepared glass of similar coefficient of thermal expansion and Poisson’s ratio to zirconia, producing a controlled modulus gradient at the surface without significant long-range residual stresses. The resultant graded glass/zirconia/glass composite exhibits significantly higher load-bearing capacity than homogeneous zirconia. PMID:20161019

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.

Mechanics of evolving thin film structures

NASA Astrophysics Data System (ADS)

Liang, Jim

In the Stranski-Krastanov system, the lattice mismatch between the film and the substrate causes the film to break into islands. During annealing, both the surface energy and the elastic energy drive the islands to coarsen. Motivated by several related studies, we suggest that stable islands should form when a stiff ceiling is placed at a small gap above the film. We show that the role of elasticity is reversed: with the ceiling, the total elastic energy stored in the system increases as the islands coarsen laterally. Consequently, the islands select an equilibrium size to minimize the combined elastic energy and surface energy. In lithographically-induced self-assembly, when a two-phase fluid confined between parallel substrates is subjected to an electric field, one phase can self-assemble into a triangular lattice of islands in another phase. We describe a theory of the stability of the island lattice. The islands select the equilibrium diameter to minimize the combined interface energy and electrostatic energy. Furthermore, we study compressed SiGe thin film islands fabricated on a glass layer, which itself lies on a silicon wafer. Upon annealing, the glass flows, and the islands relax. A small island relaxes by in-plane expansion. A large island, however, wrinkles at the center before the in-plane relaxation arrives. The wrinkles may cause significant tensile stress in the island, leading to fracture. We model the island by the von Karman plate theory and the glass layer by the Reynolds lubrication theory. Numerical simulations evolve the in-plane expansion and the wrinkles simultaneously. We determine the critical island size, below which in-plane expansion prevails over wrinkling. Finally, in devices that integrate dissimilar materials in small dimensions, crack extension in one material often accompanies inelastic deformation in another. We analyze a channel crack advancing in an elastic film under tension, while an underlayer creeps. We use a two-dimensional shear lag model to approximate the three-dimensional fracture process. Based on the computational results, we propose new experiments to measure fracture toughness and creep laws in small structures. Similarly, we study delayed crack initiation, steady crack growth, and transient crack growth when the underlayer is viscoelastic.

Longitudinal waves in carbon nanotubes in the presence of transverse magnetic field and elastic medium

NASA Astrophysics Data System (ADS)

Liu, Hu; Liu, Hua; Yang, Jialing

2017-09-01

In the present paper, the coupling effect of transverse magnetic field and elastic medium on the longitudinal wave propagation along a carbon nanotube (CNT) is studied. Based on the nonlocal elasticity theory and Hamilton's principle, a unified nonlocal rod theory which takes into account the effects of small size scale, lateral inertia and radial deformation is proposed. The existing rod theories including the classic rod theory, the Rayleigh-Love theory and Rayleigh-Bishop theory for macro solids can be treated as the special cases of the present model. A two-parameter foundation model (Pasternak-type model) is used to represent the elastic medium. The influence of transverse magnetic field, Pasternak-type elastic medium and small size scale on the longitudinal wave propagation behavior of the CNT is investigated in detail. It is shown that the influences of lateral inertia and radial deformation cannot be neglected in analyzing the longitudinal wave propagation characteristics of the CNT. The results also show that the elastic medium and the transverse magnetic field will also affect the longitudinal wave dispersion behavior of the CNT significantly. The results obtained in this paper are helpful for understanding the mechanical behaviors of nanostructures embedded in an elastic medium.

Evaluation of microcrack thermal shock damage in ceramics: Modeling and experiment

NASA Technical Reports Server (NTRS)

Chu, Y. C.; Hefetz, M.; Rokhlin, S. I.

1992-01-01

In this paper we present an experimental and theoretical study of the effect of microcrack damage on ceramic properties. For the experimental investigation, ceramic samples of aluminum oxide and reaction bonded silicon nitride (RBSN) are used. Thermal shock treatment from different temperatures up to 1000 C is applied to produce the microcracks. Both surface and bulk ultrasonic wave methods are used to correlate the change of elastic constants to microstructural degradation and to determine the change in elastic anisotropy induced by microcrack damage. For the theoretical investigation, damage mechanics, which relates microstructural damage to material service life and mechanical failure, is used. The change in elastic properties due to microcrack damage calculated from the theoretical model is compared with the experimental results for determination of the applicability of damage theory. It is shown that two independent experimental methods (bulk wave and surface wave) give the same results for shear moduli of damaged ceramics. The experimental results aagree reasonably well with the moduli predicted from the cracked solid model.

The effective propagation constants of SH wave in composites reinforced by dispersive parallel nanofibers

NASA Astrophysics Data System (ADS)

Qiang, FangWei; Wei, PeiJun; Li, Li

2012-07-01

In the present paper, the effective propagation constants of elastic SH waves in composites with randomly distributed parallel cylindrical nanofibers are studied. The surface stress effects are considered based on the surface elasticity theory and non-classical interfacial conditions between the nanofiber and the host are derived. The scattering waves from individual nanofibers embedded in an infinite elastic host are obtained by the plane wave expansion method. The scattering waves from all fibers are summed up to obtain the multiple scattering waves. The interactions among random dispersive nanofibers are taken into account by the effective field approximation. The effective propagation constants are obtained by the configurational average of the multiple scattering waves. The effective speed and attenuation of the averaged wave and the associated dynamical effective shear modulus of composites are numerically calculated. Based on the numerical results, the size effects of the nanofibers on the effective propagation constants and the effective modulus are discussed.

Wedge disclination dipole in an embedded nanowire within the surface/interface elasticity

NASA Astrophysics Data System (ADS)

Shodja, Hossein M.; Rezazadeh-Kalehbasti, Shaghayegh; Gutkin, Mikhail Yu

2013-12-01

The elastic behavior of an arbitrary oriented wedge disclination dipole located inside a nanowire, which in turn is embedded in an infinite matrix, is studied within the surface/interface theory of elasticity. The corresponding boundary value problem is provided using complex potential functions. The potential functions are defined through modeling the wedge disclination in terms of an equivalent distribution of edge dislocations. The interface effects on the stress field and strain energy of the disclination dipole and image forces acting on it, the influence of relative shear moduli of the nanowire and the matrix, as well as the different characteristics of the interface are studied thoroughly. It is shown that the positive interface modulus leads to increased strain energy and extra repulsive forces on the disclination dipole. The noticeable effect of the negative interface modulus is the non-classical oscillations in the stress field of the disclination dipole and an extra attractive image force on it.

A multidimensional anisotropic strength criterion based on Kelvin modes

NASA Astrophysics Data System (ADS)

Arramon, Yves Pierre

A new theory for the prediction of multiaxial strength of anisotropic elastic materials was proposed by Biegler and Mehrabadi (1993). This theory is based on the premise that the total elastic strain energy of an anisotropic material subjected to multiaxial stress can be decomposed into dilatational and deviatoric modes. A multidimensional strength criterion may thus be formulated by postulating that the failure would occur when the energy stored in one of these modes has reached a critical value. However, the logic employed by these authors to formulate a failure criterion based on this theory could not be extended to multiaxial stress. In this thesis, an alternate criterion is presented which redresses the biaxial restriction by reformulating the surfaces of constant modal energy as surfaces of constant eigenstress magnitude. The resulting failure envelope, in a multidimensional stress space, is piecewise smooth. Each facet of the envelope is expected to represent the locus of failure data by a particular Kelvin mode. It is further shown that the Kelvin mode theory alone provides an incomplete description of the failure of some materials, but that this weakness can be addressed by the introduction of a set of complementary modes. A revised theory which combines both Kelvin and complementary modes is thus proposed and applied seven example materials: an isotropic concrete, tetragonal paperboard, two orthotropic softwoods, two orthotropic hardwoods and an orthotropic cortical bone. The resulting failure envelopes for these examples were plotted and, with the exception of concrete, shown to produce intuitively correct failure predictions.

A “re-vitalized” Greenwood and Williamson model of elastic contact between fractal surfaces

NASA Astrophysics Data System (ADS)

Ciavarella, M.; Delfine, V.; Demelio, G.

2006-12-01

Greenwood and Williamson in 1966 (GW) proposed a theory of elastic contact mechanics of rough surfaces which is today the foundation of many theories in tribology (friction, adhesion, thermal and electrical conductance, wear, etc.). However, the theory has periodically received criticisms for the "resolution-dependence" of the asperity features. Greenwood himself has recently concluded that: "The introduction by Greenwood and Williamson in 1966 of the definition of a 'peak' as a point higher than its neighbours on a profile sampled at a finite sampling interval was, in retrospect, a mistake, although it is possible that it was a necessary mistake" [Greenwood and Wu, 2001. Surface roughness and contact: an apology. Meccanica 36 (6), 617-630]. We propose a "discrete" version of the GW model, keeping the approximation of a surface by quadratic functions near summits, where the summit arrangement is found from numerical realizations or real surfaces scans. The contact is then solved either summing the Hertzian relationships, or considering interaction effects to the first-order in a very efficient algorithm. We conduct experiments on Weierstrass-Mandelbrot fractal surfaces, concluding that: the real contact area-load relationship is well captured by the original GW theoretical model, once the correct mean radius is used. The relationship is robust and shows relatively little scatter; the conductance-load relationship is vice versa only approximately given by the original GW theoretical model. Significant deviations from linearity and significant scatter seem to be found, particularly at low fractal dimensions; the load, area and conductance dependences with separation show significant dependence on the actual phase arrangements, and hence significant scatter at large separations. Effect of interaction is seen strongly at low separations, where scatter is minimal. The discrete GW model permits to include these effects, except when the asperity description breaks down. Refinements of the original GW theory using the full random process theory (such as that by Bush Gibson and Thomas, BGT) result only in small improvements with a significant additional complication. However, the BGT relationship between contact area and load at low loads is more accurate than the more recent theory by Persson. The distribution derived from the original GW theory has been obtained, and shown to be closer to the numerical results than that predicted by the Persson model, even if the area error is removed. It is concluded that the original GW theory deserves the general success received so far, since the resolution-dependence of geometrical features is an intrinsic feature of "fractals" but not a problem for the GW theory, when interaction effects are included.

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

Large Deflection of Ideal Pseudo-Elastic Shape Memory Alloy Cantilever Beam

NASA Astrophysics Data System (ADS)

Cui, Shitang; Hu, Liming; Yan, Jun

This paper deals with the large deflections of pseudo-elastic shape memory alloy cantilever beams subjected to a concentrated load at the free end. Because of the large deflections, geometry nonlinearity arises and this analysis employs the nonlinear bending theory. The exact expression of curvature is used in the moment-curvature relationship. As a vertical force at the tip of cantilever, curvature and bending moment distribution expressions are deduced. The curvature changed distinctly when the surface material undergoes phase transformation. The length of phase transformation region was affected greatly with the force at the free end.

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.

Polymer-induced forces at interfaces

NASA Astrophysics Data System (ADS)

Rangarajan, Murali

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

Quantum trajectories in elastic atom-surface scattering: threshold and selective adsorption resonances.

PubMed

Sanz, A S; Miret-Artés, S

2005-01-01

The elastic resonant scattering of He atoms off the Cu(117) surface is fully described with the formalism of quantum trajectories provided by Bohmian mechanics. Within this theory of quantum motion, the concept of trapping is widely studied and discussed. Classically, atoms undergo impulsive collisions with the surface, and then the trapped motion takes place covering at least two consecutive unit cells. However, from a Bohmian viewpoint, atom trajectories can smoothly adjust to the equipotential energy surface profile in a sort of sliding motion; thus the trapping process could eventually occur within one single unit cell. In particular, both threshold and selective adsorption resonances are explained by means of this quantum trapping considering different space and time scales. Furthermore, a mapping between each region of the (initial) incoming plane wave and the different parts of the diffraction and resonance patterns can be easily established, an important issue only provided by a quantum trajectory formalism. (c) 2005 American Institute of Physics.

Deformation of a flexible disk bonded to an elastic half space-application to the lung.

PubMed

Lai-Fook, S J; Hajji, M A; Wilson, T A

1980-08-01

An analysis is presented of the deformation of a homogeneous, isotropic, elastic half space subjected to a constant radial strain in a circular area on the boundary. Explicit analytic expressions for the normal and radial displacements and the shear stress on the boundary are used to interpret experiments performed on inflated pig lungs. The boundary strain was induced by inflating or deflating the lung after bonding a flexible disk to the lung surface. The prediction that the surface bulges outward for positive boundary strain and inward for negative strain was observed in the experiments. Poisson's ratio at two transpulmonary pressures was measured, by use of the normal displacement equation evaluated at the surface. A direct estimate of Poisson's ratio was possible because the normal displacement of the surface depended uniquely on the compressibility of the material. Qualitative comparisons between theory and experiment support the use of continuum analyses in evaluating the behavior of the lung parenchyma when subjected to small local distortions.

Elastic modulus of nanomaterials: resonant contact-AFM measurement and reduced-size effects (Invited Paper)

NASA Astrophysics Data System (ADS)

Nysten, Bernard; Fretigny, Christian; Cuenot, Stephane

2005-05-01

Resonant contact atomic force microscopy (resonant C-AFM) is used to quantitatively measure the elastic modulus of polymer nanotubes and metallic nanowires. To achieve this, an oscillating electric field is applied between the sample holder and the microscope head to excite the oscillation of the cantilever in contact with the nanostructures suspended over the pores of a membrane. The resonance frequency of the cantilever with the tip in contact with a nanostructure is shifted to higher values with respect to the resonance frequency of the free cantilever. It is demonstrated that the system can simply be modeled by a cantilever with the tip in contact with two springs. The measurement of the frequency shift enables the direct determination of the spring stiffness, i.e. the nanowires or nanotube stiffness. The method also enables the determination of the boundary conditions of the nanobeam on the membrane. The tensile elastic modulus is then simply determined using the classical theory of beam deflection. The obtained results for the larger nanostructures fairly agree to the values reported in the literature for the macroscopic elastic modulus of the corresponding materials. The measured modulus of the nanomaterials with smaller diameters is significantly higher than that of the larger ones. The increase of the apparent elastic modulus for the smaller diameters is attributed to the surface tension effects. It is thus demonstrated that resonant C-AFM enables the measurement of the elastic modulus and of the surface tension of nanomaterials.

Surface Tension Mediated Under-Water Adhesion of Rigid Spheres on Soft, Charged Surfaces

NASA Astrophysics Data System (ADS)

Sinha, Shayandev; Das, Siddhartha

2015-11-01

Understanding the phenomenon of surface-tension-mediated under-water adhesion is necessary for studying a plethora of physiological and technical phenomena, such as the uptake of bacteria or nanoparticle by cells, attachment of virus on bacterial surfaces, biofouling on large ocean vessels and marine devices, etc. This adhesion phenomenon becomes highly non-trivial in case the soft surface where the adhesion occurs is also charged. Here we propose a theory for analyzing such an under-water adhesion of a rigid sphere on a soft, charged surface, represented by a grafted polyelectrolyte layer (PEL). We develop a model based on the minimization of free energy that, in addition to considering the elastic and the surface-tension-mediated adhesion energies, also accounts for the PEL electric double layer (EDL) induced electrostatic energies. We show that in the presence of surface charges, adhesion gets enhanced. This can be explained by the fact that the increase in the elastic energy is better balanced by the lowering of the EDL energy associated with the adhesion process. The entire behaviour is further dictated by the surface tension components that govern the adhesion energy.

Impedance method for measuring shear elasticity of liquids

NASA Astrophysics Data System (ADS)

Badmaev, B. B.; Dembelova, T. S.; Damdinov, B. B.; Gulgenov, Ch. Zh.

2017-11-01

Experimental results of studying low-frequency (74 kHz) shear elasticity of polymer liquids by the impedance method (analogous to the Mason method) are presented. A free-volume thick liquid layer is placed on the horizontal surface of a piezoelectric quartz crystal with dimensions 34.7 × 12 × 5.5 cm. The latter performs tangential vibrations at resonance frequency. The liquid layer experiences shear strain, and shear waves should propagate in it. From the theory of the method, it follows that, with an increase in the layer thickness, both real and imaginary resonance frequency shifts should exhibit damped oscillations and tend to limiting values. For the liquids under study, the imaginary frequency shift far exceeds the real one, which testifies to the presence of bulk shear elasticity.

Comment on 'Surface thermodynamics, surface stress, equations at surfaces and triple lines for deformable bodies'.

PubMed

Gutman, E M

2010-10-27

In a recent publication by Olives (2010 J. Phys.: Condens. Matter 22 085005) he studied 'the thermodynamics and mechanics of the surface of a deformable body, following and refining the general approach of Gibbs' and believed that 'a new definition of the surface stress is given'. However, using the usual way of deriving the equations of Gibbs-Duhem type the author, nevertheless, has fallen into a mathematical discrepancy because he has tried to unite in one equation different thermodynamic systems and 'a new definition of the surface stress' has appeared known in the usual theory of elasticity.

Theory connecting nonlocal sediment transport, earth surface roughness, and the Sadler effect

NASA Astrophysics Data System (ADS)

Schumer, Rina; Taloni, Alessandro; Furbish, David Jon

2017-03-01

Earth surface evolution, like many natural phenomena typified by fluctuations on a wide range of scales and deterministic smoothing, results in a statistically rough surface. We present theory demonstrating that scaling exponents of topographic and stratigraphic statistics arise from long-time averaging of noisy surface evolution rather than specific landscape evolution processes. This is demonstrated through use of "elastic" Langevin equations that generically describe disturbance from a flat earth surface using a noise term that is smoothed deterministically via sediment transport. When smoothing due to transport is a local process, the geologic record self organizes such that a specific Sadler effect and topographic power spectral density (PSD) emerge. Variations in PSD slope reflect the presence or absence and character of nonlocality of sediment transport. The range of observed stratigraphic Sadler slopes captures the same smoothing feature combined with the presence of long-range spatial correlation in topographic disturbance.

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.

An analytical model of a broadband magnetic energy nanoharvester array with consideration of flexoelectricity and surface effect

NASA Astrophysics Data System (ADS)

Wang, Wenjun; Li, Peng; Jin, Feng

2018-04-01

Based on Hamilton’s principle and Mindlin plate theory, a series of 2D equations to describe the mechanical behaviors of magneto-electro-elastic (MEE) laminated nanoplates, is established for the first time with consideration of flexoelectricity and surface effect. The equations derived are general, which not only can be reduced to the corresponding piezoelectric, piezomagnetic, and elastic cases, but can also be degenerated to the classical higher-order plate theory of conventional macroscopic MEE laminates if flexoelectricity and surface effect are neglected. As the typical application, a flexoelectric magnetic energy nanoharvester array with surface effect, consisting of a giant magnetostrictive material Terfenol-D with a nonlinear magneto-thermo-mechanical coupling constitutive relation and a linear piezoelectric layer PZT-4, is investigated systematically under coupled extensional and flexural deformations. After the correctness is confirmed, an important performance index (i.e. output current) of the harvester is discussed for different conditions, including flexoelectricity, surface effect, and nonlinear magneto-mechanical coupling. It has been revealed that flexoelectricity, surface effect, external magnetic field, and pre-stress can dramatically improve the performance of characteristics such as resonant frequencies, bandwidth, and output current of the nanoharvester. Especially, a critical thickness corresponding to the flexoelectricity or surface effect is proposed, below which the size-dependent effect is obvious and must be considered. The current work can be viewed as an innovative theoretical tool for evaluating the size-dependent and nonlinear characteristics qualitatively and quantitatively, which is essential and crucial to understanding the physical and mechanical properties of MEE nanostructures.

Influence of chemistry, interfacial width, and non-isothermal conditions on spatially heterogeneous activated relaxation and elasticity in glass-forming free standing films

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

Mirigian, Stephen; Schweizer, Kenneth S.

Here, we employ the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of activated relaxation to study several questions in free standing thin films of glass-forming molecular and polymer liquids. The influence of non-universal chemical aspects on dynamical confinement effects is found to be relatively weak, but with the caveat that for the systems examined, the bulk ECNLE polymer theory does not predict widely varying fragilities. Allowing the film model to have a realistic vapor interfacial width significantly enhances the reduction of the film-averaged glass transition temperature, T g, in a manner that depends on whether a dynamic or pseudo-thermodynamic averagingmore » of the spatial mobility gradient is adopted. The nature of film thickness effects on the spatial profiles of the alpha relaxation time and elastic modulus is studied under non-isothermal conditions and contrasted with the corresponding isothermal behavior. Modest differences are found if a film-thickness dependent T g is defined in a dynamical manner. But, adopting a pseudo-thermodynamic measure of T g leads to a qualitatively new form of the alpha relaxation time gradient where highly mobile layers near the film surface coexist with strongly vitrified regions in the film interior. Consequently, the film-averaged shear modulus can increase with decreasing film thickness, despite the T g reduction and presence of a mobile surface layer. Such a behavior stands in qualitative contrast to the predicted mechanical softening under isothermal conditions. Spatial gradients of the elastic modulus are studied as a function of temperature, film thickness, probing frequency, and experimental protocol, and a rich behavior is found.« less

Influence of chemistry, interfacial width, and non-isothermal conditions on spatially heterogeneous activated relaxation and elasticity in glass-forming free standing films

DOE PAGES

Mirigian, Stephen; Schweizer, Kenneth S.

2017-02-02

Here, we employ the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of activated relaxation to study several questions in free standing thin films of glass-forming molecular and polymer liquids. The influence of non-universal chemical aspects on dynamical confinement effects is found to be relatively weak, but with the caveat that for the systems examined, the bulk ECNLE polymer theory does not predict widely varying fragilities. Allowing the film model to have a realistic vapor interfacial width significantly enhances the reduction of the film-averaged glass transition temperature, T g, in a manner that depends on whether a dynamic or pseudo-thermodynamic averagingmore » of the spatial mobility gradient is adopted. The nature of film thickness effects on the spatial profiles of the alpha relaxation time and elastic modulus is studied under non-isothermal conditions and contrasted with the corresponding isothermal behavior. Modest differences are found if a film-thickness dependent T g is defined in a dynamical manner. But, adopting a pseudo-thermodynamic measure of T g leads to a qualitatively new form of the alpha relaxation time gradient where highly mobile layers near the film surface coexist with strongly vitrified regions in the film interior. Consequently, the film-averaged shear modulus can increase with decreasing film thickness, despite the T g reduction and presence of a mobile surface layer. Such a behavior stands in qualitative contrast to the predicted mechanical softening under isothermal conditions. Spatial gradients of the elastic modulus are studied as a function of temperature, film thickness, probing frequency, and experimental protocol, and a rich behavior is found.« less

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

Defect-driven flexochemical coupling in thin ferroelectric films

NASA Astrophysics Data System (ADS)

Eliseev, Eugene A.; Vorotiahin, Ivan S.; Fomichov, Yevhen M.; Glinchuk, Maya D.; Kalinin, Sergei V.; Genenko, Yuri A.; Morozovska, Anna N.

2018-01-01

Using the Landau-Ginzburg-Devonshire theory, we considered the impact of the flexoelectrochemical coupling on the size effects in polar properties and phase transitions of thin ferroelectric films with a layer of elastic defects. We investigated a typical case, when defects fill a thin layer below the top film surface with a constant concentration creating an additional gradient of elastic fields. The defective surface of the film is not covered with an electrode, but instead with an ultrathin layer of ambient screening charges, characterized by a surface screening length. Obtained results revealed an unexpectedly strong effect of the joint action of Vegard stresses and flexoelectric effect (shortly flexochemical coupling) on the ferroelectric transition temperature, distribution of the spontaneous polarization and elastic fields, domain wall structure and period in thin PbTi O3 films containing a layer of elastic defects. A nontrivial result is the persistence of ferroelectricity at film thicknesses below 4 nm, temperatures lower than 350 K, and relatively high surface screening length (˜0.1 nm ) . The origin of this phenomenon is the flexoelectric coupling leading to the rebuilding of the domain structure in the film (namely the cross-over from c-domain stripes to a-type closure domains) when its thickness decreases below 4 nm. The ferroelectricity persistence is facilitated by negative Vegard effect. For positive Vegard effect, thicker films exhibit the appearance of pronounced maxima on the thickness dependence of the transition temperature, whose position and height can be controlled by the defect type and concentration. The revealed features may have important implications for miniaturization of ferroelectric-based devices.

Surface density mapping of natural tissue by a scanning haptic microscope (SHM).

PubMed

Moriwaki, Takeshi; Oie, Tomonori; Takamizawa, Keiichi; Murayama, Yoshinobu; Fukuda, Toru; Omata, Sadao; Nakayama, Yasuhide

2013-02-01

To expand the performance capacity of the scanning haptic microscope (SHM) beyond surface mapping microscopy of elastic modulus or topography, surface density mapping of a natural tissue was performed by applying a measurement theory of SHM, in which a frequency change occurs upon contact of the sample surface with the SHM sensor - a microtactile sensor (MTS) that vibrates at a pre-determined constant oscillation frequency. This change was mainly stiffness-dependent at a low oscillation frequency and density-dependent at a high oscillation frequency. Two paragon examples with extremely different densities but similar macroscopic elastic moduli in the range of natural soft tissues were selected: one was agar hydrogels and the other silicon organogels with extremely low (less than 25 mg/cm(3)) and high densities (ca. 1300 mg/cm(3)), respectively. Measurements were performed in saline solution near the second-order resonance frequency, which led to the elastic modulus, and near the third-order resonance frequency. There was little difference in the frequency changes between the two resonance frequencies in agar gels. In contrast, in silicone gels, a large frequency change by MTS contact was observed near the third-order resonance frequency, indicating that the frequency change near the third-order resonance frequency reflected changes in both density and elastic modulus. Therefore, a density image of the canine aortic wall was subsequently obtained by subtracting the image observed near the second-order resonance frequency from that near the third-order resonance frequency. The elastin-rich region had a higher density than the collagen-rich region.

On the buckling of elastic rings by external confinement.

PubMed

Hazel, Andrew L; Mullin, Tom

2017-05-13

We report the results of an experimental and numerical investigation into the buckling of thin elastic rings confined within containers of circular or regular polygonal cross section. The rings float on the surface of water held in the container and controlled removal of the fluid increases the confinement of the ring. The increased compressive forces can cause the ring to buckle into a variety of shapes. For the circular container, finite perturbations are required to induce buckling, whereas in polygonal containers the buckling occurs through a linear instability that is closely related to the canonical Euler column buckling. A model based on Kirchhoff-Love beam theory is developed and solved numerically, showing good agreement with the experiments and revealing that in polygons increasing the number of sides means that buckling occurs at reduced levels of confinement.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.' © 2017 The Author(s).

Platinum-catalyzed hydrolysis etching of SiC in water: A density functional theory study

NASA Astrophysics Data System (ADS)

Van Bui, Pho; Toh, Daisetsu; Isohashi, Ai; Matsuyama, Satoshi; Inagaki, Kouji; Sano, Yasuhisa; Yamauchi, Kazuto; Morikawa, Yoshitada

2018-05-01

A comprehensive study of the physicochemical interactions and the reaction mechanism of SiC etching with water by Pt catalysts can reveal key details about the surface treatment and catalytic phenomena at interfaces. Therefore, density functional theory simulations were performed to study the kinetics of Pt-assisted water dissociation and breaking of a Si–C bond compared to the HF-assisted mechanism. These calculations carefully considered the elastic and chemical interaction energies at the Pt–SiC interface, activation barriers of Si–C bond dissociation, and the catalytic role of Pt. It was found that the Pt-catalyzed etching of SiC in water is initiated via hydrolysis reactions that break the topmost Si–C bonds. The activation barrier strongly depends on the elastic and chemical interactions. However, chemical interactions are a dominant factor and mainly contribute to the lowering of the activation barrier, resulting in an increased rate of reaction.

On the buckling of elastic rings by external confinement

PubMed Central

Hazel, Andrew L.

2017-01-01

We report the results of an experimental and numerical investigation into the buckling of thin elastic rings confined within containers of circular or regular polygonal cross section. The rings float on the surface of water held in the container and controlled removal of the fluid increases the confinement of the ring. The increased compressive forces can cause the ring to buckle into a variety of shapes. For the circular container, finite perturbations are required to induce buckling, whereas in polygonal containers the buckling occurs through a linear instability that is closely related to the canonical Euler column buckling. A model based on Kirchhoff–Love beam theory is developed and solved numerically, showing good agreement with the experiments and revealing that in polygons increasing the number of sides means that buckling occurs at reduced levels of confinement. This article is part of the themed issue ‘Patterning through instabilities in complex media: theory and applications.’ PMID:28373386

Nonlinear problems of the theory of heterogeneous slightly curved shells

NASA Technical Reports Server (NTRS)

Kantor, B. Y.

1973-01-01

An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.

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.

Thermodynamically consistent constitutive equations for nonisothermal large strain, elasto-plastic, creep behavior

NASA Technical Reports Server (NTRS)

Riff, R.; Carlson, R. L.; Simitses, G. J.

1985-01-01

The paper is concerned with the development of constitutive relations for large nonisothermal elastic-viscoplastic deformations for metals. The kinematics of elastic-plastic deformation, valid for finite strains and rotations, is presented. The resulting elastic-plastic uncoupled equations for the deformation rate combined with use of the incremental elasticity law permits a precise and purely deductive development of elastic-viscoplastic theory. It is shown that a phenomenological thermodynamic theory in which the elastic deformation and the temperature are state variables, including few internal variables, can be utilized to construct elastic-viscoplastic constitutive equations, which are appropriate for metals. The limiting case of inviscid plasticity is examined.

An experimental study of the elastic theory for granular flows

NASA Astrophysics Data System (ADS)

Guo, Tongtong; Campbell, Charles S.

2016-08-01

This paper reports annular shear cell measurements granular flows with an eye towards experimentally confirming the flow regimes laid out in the elastic theory of granular flow. Tests were carried out on four different kinds of plastic spherical particles under both constant volume flows and constant applied stress flows. In particular, observations were made of the new regime in that model, the elastic-inertial regime, and the predicted transitions between the elastic-inertial and both the elastic-quasistatic and pure inertial regimes.

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.

Soft Listeria: actin-based propulsion of liquid drops.

PubMed

Boukellal, Hakim; Campás, Otger; Joanny, Jean-François; Prost, Jacques; Sykes, Cécile

2004-06-01

We study the motion of oil drops propelled by actin polymerization in cell extracts. Drops deform and acquire a pearlike shape under the action of the elastic stresses exerted by the actin comet, a tail of cross-linked actin filaments. We solve this free boundary problem and calculate the drop shape taking into account the elasticity of the actin gel and the variation of the polymerization velocity with normal stress. The pressure balance on the liquid drop imposes a zero propulsive force if gradients in surface tension or internal pressure are not taken into account. Quantitative parameters of actin polymerization are obtained by fitting theory to experiment.

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.

Isometric immersions and self-similar buckling in elastic sheets.

NASA Astrophysics Data System (ADS)

Gemmer, John

The edges of torn elastic sheets and growing leaves often display hierarchical self-similar like buckling patterns. On the one hand, such complex, self similar patterns are usually associated with a competition between two distinct energy scales, e.g. elastic sheets with boundary conditions that preclude the possibility of relieving in plane strains, or at alloy-alloy interfaces between distinct crystal structures. On the other hand, within the non-Euclidean plate theory this complex morphology can be understood as low bending energy isometric immersions of hyperbolic Riemannian metrics. In particular, many growth patterns generate residual in-plane strains which can be entirely relieved by the sheet forming part of a surface of revolution or a helix. In this talk we will show that this complex morphology (i) arises from isometric immersions (ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. We identify the key role of branch-point (or monkey-saddle) singularities, in complex wrinkling patterns within the class of finite bending energy isometric immersions. Using these defects we will give an explicit construction of strain-free embeddings of hyperbolic surfaces that are fractal like and have lower elastic energy than their smooth counterparts US-Israel BSF Grant 2008432. NSF Grant DMS-0807501. NSF-RTG Grant DMS-1148284.

Recent advances in engineering science; Proceedings of the A. Cemal Eringen Symposium, University of California, Berkeley, June 20-22, 1988

NASA Technical Reports Server (NTRS)

Koh, Severino L. (Editor); Speziale, Charles G. (Editor)

1989-01-01

Various papers on recent advances in engineering science are presented. Some individual topics addressed include: advances in adaptive methods in computational fluid mechanics, mixtures of two medicomorphic materials, computer tests of rubber elasticity, shear bands in isotropic micropolar elastic materials, nonlinear surface wave and resonator effects in magnetostrictive crystals, simulation of electrically enhanced fibrous filtration, plasticity theory of granular materials, dynamics of viscoelastic media with internal oscillators, postcritical behavior of a cantilever bar, boundary value problems in nonlocal elasticity, stability of flexible structures with random parameters, electromagnetic tornadoes in earth's ionosphere and magnetosphere, helicity fluctuations and the energy cascade in turbulence, mechanics of interfacial zones in bonded materials, propagation of a normal shock in a varying area duct, analytical mechanics of fracture and fatigue.

Molecular organization of nematic liquid crystals between concentric cylinders: Role of the elastic anisotropy

NASA Astrophysics Data System (ADS)

Chiccoli, C.; Pasini, P.; Evangelista, L. R.; Teixeira-Souza, R. T.; Zannoni, C.

2015-02-01

The orientational order in a nematic liquid crystal sample confined to an annular region between two concentric cylinders is investigated by means of lattice Monte Carlo simulations. Strong anchoring and homeotropic orientations, parallel to the radial direction, are implemented at the confining surfaces. The elastic anisotropy is taken into account in the bulk interactions by using the pair potential introduced by Gruhn and Hess [T. Gruhn and S. Hess, Z. Naturforsch. A 51, 1 (1996)] and parametrized by Romano and Luckhurst [S. Romano, Int. J. Mod. Phys. B 12, 2305 (1998), 10.1142/S0217979298001344; Phys. Lett. A 302, 203 (2002), 10.1016/S0375-9601(02)01042-3; G. R. Luckhurst and S. Romano, Liq. Cryst. 26, 871 (1999), 10.1080/026782999204561], i.e., the so-called GHRL potential. In the case of equal elastic constants, a small but appreciable deformation along the cylinder axis direction is observed, whereas when the values of K11/K33 if K22=K33 are low enough, all the spins in the bulk follow the orientation imposed by the surfaces. For larger values of K11/K33 , spontaneous deformations, perpendicular to the polar plane, increase significantly. Our findings indicate that the onset of these deformations also depends on the ratio K22/K33 and on the radius of the cylindrical surfaces. Although expected from the elastic theory, no tangential component of the deformations was observed in the simulations for the set of parameters analyzed.

Cones of localized shear strain in incompressible elasticity with prestress: Green's function and integral representations

PubMed Central

Argani, L. P.; Bigoni, D.; Capuani, D.; Movchan, N. V.

2014-01-01

The infinite-body three-dimensional Green's function set (for incremental displacement and mean stress) is derived for the incremental deformation of a uniformly strained incompressible, nonlinear elastic body. Particular cases of the developed formulation are the Mooney–Rivlin elasticity and the J2-deformation theory of plasticity. These Green's functions are used to develop a boundary integral equation framework, by introducing an ad hoc potential, which paves the way for a boundary element formulation of three-dimensional problems of incremental elasticity. Results are used to investigate the behaviour of a material deformed near the limit of ellipticity and to reveal patterns of shear failure. In fact, within the investigated three-dimensional framework, localized deformations emanating from a perturbation are shown to be organized in conical geometries rather than in planar bands, so that failure is predicted to develop through curved and thin surfaces of intense shearing, as can for instance be observed in the cup–cone rupture of ductile metal bars. PMID:25197258

Thermo-Elastic Triangular Sandwich Element for the Complete Stress Field Based on a Single-Layer Theory

NASA Technical Reports Server (NTRS)

Das, M.; Barut, A.; Madenci, E.; Ambur, D. R.

2004-01-01

This study presents a new triangular finite element for modeling thick sandwich panels, subjected to thermo-mechanical loading, based on a {3,2}-order single-layer plate theory. A hybrid energy functional is employed in the derivation of the element because of a C interelement continuity requirement. The single-layer theory is based on five weighted-average field variables arising from the cubic and quadratic representations of the in-plane and transverse displacement fields, respectively. The variations of temperature and distributed loading acting on the top and bottom surfaces are non-uniform. The temperature varies linearly through the thickness.

Scanning tunneling microscopy current from localized basis orbital density functional theory

NASA Astrophysics Data System (ADS)

Gustafsson, Alexander; Paulsson, Magnus

2016-03-01

We present a method capable of calculating elastic scanning tunneling microscopy (STM) currents from localized atomic orbital density functional theory (DFT). To overcome the poor accuracy of the localized orbital description of the wave functions far away from the atoms, we propagate the wave functions, using the total DFT potential. From the propagated wave functions, the Bardeen's perturbative approach provides the tunneling current. To illustrate the method we investigate carbon monoxide adsorbed on a Cu(111) surface and recover the depression/protrusion observed experimentally with normal/CO-functionalized STM tips. The theory furthermore allows us to discuss the significance of s - and p -wave tips.

Asymptotic quantum inelastic generalized Lorenz Mie theory

NASA Astrophysics Data System (ADS)

Gouesbet, G.

2007-10-01

The (electromagnetic) generalized Lorenz-Mie theory describes the interaction between an electromagnetic arbitrary shaped beam and a homogeneous sphere. It is a generalization of the Lorenz-Mie theory which deals with the simpler case of a plane wave illumination. In a recent paper, we consider (i) elastic cross-sections in electromagnetic generalized Lorenz-Mie theory and (ii) elastic cross-sections in an associated quantum generalized Lorenz-Mie theory. We demonstrated that the electromagnetic problem is equivalent to a superposition of two effective quantum problems. We now intend to generalize this result from elastic cross-sections to inelastic cross-sections. A prerequisite is to build an asymptotic quantum inelastic generalized Lorenz-Mie theory, which is presented in this paper.

Spontaneous formation of non-uniform double helices for elastic rods under torsion

NASA Astrophysics Data System (ADS)

Li, Hongyuan; Zhao, Shumin; Xia, Minggang; He, Siyu; Yang, Qifan; Yan, Yuming; Zhao, Hanqiao

2017-02-01

The spontaneous formation of double helices for filaments under torsion is common and significant. For example, the research on the supercoiling of DNA is helpful for understanding the replication and transcription of DNA. Similar double helices can appear in carbon nanotube yarns, cables, telephone wires and so forth. We noticed that non-uniform double helices can be produced due to the surface friction induced by the self-contact. Therefore an ideal model was presented to investigate the formation of double helices for elastic rods under torque. A general equilibrium condition which is valid for both the smooth surface and the rough surface situations is derived by using the variational method. By adding further constraints, the smooth and rough surface situations are investigated in detail respectively. Additionally, the model showed that the specific process of how to twist and slack the rod can determine the surface friction and hence influence the configuration of the double helix formed by rods with rough surfaces. Based on this principle, a method of manufacturing double helices with designed configurations was proposed and demonstrated. Finally, experiments were performed to verify the model and the results agreed well with the theory.

Surface effect on resonant properties of nanowires predicted by an elastic theory for nanomaterials

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

Yao, Yin; Chen, Shaohua, E-mail: chenshaohua72@hotmail.com, E-mail: shchen@LNM.imech.ac.cn

2015-07-28

A recently developed continuum theory considering surface effect in nanomaterials is adopted to investigate the resonant properties of nanowires with different boundary conditions in the present paper. The main feature of the adopted theory is that the surface effect in nanomaterials is characterized by the surface energy density of the corresponding bulk materials and the surface relaxation parameter in nanoscale. Based on a fixed-fixed beam model and a cantilever one, the governing equation of resonant frequency for corresponding nanowires is obtained. Numerical calculation of the fundamental resonant frequency is carried out, the result of which is well consistent with themore » existing numerical ones. Comparing to the result predicted by the conventionally structural dynamics, the resonant frequency of a fixed-fixed nanowire is improved, while that of a cantilever nanowire is weakened due to the surface effect. Both a decreasing characteristic size (height or diameter) and an increasing aspect ratio could further enhance the varying trend of resonant properties for both kinds of nanowires. The present result should be helpful for the design of nano-devices and nanostructures related to nanowires.« less

Experimental Techniques Verified for Determining Yield and Flow Surfaces

NASA Technical Reports Server (NTRS)

Lerch, Brad A.; Ellis, Rod; Lissenden, Cliff J.

1998-01-01

Structural components in aircraft engines are subjected to multiaxial loads when in service. For such components, life prediction methodologies are dependent on the accuracy of the constitutive models that determine the elastic and inelastic portions of a loading cycle. A threshold surface (such as a yield surface) is customarily used to differentiate between reversible and irreversible flow. For elastoplastic materials, a yield surface can be used to delimit the elastic region in a given stress space. The concept of a yield surface is central to the mathematical formulation of a classical plasticity theory, but at elevated temperatures, material response can be highly time dependent. Thus, viscoplastic theories have been developed to account for this time dependency. Since the key to many of these theories is experimental validation, the objective of this work (refs. 1 and 2) at the NASA Lewis Research Center was to verify that current laboratory techniques and equipment are sufficient to determine flow surfaces at elevated temperatures. By probing many times in the axial-torsional stress space, we could define the yield and flow surfaces. A small offset definition of yield (10 me) was used to delineate the boundary between reversible and irreversible behavior so that the material state remained essentially unchanged and multiple probes could be done on the same specimen. The strain was measured with an off-the-shelf multiaxial extensometer that could measure the axial and torsional strains over a wide range of temperatures. The accuracy and resolution of this extensometer was verified by comparing its data with strain gauge data at room temperature. The extensometer was found to have sufficient resolution for these experiments. In addition, the amount of crosstalk (i.e., the accumulation of apparent strain in one direction when strain in the other direction is applied) was found to be negligible. Tubular specimens were induction heated to determine the flow surfaces at elevated temperatures. The heating system induced a large amount of noise in the data. By reducing thermal fluctuations and using appropriate data averaging schemes, we could render the noise inconsequential. Thus, accurate and reproducible flow surfaces (see the figure) could be obtained.

A numerical investigation of the crystallographic texture effect on the surface roughening in aluminum polycrystals

NASA Astrophysics Data System (ADS)

Romanova, V.; Balokhonov, R.; Batukhtina, E.; Zinovieva, O.; Bezmozgiy, I.

2015-10-01

The results of a numerical analysis of the mesoscale surface roughening in a polycrystalline aluminum alloy exposed to uniaxial tension are presented. A 3D finite-element model taking an explicit account of grain structure is developed. The model describes a constitutive behavior of the material on the grain scale, using anisotropic elasticity and crystal plasticity theory. The effects of the grain shape and texture on the deformation-induced roughening are investigated. Calculation results have shown that surface roughness is much higher and develops at the highest rate in a polycrystal with equiaxed grains where both the micro- and mesoscale surface displacements are observed.

Quantitative estimation of minimum offset for multichannel surface-wave survey with actively exciting source

USGS Publications Warehouse

Xu, Y.; Xia, J.; Miller, R.D.

2006-01-01

Multichannel analysis of surface waves is a developing method widely used in shallow subsurface investigations. The field procedures and related parameters are very important for successful applications. Among these parameters, the source-receiver offset range is seldom discussed in theory and normally determined by empirical or semi-quantitative methods in current practice. This paper discusses the problem from a theoretical perspective. A formula for quantitatively evaluating a layered homogenous elastic model was developed. The analytical results based on simple models and experimental data demonstrate that the formula is correct for surface wave surveys for near-surface applications. ?? 2005 Elsevier B.V. All rights reserved.

The dynamics and control of large flexible space structures, 3. Part A: Shape and orientation control of a platform in orbit using point actuators

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Reddy, A. S. S. R.; Krishna, R.; James, P. K.

1980-01-01

The dynamics, attitude, and shape control of a large thin flexible square platform in orbit are studied. Attitude and shape control are assumed to result from actuators placed perpendicular to the main surface and one edge and their effect on the rigid body and elastic modes is modelled to first order. The equations of motion are linearized about three different nominal orientations: (1) the platform following the local vertical with its major surface perpendicular to the orbital plane; (2) the platform following the local horizontal with its major surface normal to the local vertical; and (3) the platform following the local vertical with its major surface perpendicular to the orbit normal. The stability of the uncontrolled system is investigated analytically. Once controllability is established for a set of actuator locations, control law development is based on decoupling, pole placement, and linear optimal control theory. Frequencies and elastic modal shape functions are obtained using a finite element computer algorithm, two different approximate analytical methods, and the results of the three methods compared.

Surface Structure of Bi(111) from Helium Atom Scattering Measurements. Inelastic Close-Coupling Formalism

PubMed Central

2015-01-01

Elastic and inelastic close-coupling (CC) calculations have been used to extract information about the corrugation amplitude and the surface vibrational atomic displacement by fitting to several experimental diffraction patterns. To model the three-dimensional interaction between the He atom and the Bi(111) surface under investigation, a corrugated Morse potential has been assumed. Two different types of calculations are used to obtain theoretical diffraction intensities at three surface temperatures along the two symmetry directions. Type one consists of solving the elastic CC (eCC) and attenuating the corresponding diffraction intensities by a global Debye–Waller (DW) factor. The second one, within a unitary theory, is derived from merely solving the inelastic CC (iCC) equations, where no DW factor is necessary to include. While both methods arrive at similar predictions for the peak-to-peak corrugation value, the variance of the value obtained by the iCC method is much better. Furthermore, the more extensive calculation is better suited to model the temperature induced signal asymmetries and renders the inclusion for a second Debye temperature for the diffraction peaks futile. PMID:26257838

Derivation of force field parameters for SnO2-H2O surface systems from plane-wave density functional theory calculations.

PubMed

Bandura, A V; Sofo, J O; Kubicki, J D

2006-04-27

Plane-wave density functional theory (DFT-PW) calculations were performed on bulk SnO2 (cassiterite) and the (100), (110), (001), and (101) surfaces with and without H2O present. A classical interatomic force field has been developed to describe bulk SnO2 and SnO2-H2O surface interactions. Periodic density functional theory calculations using the program VASP (Kresse et al., 1996) and molecular cluster calculations using Gaussian 03 (Frisch et al., 2003) were used to derive the parametrization of the force field. The program GULP (Gale, 1997) was used to optimize parameters to reproduce experimental and ab initio results. The experimental crystal structure and elastic constants of SnO2 are reproduced reasonably well with the force field. Furthermore, surface atom relaxations and structures of adsorbed H2O molecules agree well between the ab initio and force field predictions. H2O addition above that required to form a monolayer results in consistent structures between the DFT-PW and classical force field results as well.

An improved plate theory of order (1,2) for thick composite laminates

NASA Technical Reports Server (NTRS)

Tessler, A.

1992-01-01

A new (1,2)-order theory is proposed for the linear elasto-static analysis of laminated composite plates. The basic assumptions are those concerning the distribution through the laminate thickness of the displacements, transverse shear strains and the transverse normal stress, with these quantities regarded as some weighted averages of their exact elasticity theory representations. The displacement expansions are linear for the inplane components and quadratic for the transverse component, whereas the transverse shear strains and transverse normal stress are respectively quadratic and cubic through the thickness. The main distinguishing feature of the theory is that all strain and stress components are expressed in terms of the assumed displacements prior to the application of a variational principle. This is accomplished by an a priori least-square compatibility requirement for the transverse strains and by requiring exact stress boundary conditions at the top and bottom plate surfaces. Equations of equilibrium and associated Poisson boundary conditions are derived from the virtual work principle. It is shown that the theory is particularly suited for finite element discretization as it requires simple C(sup 0)- and C(sup -1)-continuous displacement interpolation fields. Analytic solutions for the problem of cylindrical bending are derived and compared with the exact elasticity solutions and those of our earlier (1,2)-order theory based on the assumed displacements and transverse strains.

The elastic energy and character of quakes in solid stars and planets

NASA Technical Reports Server (NTRS)

Pines, D.; Shaham, J.

1972-01-01

The quadrupolar mechanical energy of a rotating axially symmetric solid planet (with or without a liquid interior) is calculated using methods previously developed for neutron stars in which an elastic reference tensor is introduced to describe the build-up of elastic energy in the star. The basic parameters of the theory (the gravitational energy A and elastic energy B) depend upon the internal structure of the planet and may be calculated from specific planetary models. Explicit expressions are obtained for the Love numbers, and for the planetary wobble frequency. The theory provides a simple relationship between changes in shape or axis of figure of the planet and elastic energy release. The theory is extended to describe the Earth by taking into account isostasy, triaxiality and the observed lithospheric configuration.

From elasticity to capillarity in soft materials indentation

NASA Astrophysics Data System (ADS)

Pham, Jonathan T.; Schellenberger, Frank; Kappl, Michael; Butt, Hans-Jürgen

2017-06-01

For soft materials with Young's moduli below 100 kPa, quantifying mechanical and interfacial properties by small scale indentation is challenging because in addition to adhesion and elasticity, surface tension plays a critical role. Until now, microscale contact of very soft materials has only been studied by static experiments under zero external loading. Here we introduce a combination of the colloidal probe technique and confocal microscopy to characterize the force-indentation and force-contact radius relationships during microindentation of soft silicones. We confirm that the widespread Johnson-Kendall-Roberts theory must be extended to predict the mechanical contact for soft materials. Typically a liquid component is found within very soft materials. With a simple analytical model, we illustrate that accounting for this liquid surface tension can capture the contact behavior. Our results highlight the importance of considering liquid that is often associated with soft materials during small scale contact.

Unveiling Extreme Anisotropy in Elastic Structured Media

NASA Astrophysics Data System (ADS)

Lefebvre, G.; Antonakakis, T.; Achaoui, Y.; Craster, R. V.; Guenneau, S.; Sebbah, P.

2017-06-01

Periodic structures can be engineered to exhibit unique properties observed at symmetry points, such as zero group velocity, Dirac cones, and saddle points; identifying these and the nature of the associated modes from a direct reading of the dispersion surfaces is not straightforward, especially in three dimensions or at high frequencies when several dispersion surfaces fold back in the Brillouin zone. A recently proposed asymptotic high-frequency homogenization theory is applied to a challenging time-domain experiment with elastic waves in a pinned metallic plate. The prediction of a narrow high-frequency spectral region where the effective medium tensor dramatically switches from positive definite to indefinite is confirmed experimentally; a small frequency shift of the pulse carrier results in two distinct types of highly anisotropic modes. The underlying effective equation mirrors this behavior with a change in form from elliptic to hyperbolic exemplifying the high degree of wave control available and the importance of a simple and effective predictive model.

Experimental Observation of Two Features Unexpected from the Classical Theories of Rubber Elasticity

NASA Astrophysics Data System (ADS)

Nishi, Kengo; Fujii, Kenta; Chung, Ung-il; Shibayama, Mitsuhiro; Sakai, Takamasa

2017-12-01

Although the elastic modulus of a Gaussian chain network is thought to be successfully described by classical theories of rubber elasticity, such as the affine and phantom models, verification experiments are largely lacking owing to difficulties in precisely controlling of the network structure. We prepared well-defined model polymer networks experimentally, and measured the elastic modulus G for a broad range of polymer concentrations and connectivity probabilities, p . In our experiment, we observed two features that were distinct from those predicted by classical theories. First, we observed the critical behavior G ˜|p -pc|1.95 near the sol-gel transition. This scaling law is different from the prediction of classical theories, but can be explained by analogy between the electric conductivity of resistor networks and the elasticity of polymer networks. Here, pc is the sol-gel transition point. Furthermore, we found that the experimental G -p relations in the region above C* did not follow the affine or phantom theories. Instead, all the G /G0-p curves fell onto a single master curve when G was normalized by the elastic modulus at p =1 , G0. We show that the effective medium approximation for Gaussian chain networks explains this master curve.

Mechanics of couple-stress fluid coatings

NASA Technical Reports Server (NTRS)

Waxman, A. M.

1982-01-01

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

Asymptotic quantum elastic generalized Lorenz Mie theory

NASA Astrophysics Data System (ADS)

Gouesbet, G.

2006-10-01

The (electromagnetic) generalized Lorenz-Mie theory describes the interaction between an electromagnetic arbitrary shaped beam and a homogeneous sphere. It is a generalization of the Lorenz-Mie theory which deals with the simpler case of a plane-wave illumination. In a recent paper, we established that, if we restrict ourselves to the study of cross-sections, both for elastic and inelastic scatterings, a macroscopic sphere in Lorenz-Mie theory is formally equivalent to a quantum-like radial potential. To generalize this result, a prerequisite is to possess an asymptotic quantum generalized Lorenz-Mie theory expressing cross-sections in the case of a quantum radial potential interacting with a sub-class of quantum arbitrary wave-packets. Such a theory, restricted however to elastic scattering, is presented in this paper.

Temperature Dependence Of Elastic Constants Of Polymers

NASA Technical Reports Server (NTRS)

Simha, Robert; Papazoglou, Elisabeth

1989-01-01

Two papers extend theory of elastic constants of disordered solids to finite temperatures below glass-transition temperatures. First paper, entitled "Elastic Constants of Disordered Solids II: Temperature Dependence," applies to cryogenic temperatures. Second paper, entitled "Theory of Thermoelastic Properties for Polymer Glasses," develops unified treatment for static compressional and elongational properties at temperatures up to glass-transition temperatures.

A simple and efficient shear-flexible plate bending element

NASA Technical Reports Server (NTRS)

Chaudhuri, Reaz A.

1987-01-01

A shear-flexible triangular element formulation, which utilizes an assumed quadratic displacement potential energy approach and is numerically integrated using Gauss quadrature, is presented. The Reissner/Mindlin hypothesis of constant cross-sectional warping is directly applied to the three-dimensional elasticity theory to obtain a moderately thick-plate theory or constant shear-angle theory (CST), wherein the middle surface is no longer considered to be the reference surface and the two rotations are replaced by the two in-plane displacements as nodal variables. The resulting finite-element possesses 18 degrees of freedom (DOF). Numerical results are obtained for two different numerical integration schemes and a wide range of meshes and span-to-thickness ratios. These, when compared with available exact, series or finite-element solutions, demonstrate accuracy and rapid convergence characteristics of the present element. This is especially true in the case of thin to very thin plates, when the present element, used in conjunction with the reduced integration scheme, outperforms its counterpart, based on discrete Kirchhoff constraint theory (DKT).

Mammalian phospholipid homeostasis: evidence that membrane curvature elastic stress drives homeoviscous adaptation in vivo

PubMed Central

2016-01-01

Several theories of phospholipid homeostasis have postulated that cells regulate the molecular composition of their bilayer membranes, such that a common biophysical membrane parameter is under homeostatic control. Two commonly cited theories are the intrinsic curvature hypothesis, which states that cells control membrane curvature elastic stress, and the theory of homeoviscous adaptation, which postulates cells control acyl chain packing order (membrane order). In this paper, we present evidence from data-driven modelling studies that these two theories correlate in vivo. We estimate the curvature elastic stress of mammalian cells to be 4–7 × 10−12 N, a value high enough to suggest that in mammalian cells the preservation of membrane order arises through a mechanism where membrane curvature elastic stress is controlled. These results emerge from analysing the molecular contribution of individual phospholipids to both membrane order and curvature elastic stress in nearly 500 cellular compositionally diverse lipidomes. Our model suggests that the de novo synthesis of lipids is the dominant mechanism by which cells control curvature elastic stress and hence membrane order in vivo. These results also suggest that cells can increase membrane curvature elastic stress disproportionately to membrane order by incorporating polyunsaturated fatty acids into lipids. PMID:27534697

Mammalian phospholipid homeostasis: evidence that membrane curvature elastic stress drives homeoviscous adaptation in vivo.

PubMed

Dymond, Marcus K

2016-08-01

Several theories of phospholipid homeostasis have postulated that cells regulate the molecular composition of their bilayer membranes, such that a common biophysical membrane parameter is under homeostatic control. Two commonly cited theories are the intrinsic curvature hypothesis, which states that cells control membrane curvature elastic stress, and the theory of homeoviscous adaptation, which postulates cells control acyl chain packing order (membrane order). In this paper, we present evidence from data-driven modelling studies that these two theories correlate in vivo. We estimate the curvature elastic stress of mammalian cells to be 4-7 × 10(-12) N, a value high enough to suggest that in mammalian cells the preservation of membrane order arises through a mechanism where membrane curvature elastic stress is controlled. These results emerge from analysing the molecular contribution of individual phospholipids to both membrane order and curvature elastic stress in nearly 500 cellular compositionally diverse lipidomes. Our model suggests that the de novo synthesis of lipids is the dominant mechanism by which cells control curvature elastic stress and hence membrane order in vivo These results also suggest that cells can increase membrane curvature elastic stress disproportionately to membrane order by incorporating polyunsaturated fatty acids into lipids. © 2016 The Author(s).

Research on friction torque analysis of planetary roller screw mechanism considering load distribution

NASA Astrophysics Data System (ADS)

Gan, Fajin; Mao, Pengcheng; Zheng, Shicheng; Li, Guangliang; Xin, Shupeng

2018-04-01

Based on the Hertzian contact theory, frictional moment of planetary roller screw mechanism (RSM) caused by elastic hysteresis, roller's spinning sliding, and differential sliding was analyzed, which were considering load distribution of rollers threads. The relationship between friction torque of screw pairs and its input axial load were obtained. Finally, the frictional moment of the screw pairs under the situation overstress will created at some localized contact surfaces were discussed. Results shows that the frictional moment caused by elastic hysteresis gives the greatest rise to the total frictional moment and that due to differential sliding can be ignored. The stress uniformity has great influence on the frictional moment.

Development of a non-linear simulation for generic hypersonic vehicles - ASUHS1

NASA Technical Reports Server (NTRS)

Salas, Juan; Lovell, T. Alan; Schmidt, David K.

1993-01-01

A nonlinear simulation is developed to model the longitudinal motion of a vehicle in hypersonic flight. The equations of motion pertinent to this study are presented. Analytic expressions for the aerodynamic forces acting on a hypersonic vehicle which were obtained from Newtonian Impact Theory are further developed. The control surface forces are further examined to incorporate vehicle elastic motion. The purpose is to establish feasible equations of motion which combine rigid body, elastic, and aeropropulsive dynamics for use in nonlinear simulations. The software package SIMULINK is used to implement the simulation. Also discussed are issues needing additional attention and potential problems associated with the implementation (with proposed solutions).

Influence of a thin compressible insoluble liquid film on the eddy currents generated by interacting surface waves

NASA Astrophysics Data System (ADS)

Parfenyev, Vladimir M.; Vergeles, Sergey S.

2018-06-01

Recently the generation of eddy currents by interacting surface waves was observed experimentally. The phenomenon provides the possibility for manipulation of particles which are immersed in the fluid. The analysis shows that the amplitude of the established eddy currents produced by stationary surface waves does not depend on the fluid viscosity in the free surface case. The currents become parametrically larger, being inversely proportional to the square root of the fluid viscosity in the case when the fluid surface is covered by an almost incompressible thin liquid (i.e., shear elasticity is zero) film formed by an insoluble agent with negligible internal viscous losses as compared to the dissipation in the fluid bulk. Here we extend the theory for a thin insoluble film with zero shear elasticity and small shear and dilational viscosities on the case of an arbitrary elastic compression modulus. We find both contributions into the Lagrangian motion of passive tracers, which are the advection by the Eulerian vertical vorticity and the Stokes drift. Whereas the Stokes drift contribution preserves its value for the free surface case outside a thin viscous sublayer, the Eulerian vertical vorticity strongly depends on the fluid viscosity at high values of the film compression modulus. The Stokes drift acquires a strong dependence on the fluid viscosity inside the viscous sublayer; however, the change is compensated by an opposite change in the Eulerian vertical vorticity. As a result, the vertical dependence of the intensity of eddy currents is given by a sum of two decaying exponents with both decrements being of the order of the wave number. The decrements are numerically different, so the Eulerian contribution becomes dominant at some depth for the surface film with any compression modulus.

Gravitational potential as a source of earthquake energy

USGS Publications Warehouse

Barrows, L.; Langer, C.J.

1981-01-01

Some degree of tectonic stress within the earth originates from gravity acting upon density structures. The work performed by this "gravitational tectonics stress" must have formerly existed as gravitational potential energy contained in the stress-causing density structure. According to the elastic rebound theory (Reid, 1910), the energy of earthquakes comes from an elastic strain field built up by fairly continuous elastic deformation in the period between events. For earthquakes resulting from gravitational tectonic stress, the elastic rebound theory requires the transfer of energy from the gravitational potential of the density structures into an elastic strain field prior to the event. An alternate theory involves partial gravitational collapse of the stress-causing density structures. The earthquake energy comes directly from a net decrease in gravitational potential energy. The gravitational potential energy released at the time of the earthquake is split between the energy released by the earthquake, including work done in the fault zone and an increase in stored elastic strain energy. The stress associated with this elastic strain field should oppose further fault slip. ?? 1981.

Study of free edge effect on sub-laminar scale for thermoplastic composite laminates

NASA Astrophysics Data System (ADS)

Shen, Min; Lu, Huanbao; Tong, Jingwei; Su, Yishi; Li, Hongqi; Lv, Yongmin

2008-11-01

The interlaminar deformation on the free edge surface in thermoplastic composite AS4/PEEK laminates under bending loading are studied by means of digital image correlation method (DICM) using a white-light industrial microscopic. During the test, any artificial stochastic spray is not applied to the specimen surface. In laminar scale, the interlaminare displacements of [0/90]3s laminate are measured. In sub-laminar scale, the tested area includes a limited number of fibers; the fiber is elastic with actual diameter about 7μm, and PEEK matrix has elastic-plastic behavior. The local mesoscopic fields of interlaminar displacement near the areas of fiber-matrix interface are obtained by DICM. The distributions of in-plane elastic-plastic stresses near the interlaminar interface between different layers are indirectly obtained using the coupling the results of DICM with finite element method. Based on above DICM experiments, the influences of random fiber distribution and the PEEK matrix ductility in sub-laminar scale on the ineterlaminar mesomechanical behavior are investigated. The experimental results in the present work are important for multi-scale theory and numerical analysis of interlaminar deformation and stresses in these composite laminates.

Strain tensor selection and the elastic theory of incompatible thin sheets.

PubMed

Oshri, Oz; Diamant, Haim

2017-05-01

The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids 57, 762 (2009)JMPSA80022-509610.1016/j.jmps.2008.12.004]. For a class of simple axisymmetric problems we examine an alternative formulation, defining the strain based on deviations of distances (rather than distances squared) from their rest values. While the two formulations converge in the limit of small slopes and in the limit of an incompressible sheet, for other cases they are found not to be equivalent. The alternative formulation offers several features which are absent in the existing theory. (a) In the case of planar deformations of flat incompatible sheets, it yields linear, exactly solvable, equations of equilibrium. (b) When reduced to uniaxial (one-dimensional) deformations, it coincides with the theory of extensible elastica; in particular, for a uniaxially bent sheet it yields an unstrained cylindrical configuration. (c) It gives a simple criterion determining whether an isometric immersion of an incompatible sheet is at mechanical equilibrium with respect to normal forces. For a reference metric of constant positive Gaussian curvature, a spherical cap is found to satisfy this criterion except in an arbitrarily narrow boundary layer.

Strain tensor selection and the elastic theory of incompatible thin sheets

NASA Astrophysics Data System (ADS)

Oshri, Oz; Diamant, Haim

2017-05-01

The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids 57, 762 (2009), 10.1016/j.jmps.2008.12.004]. For a class of simple axisymmetric problems we examine an alternative formulation, defining the strain based on deviations of distances (rather than distances squared) from their rest values. While the two formulations converge in the limit of small slopes and in the limit of an incompressible sheet, for other cases they are found not to be equivalent. The alternative formulation offers several features which are absent in the existing theory. (a) In the case of planar deformations of flat incompatible sheets, it yields linear, exactly solvable, equations of equilibrium. (b) When reduced to uniaxial (one-dimensional) deformations, it coincides with the theory of extensible elastica; in particular, for a uniaxially bent sheet it yields an unstrained cylindrical configuration. (c) It gives a simple criterion determining whether an isometric immersion of an incompatible sheet is at mechanical equilibrium with respect to normal forces. For a reference metric of constant positive Gaussian curvature, a spherical cap is found to satisfy this criterion except in an arbitrarily narrow boundary layer.

Multiscale Multiphysics and Multidomain Models I: Basic Theory

PubMed Central

Wei, Guo-Wei

2013-01-01

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

Multiscale Multiphysics and Multidomain Models I: Basic Theory.

PubMed

Wei, Guo-Wei

2013-12-01

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

Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media

USGS Publications Warehouse

Zhang, K.; Luo, Y.; Xia, J.; Chen, C.

2011-01-01

Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media as compared with elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world. We apply a pseudospectral method to the calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity-stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic half-space comparing the phase velocities of Rayleigh wave between the theoretical values and the dispersive image generated by high-resolution linear Radon transform. We then simulate three types of two-layer models to analyze dispersive-energy characteristics for near-surface applications. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media and the fundamental mode increases by 10-16% when the frequency is above 10. Hz due to the velocity dispersion of P and S waves. ?? 2011 Elsevier Ltd.

Geometric charges in theories of elasticity and plasticity

NASA Astrophysics Data System (ADS)

Moshe, Michael

The mechanics of many natural systems is governed by localized sources of stresses. Examples include ''plastic events'' that occur in amorphous solids under external stress, defects formation in crystalline material, and force-dipoles applied by cells adhered to an elastic substrate. Recent developments in a geometric formulation of elasticity theory paved the way for a unifying mathematical description of such singular sources of stress, as ''elastic charges''. In this talk I will review basic results in this emerging field, focusing on the geometry and mechanics of elastic charges in two-dimensional solid bodies. I will demonstrate the applicability of this new approach in three different problems: failure of an amorphous solid under load, mechanics of Kirigami, and wrinkle patterns in geometrically-incompatible elastic sheets.

Localization through surface folding in solid foams under compression.

PubMed

Reis, P M; Corson, F; Boudaoud, A; Roman, B

2009-07-24

We report a combined experimental and theoretical study of the compression of a solid foam coated with a thin elastic film. Past a critical compression threshold, a pattern of localized folds emerges with a characteristic size that is imposed by an instability of the thin surface film. We perform optical surface measurements of the statistical properties of these localization zones and find that they are characterized by robust exponential tails in the strain distributions. Following a hybrid continuum and statistical approach, we develop a theory that accurately describes the nucleation and length scale of these structures and predicts the characteristic strains associated with the localized regions.

On the application of the partition of unity method for nonlocal response of low-dimensional structures

NASA Astrophysics Data System (ADS)

Natarajan, Sundararajan

2014-12-01

The main objectives of the paper are to (1) present an overview of nonlocal integral elasticity and Aifantis gradient elasticity theory and (2) discuss the application of partition of unity methods to study the response of low-dimensional structures. We present different choices of approximation functions for gradient elasticity, namely Lagrange intepolants, moving least-squares approximants and non-uniform rational B-splines. Next, we employ these approximation functions to study the response of nanobeams based on Euler-Bernoulli and Timoshenko theories as well as to study nanoplates based on first-order shear deformation theory. The response of nanobeams and nanoplates is studied using Eringen's nonlocal elasticity theory. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the global response is numerically studied. The influence of a crack on the axial vibration and buckling characteristics of nanobeams is also numerically studied.

A Global Upper-Mantle Tomographic Model of Shear Attenuation

NASA Astrophysics Data System (ADS)

Karaoglu, H.; Romanowicz, B. A.

2016-12-01

Mapping anelastic 3D structure within the earth's mantle is key to understanding present day mantle dynamics, as it provides complementary constraints to those obtained from elastic structure, with the potential to distinguish between thermal and compositional heterogeneity. For this, we need to measure seismic wave amplitudes, which are sensitive to both elastic (through focusing and scattering) and anelastic structure. The elastic effects are less pronounced at long periods, so previous global upper-mantle attenuation models are based on teleseismic surface wave data, sometimes including overtones. In these studies, elastic effects are considered either indirectly, by eliminating data strongly contaminated by them (e.g. Romanowicz, 1995; Gung and Romanowicz, 2004), or by correcting for elastic focusing effects using an approximate linear approach (Dalton et al., 2008). Additionally, in these studies, the elastic structure is held fixed when inverting for intrinsic attenuation . The importance of (1) having a good starting elastic model, (2) accurate modeling of the seismic wavefield and (3) joint inversion for elastic and anelastic structure, becomes more evident as the targeted resolution level increases. Also, velocity dispersion effects due to anelasticity need to be taken into account. Here, we employ a hybrid full waveform inversion method, inverting jointly for global elastic and anelastic upper mantle structure, starting from the latest global 3D shear velocity model built by our group (French and Romanowicz, 2014), using the spectral element method for the forward waveform modeling (Capdeville et al., 2003), and normal-mode perturbation theory (NACT - Li and Romanowicz, 1995) for kernel computations. We present a 3D upper-mantle anelastic model built by using three component fundamental and overtone surface waveforms down to 60 s as well as long period body waveforms down to 30 s. We also include source and site effects to first order as frequency independent scalar factors. The robustness of the inversion method is assessed through synthetic and resolution tests. We discuss salient features of the resulting anelastic model and in particular the well-resolved strong correlation with tectonics observed in the first 200 km of the mantle.

Nonlinear vibration of double-walled boron nitride and carbon nanopeapods under multi-physical fields with consideration of surface stress effects

NASA Astrophysics Data System (ADS)

Ghorbanpour Arani, A.; Sabzeali, M.; BabaAkbar Zarei, H.

2017-12-01

In this study, the nonlinear thermo-electro vibrations of double-walled boron nitride nanopeapods (DWBNNPPs) and double-walled carbon nanopeapods (DWCNPPs) under magnetic field embedded in an elastic medium is investigated. DWBNNPPs are made of piezoelectric and smart materials therefore, electric field is effective on them; meanwhile, DWCNPPs are made of carbon thus, magnetic field can be useful to control them. The Pasternak model is used to simulate the effects of elastic medium which surrounds the system. Nanotubes are modeled with assumption of the Euler-Bernoulli beam (EBB) theory and the surface effects are considered to achieve accurate response of the system. Moreover, interaction between two layers is modeled by van der Waals (vdW) forces. The equations of motion are derived using the energy method and the Hamilton principle. Then the governing equations are solved by using Galerkin's method and incremental harmonic balance method (IHBM). The influences of various parameters such as the magnetic field, different types of DWCNPPs and DWBNNPPs, elastic medium, existence of fullerene and surface effect on the vibration behavior of the system are investigated. The results demonstrate that DWBNNPPs have more influence on the frequency of the system than DWCNPPs. In addition, the presence of fullerene in nanotubes has a negative impact on the frequency behavior of revisionthe system.

Pressure wave propagation in fluid-filled co-axial elastic tubes. Part 1: Basic theory.

PubMed

Berkouk, K; Carpenter, P W; Lucey, A D

2003-12-01

Our work is motivated by ideas about the pathogenesis of syringomyelia. This is a serious disease characterized by the appearance of longitudinal cavities within the spinal cord. Its causes are unknown, but pressure propagation is probably implicated. We have developed an inviscid theory for the propagation of pressure waves in co-axial, fluid-filled, elastic tubes. This is intended as a simple model of the intraspinal cerebrospinal-fluid system. Our approach is based on the classic theory for the propagation of longitudinal waves in single, fluid-filled, elastic tubes. We show that for small-amplitude waves the governing equations reduce to the classic wave equation. The wave speed is found to be a strong function of the ratio of the tubes' cross-sectional areas. It is found that the leading edge of a transmural pressure pulse tends to generate compressive waves with converging wave fronts. Consequently, the leading edge of the pressure pulse steepens to form a shock-like elastic jump. A weakly nonlinear theory is developed for such an elastic jump.

Surface Stresses and a Force Balance at a Contact Line.

PubMed

Liang, Heyi; Cao, Zhen; Wang, Zilu; Dobrynin, Andrey V

2018-06-26

Results of the coarse-grained molecular dynamics simulations are used to show that the force balance analysis at the triple-phase contact line formed at an elastic substrate has to include a quartet of forces: three surface tensions (surface free energies) and an elastic force per unit length. In the case of the contact line formed by a droplet on an elastic substrate an elastic force is due to substrate deformation generated by formation of the wetting ridge. The magnitude of this force f el is proportional to the product of the ridge height h and substrate shear modulus G. Similar elastic line force should be included in the force analysis at the triple-phase contact line of a solid particle in contact with an elastic substrate. For this contact problem elastic force obtained from contact angles and surface tensions is a sum of the elastic forces acting from the side of a solid particle and an elastic substrate. By considering only three line forces acting at the triple-phase contact line, one implicitly accounts the bulk stress contribution as a part of the resultant surface stresses. This "contamination" of the surface properties by a bulk contribution could lead to unphysically large values of the surface stresses in soft materials.

Dehydrogenation of benzene on Pt(111) surface

NASA Astrophysics Data System (ADS)

Gao, W.; Zheng, W. T.; Jiang, Q.

2008-10-01

The dehydrogenation of benzene on Pt(111) surface is studied by ab initio density functional theory. The minimum energy pathways for benzene dehydrogenation are found with the nudge elastic band method including several factors of the associated barriers, reactive energies, intermediates, and transient states. The results show that there are two possible parallel minimum energy pathways on the Pt(111) surface. Moreover, the tilting angle of the H atom in benzene can be taken as an index for the actual barrier of dehydrogenation. In addition, the properties of dehydrogenation radicals on the Pt(111) surface are explored through their adsorption energy, adsorption geometry, and electronic structure on the surface. The vibrational frequencies of the dehydrogenation radicals derived from the calculations are in agreement with literature data.

Dehydrogenation of benzene on Pt(111) surface.

PubMed

Gao, W; Zheng, W T; Jiang, Q

2008-10-28

The dehydrogenation of benzene on Pt(111) surface is studied by ab initio density functional theory. The minimum energy pathways for benzene dehydrogenation are found with the nudge elastic band method including several factors of the associated barriers, reactive energies, intermediates, and transient states. The results show that there are two possible parallel minimum energy pathways on the Pt(111) surface. Moreover, the tilting angle of the H atom in benzene can be taken as an index for the actual barrier of dehydrogenation. In addition, the properties of dehydrogenation radicals on the Pt(111) surface are explored through their adsorption energy, adsorption geometry, and electronic structure on the surface. The vibrational frequencies of the dehydrogenation radicals derived from the calculations are in agreement with literature data.

A review of micro-contact physics for microelectromechanical systems (MEMS) metal contact switches

NASA Astrophysics Data System (ADS)

Toler, Benjamin F.; Coutu, Ronald A., Jr.; McBride, John W.

2013-10-01

Innovations in relevant micro-contact areas are highlighted, these include, design, contact resistance modeling, contact materials, performance and reliability. For each area the basic theory and relevant innovations are explored. A brief comparison of actuation methods is provided to show why electrostatic actuation is most commonly used by radio frequency microelectromechanical systems designers. An examination of the important characteristics of the contact interface such as modeling and material choice is discussed. Micro-contact resistance models based on plastic, elastic-plastic and elastic deformations are reviewed. Much of the modeling for metal contact micro-switches centers around contact area and surface roughness. Surface roughness and its effect on contact area is stressed when considering micro-contact resistance modeling. Finite element models and various approaches for describing surface roughness are compared. Different contact materials to include gold, gold alloys, carbon nanotubes, composite gold-carbon nanotubes, ruthenium, ruthenium oxide, as well as tungsten have been shown to enhance contact performance and reliability with distinct trade offs for each. Finally, a review of physical and electrical failure modes witnessed by researchers are detailed and examined.

Bistable director alignments of nematic liquid crystals confined in frustrated substrates

NASA Astrophysics Data System (ADS)

Araki, Takeaki; Nagura, Jumpei

2017-01-01

We studied in-plane bistable alignments of nematic liquid crystals confined by two frustrated surfaces by means of Monte Carlo simulations of the Lebwohl-Lasher spin model. The surfaces are prepared with orientational checkerboard patterns, on which the director field is locally anchored to be planar yet orthogonal between the neighboring blocks. We found the director field in the bulk tends to be aligned along the diagonal axes of the checkerboard pattern, as reported experimentally [J.-H. Kim et al., Appl. Phys. Lett. 78, 3055 (2001), 10.1063/1.1371246]. The energy barrier between the two stable orientations is increased, when the system is brought to the isotropic-nematic transition temperature. Based on an elastic theory, we found that the bistability is attributed to the spatial modulation of the director field near the frustrated surfaces. As the block size is increased and/or the elastic modulus is reduced, the degree of the director inhomogeneity is increased, enlarging the energy barrier. We also found that the switching rate between the stable states is decreased when the block size is comparable to the cell thickness.

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

NASA Astrophysics Data System (ADS)

Jin, Yongmei

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

Role of surface elasticity in the drainage of soap films

NASA Astrophysics Data System (ADS)

Sonin, A. A.; Bonfillon, A.; Langevin, D.

1993-10-01

We present measurements of the thinning velocity of circular horizontal soap films made from dilute surfactant solutions (around the critical micellar concentration). We have solved numerically the hydrodynamic equations for the drainage process. After data fitting, we deduce the values of the elasticities of the surfactant monolayer that stabilizes the soap film. These elasticity values have been compared to elasticities obtained independently from the study of waves at the surface of the solution. The comparison reveals the importance of surface convection in the drainage process and demonstrates the important role of surface elasticity.

Molecular Dynamics Simulation Studies of Fracture in Two Dimensions

DTIC Science & Technology

1980-05-01

reversibility of trajectories. The microscopic elastic constants, dispersion relation and phonon spectrum of the system were determined by lattice dynamics. These... linear elasticity theory of a two-dimensional crack embedded in an infinite medium. System con- sists of 436 particles arranged in a tri- angular lattice ...satisfying these demands. In evaluating the mechanical energy of his model, Griffith used a result from linear elasticity theory, namely that for any body

Acoustic resonances of fluid-immersed elastic cylinders and spheroids: Theory and experiment

NASA Astrophysics Data System (ADS)

Niemiec, Jan; Überall, Herbert; Bao, X. L.

2002-05-01

Frequency resonances in the scattering of acoustic waves from a target object are caused by the phase matching of surface waves repeatedly encircling the object. This is exemplified here by considering elastic finite cylinders and spheroids, and the phase-matching condition provides a means of calculating the complex resonance frequencies of such objects. Tank experiments carried out at Catholic University, or at the University of Le Havre, France by G. Maze and J. Ripoche, have been interpreted using this approach. The experiments employed sound pulses to measure arrival times, which allowed identification of the surface paths taken by the surface waves, thus giving rise to resonances in the scattering amplitude. A calculation of the resonance frequencies using the T-matrix approach showed satisfactory agreement with the experimental resonance frequencies that were either measured directly (as at Le Havre), or that were obtained by the interpretation of measured arrival times (at Catholic University) using calculated surface wave paths, and the extraction of resonance frequencies therefrom, on the basis of the phase-matching condition. Results for hemispherically endcapped, evacuated steel cylinders obtained in a lake experiment carried out by the NSWC were interpreted in the same fashion.

Documentation of programs that compute 1) quasi-static tilts produced by an expanding dislocation loop in an elastic and viscoelastic material, and 2) surface shear stresses, strains, and shear displacements produced by screw dislocations in a vertical slab with modulus contrast

USGS Publications Warehouse

McHugh, Stuart

1976-01-01

The material in this report can be grouped into two categories: 1) programs that compute tilts produced by a vertically oriented expanding rectangular dislocation loop in an elastic or viscoelastic material and 2) programs that compute the shear stresses, strains, and shear displacements in a three-phase half-space (i.e. a half-space containing a vertical slab). Each section describes the relevant theory, and provides a detailed guide to the operation of the programs. A series of examples is provided at the end of each section.

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.

Numerical study on influence of single control surface on aero elastic behavior of forward-swept wing

NASA Astrophysics Data System (ADS)

Wang, Ning; Su, Xinbing; Ma, Binlin; Zhang, Xiaofei

2017-10-01

In order to study the influence of elastic forward-swept wing (FSW) with single control surface, the computational fluid dynamics/computational structural dynamics (CFD/CSD) loose coupling static aero elastic numerical calculation method was adopted for numerical simulation. The effects of the elastic FSW with leading- or trailing-edge control surface on aero elastic characteristics were calculated and analysed under the condition of high subsonic speed. The result shows that, the deflection of every single control surface could change the aero elastic characteristics of elastic FSW greatly. Compared with the baseline model, when leading-edge control surface deflected up, under the condition of small angles of attack, the aerodynamic characteristics was poor, but the bending and torsional deformation decreased. Under the condition of moderate angles of attack, the aerodynamic characteristics was improved, but bending and torsional deformation increased; When leading-edge control surface deflected down, the aerodynamic characteristics was improved, the bending and torsional deformation decreased/increased under the condition of small/moderate angles of attack. Compared with the baseline model, when trailing-edge control surface deflected down, the aerodynamic characteristics was improved. The bending and torsional deformation increased under the condition of small angles of attack. The bending deformation increased under the condition of small angles of attack, but torsional deformation decreases under the condition of moderate angles of attack. So, for the elastic FSW, the deflection of trailing-edge control surface play a more important role on the improvement of aerodynamic and elastic deformation characteristics.

Characterization and Analysis of Viscoelastically Loaded Thin Film Piezoelectric Resonators Incorporated in AN Oscillator Microsensing System.

NASA Astrophysics Data System (ADS)

O'Toole, Ronald Patrick

1994-01-01

In the recent advancement of piezoelectric resonator technology, there has been a large growth in the application of these devices for chemical sensing. These sensors operate by detecting changes in their environment which perturb the electrical - acoustic operation and in turn can be harnessed by means of supporting electronics and signal processing to monitor various processes. Examples include remote environmental monitoring, chemical process control, and commercial gas phase detectors. In this dissertation, the chemical sensing theory and properties of piezoelectric resonators such as the bulk-acoustic wave thin-film resonator (TFR) and the quartz crystal microbalance (QCM) are developed. This analysis concentrates on characterizing the resonance behavior of thickness mode resonators based upon the physical properties at the electrode interface which include interfacial mass density, elasticity, viscosity, and thickness of the composite device consisting of the piezoelectric material, the electrodes, and any deposited layer on the electrode surface in contact with the surrounding medium. In this work, no approximation is made as to the stress or particle displacement variation across the visco-elastic film which allows a complete study of the perturbational mechanical variations on the electrical and resonance properties of the composite resonator. The derivation and verification of equivalent circuit models based on the physical properties of the piezoelectric resonator and visco-elastic sensing film are presented. The results and models from this research will be beneficial to surface chemistry studies and also have application to fabrication techniques and electrical modeling. The use of this theory is employed in a study of a QCM coated with a commercially developed negative resist. Photo-polymerization of the resist results in induced visco-elastic structural changes which can be monitored and characterized using the full admittance theory of the composite thickness mode resonator. In order to validate the chemical sensing concept, the design and implementation of a TFR controlled chemical sensing system is demonstrated. This system employs the frequency selectivity of the chemical sensing TFR as the feedback element in integrated Colpitts oscillators which are downconverted by superheterodyne techniques. The integrated system design philosophy and performance tradeoffs are discussed. This analysis also investigates the phase noise performance and injection locking considerations of the design. The sensor system detection limit is derived which sets the lower limit of signal detection based upon measurand sensitivity and measured phase noise.

A nonlinear theory for elastic plates with application to characterizing paper properties

Treesearch

M. W. Johnson; Thomas J. Urbanik

1984-03-01

A theory of thin plates which is physically as well as kinematically nonlinear is, developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a...

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.

Rubber elasticity for percolation network consisting of Gaussian chains.

PubMed

Nishi, Kengo; Noguchi, Hiroshi; Sakai, Takamasa; Shibayama, Mitsuhiro

2015-11-14

A theory describing the elastic modulus for percolation networks of Gaussian chains on general lattices such as square and cubic lattices is proposed and its validity is examined with simulation and mechanical experiments on well-defined polymer networks. The theory was developed by generalizing the effective medium approximation (EMA) for Hookian spring network to Gaussian chain networks. From EMA theory, we found that the ratio of the elastic modulus at p, G to that at p = 1, G0, must be equal to G/G0 = (p - 2/f)/(1 - 2/f) if the position of sites can be determined so as to meet the force balance, where p is the degree of cross-linking reaction. However, the EMA prediction cannot be applicable near its percolation threshold because EMA is a mean field theory. Thus, we combine real-space renormalization and EMA and propose a theory called real-space renormalized EMA, i.e., REMA. The elastic modulus predicted by REMA is in excellent agreement with the results of simulations and experiments of near-ideal diamond lattice gels.

Rubber elasticity for percolation network consisting of Gaussian chains

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

Nishi, Kengo, E-mail: kengo.nishi@phys.uni-goettingen.de, E-mail: sakai@tetrapod.t.u-tokyo.ac.jp, E-mail: sibayama@issp.u-tokyo.ac.jp; Noguchi, Hiroshi; Shibayama, Mitsuhiro, E-mail: kengo.nishi@phys.uni-goettingen.de, E-mail: sakai@tetrapod.t.u-tokyo.ac.jp, E-mail: sibayama@issp.u-tokyo.ac.jp

2015-11-14

A theory describing the elastic modulus for percolation networks of Gaussian chains on general lattices such as square and cubic lattices is proposed and its validity is examined with simulation and mechanical experiments on well-defined polymer networks. The theory was developed by generalizing the effective medium approximation (EMA) for Hookian spring network to Gaussian chain networks. From EMA theory, we found that the ratio of the elastic modulus at p, G to that at p = 1, G{sub 0}, must be equal to G/G{sub 0} = (p − 2/f)/(1 − 2/f) if the position of sites can be determined somore » as to meet the force balance, where p is the degree of cross-linking reaction. However, the EMA prediction cannot be applicable near its percolation threshold because EMA is a mean field theory. Thus, we combine real-space renormalization and EMA and propose a theory called real-space renormalized EMA, i.e., REMA. The elastic modulus predicted by REMA is in excellent agreement with the results of simulations and experiments of near-ideal diamond lattice gels.« less

Gesellschaft fuer angewandte Mathematik und Mechanik, Annual Scientific Meeting, Universitaet Regensburg, Regensburg, West Germany, April 16-19, 1984, Proceedings

NASA Astrophysics Data System (ADS)

Problems in applied mathematics and mechanics are addressed in reviews and reports. Areas covered are vibration and stability, elastic and plastic mechanics, fluid mechanics, the numerical treatment of differential equations (general theory and finite-element methods in particular), optimization, decision theory, stochastics, actuarial mathematics, applied analysis and mathematical physics, and numerical analysis. Included are major lectures on separated flows, the transition regime of rarefied-gas dynamics, recent results in nonlinear elasticity, fluid-elastic vibration, the new computer arithmetic, and unsteady wave propagation in layered elastic bodies.

Thick shell tectonics on one-plate planets - Applications to Mars

NASA Technical Reports Server (NTRS)

Banerdt, W. B.; Saunders, R. S.; Phillips, R. J.; Sleep, N. H.

1982-01-01

Using the zero frequency equations of a self-gravitating elastic spherical shell overlying a strengthless fluid, a theory for stress distribution in thick lithospheric shells on one-plate planets is developed. For both the compensated and flexural modes, stress distributions in lithospheres are reviewed. For compensated modes, surface stresses depend only on surface topography, whereas for flexural modes it is shown that, for long wavelengths, stress trajectories are mainly dependent on the lithospheric lateral density distribution and not on elastic properties. Computational analyses are performed for Mars, and it is found that isostatically compensated models correctly predict the graben structure in the immediate Tharsis region and a flexural loading model is satisfactory in explaining the graben in the regions surrounding Tharsis. A three-stage model for the evolution of Tharsis is hypothesized: isostasy with north-south graben formation on Tharsis, followed by flexural loading and radial graben formation on the perimeter of Tharsis, followed by a last stage of loading with little or no regional deformation.

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.

The elasticity and failure of fluid-filled cellular solids: Theory and experiment

NASA Astrophysics Data System (ADS)

Warner, M.; Thiel, B. L.; Donald, A. M.

2000-02-01

We extend and apply theories of filled foam elasticity and failure to recently available data on foods. The predictions of elastic modulus and failure mode dependence on internal pressure and on wall integrity are borne out by photographic evidence of distortion and failure under compressive loading and under the localized stress applied by a knife blade, and by mechanical data on vegetables differing only in their turgor pressure. We calculate the dry modulus of plate-like cellular solids and the cross over between dry-like and fully fluid-filled elastic response. The bulk elastic properties of limp and aging cellular solids are calculated for model systems and compared with our mechanical data, which also show two regimes of response. The mechanics of an aged, limp beam is calculated, thus offering a practical procedure for comparing experiment and theory. This investigation also thereby offers explanations of the connection between turgor pressure and crispness and limpness of cellular materials.

The elasticity and failure of fluid-filled cellular solids: theory and experiment.

PubMed

Warner, M; Thiel, B L; Donald, A M

2000-02-15

We extend and apply theories of filled foam elasticity and failure to recently available data on foods. The predictions of elastic modulus and failure mode dependence on internal pressure and on wall integrity are borne out by photographic evidence of distortion and failure under compressive loading and under the localized stress applied by a knife blade, and by mechanical data on vegetables differing only in their turgor pressure. We calculate the dry modulus of plate-like cellular solids and the cross over between dry-like and fully fluid-filled elastic response. The bulk elastic properties of limp and aging cellular solids are calculated for model systems and compared with our mechanical data, which also show two regimes of response. The mechanics of an aged, limp beam is calculated, thus offering a practical procedure for comparing experiment and theory. This investigation also thereby offers explanations of the connection between turgor pressure and crispness and limpness of cellular materials.

The elasticity and failure of fluid-filled cellular solids: Theory and experiment

PubMed Central

Warner, M.; Thiel, B. L.; Donald, A. M.

2000-01-01

We extend and apply theories of filled foam elasticity and failure to recently available data on foods. The predictions of elastic modulus and failure mode dependence on internal pressure and on wall integrity are borne out by photographic evidence of distortion and failure under compressive loading and under the localized stress applied by a knife blade, and by mechanical data on vegetables differing only in their turgor pressure. We calculate the dry modulus of plate-like cellular solids and the cross over between dry-like and fully fluid-filled elastic response. The bulk elastic properties of limp and aging cellular solids are calculated for model systems and compared with our mechanical data, which also show two regimes of response. The mechanics of an aged, limp beam is calculated, thus offering a practical procedure for comparing experiment and theory. This investigation also thereby offers explanations of the connection between turgor pressure and crispness and limpness of cellular materials. PMID:10660680

Non-affine deformations in polymer hydrogels

PubMed Central

Wen, Qi; Basu, Anindita; Janmey, Paul A.; Yodh, A. G.

2012-01-01

Most theories of soft matter elasticity assume that the local strain in a sample after deformation is identical everywhere and equal to the macroscopic strain, or equivalently that the deformation is affine. We discuss the elasticity of hydrogels of crosslinked polymers with special attention to affine and non-affine theories of elasticity. Experimental procedures to measure non-affine deformations are also described. Entropic theories, which account for gel elasticity based on stretching out individual polymer chains, predict affine deformations. In contrast, simulations of network deformation that result in bending of the stiff constituent filaments generally predict non-affine behavior. Results from experiments show significant non-affine deformation in hydrogels even when they are formed by flexible polymers for which bending would appear to be negligible compared to stretching. However, this finding is not necessarily an experimental proof of the non-affine model for elasticity. We emphasize the insights gained from experiments using confocal rheoscope and show that, in addition to filament bending, sample micro-inhomogeneity can be a significant alternative source of non-affine deformation. PMID:23002395

Analytical bond order potential for simulations of BeO 1D and 2D nanostructures and plasma-surface interactions

NASA Astrophysics Data System (ADS)

Byggmästar, J.; Hodille, E. A.; Ferro, Y.; Nordlund, K.

2018-04-01

An analytical interatomic bond order potential for the Be-O system is presented. The potential is fitted and compared to a large database of bulk BeO and point defect properties obtained using density functional theory. Its main applications include simulations of plasma-surface interactions involving oxygen or oxide layers on beryllium, as well as simulations of BeO nanotubes and nanosheets. We apply the potential in a study of oxygen irradiation of Be surfaces, and observe the early stages of an oxide layer forming on the Be surface. Predicted thermal and elastic properties of BeO nanotubes and nanosheets are simulated and compared with published ab initio data.

A corrected model for static and dynamic electromechanical instability of narrow nanotweezers: Incorporation of size effect, surface layer and finite dimensions

NASA Astrophysics Data System (ADS)

Koochi, Ali; Hosseini-Toudeshky, Hossein; Abadyan, Mohamadreza

2018-03-01

Herein, a corrected theoretical model is proposed for modeling the static and dynamic behavior of electrostatically actuated narrow-width nanotweezers considering the correction due to finite dimensions, size dependency and surface energy. The Gurtin-Murdoch surface elasticity in conjunction with the modified couple stress theory is employed to consider the coupling effect of surface stresses and size phenomenon. In addition, the model accounts for the external force corrections by incorporating the impact of narrow width on the distribution of Casimir attraction, van der Waals (vdW) force and the fringing field effect. The proposed model is beneficial for the precise modeling of the narrow nanotweezers in nano-scale.

First principles investigation of heterogeneous catalysis on metal oxide surfaces

NASA Astrophysics Data System (ADS)

Ghoussoub, Mireille

Metal oxides possess unique electronic and structural properties that render them highly favourable for applications in heterogeneous catalysis. In this study, computational atomistic modelling based on Density Functional Theory was used to investigate the reduction of carbon dioxide over hydroxylated indium oxide nanoparticles, as well at the activation of methane over oxygen-covered bimetallic surfaces. The first study employed metadynamics-biased ab initio molecular dynamics to obtain the free energy surface of the various reaction steps at finite temperature. In the second study, the nudged elastic band method was used to probe the C-H activation mechanisms for different surface configurations. In both cases, activation energies, reaction energies, transition state structures, and charge analysis results are used to explain the underlying mechanistic pathways.

Geometric Structure-Preserving Discretization Schemes for Nonlinear Elasticity

DTIC Science & Technology

2015-08-13

conditions. 15.  SUBJECT TERMS geometric theory for nonlinear elasticity, discrete exterior calculus 16.  SECURITY CLASSIFICATION OF: 17.  LIMITATION...associated Laplacian. We use the general theory for approximation of Hilbert complexes and the finite element exterior calculus and introduce some stable mixed

Dynamic surface tension measurements of ionic surfactants using maximum bubble pressure tensiometry

NASA Astrophysics Data System (ADS)

Ortiz, Camilla U.; Moreno, Norman; Sharma, Vivek

Dynamic surface tension refers to the time dependent variation in surface tension, and is intimately linked with the rate of mass transfer of a surfactant from liquid sub-phase to the interface. The diffusion- or adsorption-limited kinetics of mass transfer to interfaces is said to impact the so-called foamability and the Gibbs-Marangoni elasticity of surfaces. Dynamic surface tension measurements carried out with conventional methods like pendant drop analysis, Wilhelmy plate, etc. are limited in their temporal resolution (>50 ms). In this study, we describe design and application of maximum bubble pressure tensiometry for the measurement of dynamic surface tension effects at extremely short (1-50 ms) timescales. Using experiments and theory, we discuss the overall adsorption kinetics of charged surfactants, paying special attention to the influence of added salt on dynamic surface tension.

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

PubMed

Grason, Gregory M

2012-03-01

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

Simulation of Nonisothermal Consolidation of Saturated Soils Based on a Thermodynamic Model

PubMed Central

Cheng, Xiaohui

2013-01-01

Based on the nonequilibrium thermodynamics, a thermo-hydro-mechanical coupling model for saturated soils is established, including a constitutive model without such concepts as yield surface and flow rule. An elastic potential energy density function is defined to derive a hyperelastic relation among the effective stress, the elastic strain, and the dry density. The classical linear non-equilibrium thermodynamic theory is employed to quantitatively describe the unrecoverable energy processes like the nonelastic deformation development in materials by the concepts of dissipative force and dissipative flow. In particular the granular fluctuation, which represents the kinetic energy fluctuation and elastic potential energy fluctuation at particulate scale caused by the irregular mutual movement between particles, is introduced in the model and described by the concept of granular entropy. Using this model, the nonisothermal consolidation of saturated clays under cyclic thermal loadings is simulated in this paper to validate the model. The results show that the nonisothermal consolidation is heavily OCR dependent and unrecoverable. PMID:23983623

Simulation of nonisothermal consolidation of saturated soils based on a thermodynamic model.

PubMed

Zhang, Zhichao; Cheng, Xiaohui

2013-01-01

Based on the nonequilibrium thermodynamics, a thermo-hydro-mechanical coupling model for saturated soils is established, including a constitutive model without such concepts as yield surface and flow rule. An elastic potential energy density function is defined to derive a hyperelastic relation among the effective stress, the elastic strain, and the dry density. The classical linear non-equilibrium thermodynamic theory is employed to quantitatively describe the unrecoverable energy processes like the nonelastic deformation development in materials by the concepts of dissipative force and dissipative flow. In particular the granular fluctuation, which represents the kinetic energy fluctuation and elastic potential energy fluctuation at particulate scale caused by the irregular mutual movement between particles, is introduced in the model and described by the concept of granular entropy. Using this model, the nonisothermal consolidation of saturated clays under cyclic thermal loadings is simulated in this paper to validate the model. The results show that the nonisothermal consolidation is heavily OCR dependent and unrecoverable.

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.

Atomic and molecular oxygen adsorbed on (111) transition metal surfaces: Cu and Ni

NASA Astrophysics Data System (ADS)

López-Moreno, S.; Romero, A. H.

2015-04-01

Density functional theory is used to investigate the reaction of oxygen with clean copper and nickel [111]-surfaces. We study several alternative adsorption sites for atomic and molecular oxygen on both surfaces. The minimal energy geometries and adsorption energies are in good agreement with previous theoretical studies and experimental data. From all considered adsorption sites, we found a new O2 molecular precursor with two possible dissociation paths on the Cu(111) surface. Cross barrier energies for the molecular oxygen dissociation have been calculated by using the climbing image nudge elastic band method, and direct comparison with experimental results is performed. Finally, the structural changes and adsorption energies of oxygen adsorbed on surface when there is a vacancy nearby the adsorption site are also considered.

Atomic and molecular oxygen adsorbed on (111) transition metal surfaces: Cu and Ni.

PubMed

López-Moreno, S; Romero, A H

2015-04-21

Density functional theory is used to investigate the reaction of oxygen with clean copper and nickel [111]-surfaces. We study several alternative adsorption sites for atomic and molecular oxygen on both surfaces. The minimal energy geometries and adsorption energies are in good agreement with previous theoretical studies and experimental data. From all considered adsorption sites, we found a new O2 molecular precursor with two possible dissociation paths on the Cu(111) surface. Cross barrier energies for the molecular oxygen dissociation have been calculated by using the climbing image nudge elastic band method, and direct comparison with experimental results is performed. Finally, the structural changes and adsorption energies of oxygen adsorbed on surface when there is a vacancy nearby the adsorption site are also considered.

Solution of elastic-plastic stress analysis problems by the p-version of the finite element method

NASA Technical Reports Server (NTRS)

Szabo, Barna A.; Actis, Ricardo L.; Holzer, Stefan M.

1993-01-01

The solution of small strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus. Numerical examples which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors are presented.

Investigation of surface wave amplitudes in 3-D velocity and 3-D Q models

NASA Astrophysics Data System (ADS)

Ruan, Y.; Zhou, Y.

2010-12-01

It has been long recognized that seismic amplitudes depend on both wave speed structures and anelasticity (Q) structures. However, the effects of lateral heterogeneities in wave speed and Q structures on seismic amplitudes has not been well understood. We investigate the effects of 3-D wave speed and 3-D anelasticity (Q) structures on surface-wave amplitudes based upon wave propagation simulations of twelve globally-distributed earthquakes and 801 stations in Earth models with and without lateral heterogeneities in wave speed and anelasticity using a Spectral Element Method (SEM). Our tomographic-like 3-D Q models are converted from a velocity model S20RTS using a set of reasonable mineralogical parameters, assuming lateral perturbations in both velocity and Q are due to temperature perturbations. Surface-wave amplitude variations of SEM seismograms are measured in the period range of 50--200 s using boxcar taper, cosine taper and Slepian multi-tapers. We calculate ray-theoretical predictions of surface-wave amplitude perturbations due to elastic focusing, attenuation, and anelastic focusing which respectively depend upon the second spatial derivative (''roughness'') of perturbations in phase velocity, 1/Q, and the roughness of perturbations in 1/Q. Both numerical experiments and theoretical calculations show that (1) for short-period (~ 50 s) surface waves, the effects of amplitude attenuation due to 3-D Q structures are comparable with elastic focusing effects due to 3-D wave speed structures; and (2) for long-period (> 100 s) surface waves, the effects of attenuation become much weaker than elastic focusing; and (3) elastic focusing effects are correlated with anelastic focusing at all periods due to the correlation between velocity and Q models; and (4) amplitude perturbations are depend on measurement techniques and therefore cannot be directly compared with ray-theoretical predictions because ray theory does not account for the effects of measurement techniques. We calculate 3-D finite-frequency sensitivity of surface-wave amplitude to perturbations in wave speed and anelasticity (Q) which fully account for the effects of elastic focusing, attenuation, anelastic focusing as well as measurement techniques. We show that amplitude perturbations calculated using wave speed and Q sensitivity kernels agree reasonably well with SEM measurements and therefore the sensitivity kernels can be used in a joint inversion of seismic phase delays and amplitudes to simultaneously image high resolution 3-D wave speed and 3-D Q structures in the upper mantle.

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

NASA Astrophysics Data System (ADS)

Capecchi, Danilo

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

Inclusive Breakup Theory of Three-Body Halos

NASA Astrophysics Data System (ADS)

Hussein, Mahir S.; Souza, Lucas A.; Chimanski, Emanuel; Carlson, Brett; Frederico, Tobias

2017-11-01

We present a recently developed theory for the inclusive breakup of three-fragment projectiles within a four-body spectator model [1], for the treatment of the elastic and inclusive non-elastic break up reactions involving weakly bound three-cluster nuclei in A (a; b) X / a = x1 + x2 + b collisions. The four-body theory is an extension of the three-body approaches developed in the 80's by Ichimura, Autern and Vincent (IAV) [2], Udagawa and Tamura (UT) [3] and Hussein and McVoy (HM) [4]. We expect that experimentalists shall be encouraged to search for more information about the x1 + x2 system in the elastic breakup cross section and that also further developments and extensions of the surrogate method will be pursued, based on the inclusive non-elastic breakup part of the b spectrum.

Elasticity Theory Solution of the Problem on Plane Bending of a Narrow Layered Cantilever Beam by Loads at Its Free End

NASA Astrophysics Data System (ADS)

Goryk, A. V.; Koval'chuk, S. B.

2018-05-01

An exact elasticity theory solution for the problem on plane bending of a narrow layered composite cantilever beam by tangential and normal loads distributed on its free end is presented. Components of the stress-strain state are found for the whole layers package by directly integrating differential equations of the plane elasticity theory problem by using an analytic representation of piecewise constant functions of the mechanical characteristics of layer materials. The continuous solution obtained is realized for a four-layer beam with account of kinematic boundary conditions simulating the rigid fixation of its one end. The solution obtained allows one to predict the strength and stiffness of composite cantilever beams and to construct applied analytical solutions for various problems on the elastic bending of layered beams.

Pareto Joint Inversion of Love and Quasi Rayleigh's waves - synthetic study

NASA Astrophysics Data System (ADS)

Bogacz, Adrian; Dalton, David; Danek, Tomasz; Miernik, Katarzyna; Slawinski, Michael A.

2017-04-01

In this contribution the specific application of Pareto joint inversion in solving geophysical problem is presented. Pareto criterion combine with Particle Swarm Optimization were used to solve geophysical inverse problems for Love and Quasi Rayleigh's waves. Basic theory of forward problem calculation for chosen surface waves is described. To avoid computational problems some simplification were made. This operation allowed foster and more straightforward calculation without lost of solution generality. According to the solving scheme restrictions, considered model must have exact two layers, elastic isotropic surface layer and elastic isotropic half space with infinite thickness. The aim of the inversion is to obain elastic parameters and model geometry using dispersion data. In calculations different case were considered, such as different number of modes for different wave types and different frequencies. Created solutions are using OpenMP standard for parallel computing, which help in reduction of computational times. The results of experimental computations are presented and commented. This research was performed in the context of The Geomechanics Project supported by Husky Energy. Also, this research was partially supported by the Natural Sciences and Engineering Research Council of Canada, grant 238416-2013, and by the Polish National Science Center under contract No. DEC-2013/11/B/ST10/0472.

Controlled-source seismic interferometry with one way wave fields

NASA Astrophysics Data System (ADS)

van der Neut, J.; Wapenaar, K.; Thorbecke, J. W.

2008-12-01

In Seismic Interferometry we generally cross-correlate registrations at two receiver locations and sum over an array of sources to retrieve a Green's function as if one of the receiver locations hosts a (virtual) source and the other receiver location hosts an actual receiver. One application of this concept is to redatum an area of surface sources to a downhole receiver location, without requiring information about the medium between the sources and receivers, thus providing an effective tool for imaging below complex overburden, which is also known as the Virtual Source method. We demonstrate how elastic wavefield decomposition can be effectively combined with controlled-source Seismic Interferometry to generate virtual sources in a downhole receiver array that radiate only down- or upgoing P- or S-waves with receivers sensing only down- or upgoing P- or S- waves. For this purpose we derive exact Green's matrix representations from a reciprocity theorem for decomposed wavefields. Required is the deployment of multi-component sources at the surface and multi- component receivers in a horizontal borehole. The theory is supported with a synthetic elastic model, where redatumed traces are compared with those of a directly modeled reflection response, generated by placing active sources at the virtual source locations and applying elastic wavefield decomposition on both source and receiver side.

Thermoelastic Damping in FGM Nano-Electromechanical System in Axial Vibration Based on Eringen Nonlocal Theory

NASA Astrophysics Data System (ADS)

Rahimi, Z.; Rashahmadi, S.

2017-11-01

The thermo-elastic damping is a dominant source of internal damping in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS). The internal damping cannot neither be controlled nor minimized unless either mechanical or geometrical properties are changed. Therefore, a novel FGMNEM system with a controllable thermo-elastic damping of axial vibration based on Eringen nonlocal theory is considered. The effects of different parameter like the gradient index, nonlocal parameter, length of nanobeam and ambient temperature on the thermo-elastic damping quality factor are presented. It is shown that the thermo-elastic damping can be controlled by changing different parameter.

Investigation of structural, electronic, elastic and optical properties of Cd1-x-yZnxHgyTe alloys

NASA Astrophysics Data System (ADS)

Tamer, M.

2016-06-01

Structural, optical and electronic properties and elastic constants of Cd1-x-yZnx HgyTe alloys have been studied by employing the commercial code Castep based on density functional theory. The generalized gradient approximation and local density approximation were utilized as exchange correlation. Using elastic constants for compounds, bulk modulus, band gap, Fermi energy and Kramers-Kronig relations, dielectric constants and the refractive index have been found through calculations. Apart from these, X-ray measurements revealed elastic constants and Vegard's law. It is seen that results obtained from theory and experiments are all in agreement.

Singularity-free dislocation dynamics with strain gradient elasticity

NASA Astrophysics Data System (ADS)

Po, Giacomo; Lazar, Markus; Seif, Dariush; Ghoniem, Nasr

2014-08-01

The singular nature of the elastic fields produced by dislocations presents conceptual challenges and computational difficulties in the implementation of discrete dislocation-based models of plasticity. In the context of classical elasticity, attempts to regularize the elastic fields of discrete dislocations encounter intrinsic difficulties. On the other hand, in gradient elasticity, the issue of singularity can be removed at the outset and smooth elastic fields of dislocations are available. In this work we consider theoretical and numerical aspects of the non-singular theory of discrete dislocation loops in gradient elasticity of Helmholtz type, with interest in its applications to three dimensional dislocation dynamics (DD) simulations. The gradient solution is developed and compared to its singular and non-singular counterparts in classical elasticity using the unified framework of eigenstrain theory. The fundamental equations of curved dislocation theory are given as non-singular line integrals suitable for numerical implementation using fast one-dimensional quadrature. These include expressions for the interaction energy between two dislocation loops and the line integral form of the generalized solid angle associated with dislocations having a spread core. The single characteristic length scale of Helmholtz elasticity is determined from independent molecular statics (MS) calculations. The gradient solution is implemented numerically within our variational formulation of DD, with several examples illustrating the viability of the non-singular solution. The displacement field around a dislocation loop is shown to be smooth, and the loop self-energy non-divergent, as expected from atomic configurations of crystalline materials. The loop nucleation energy barrier and its dependence on the applied shear stress are computed and shown to be in good agreement with atomistic calculations. DD simulations of Lome-Cottrell junctions in Al show that the strength of the junction and its configuration are easily obtained, without ad-hoc regularization of the singular fields. Numerical convergence studies related to the implementation of the non-singular theory in DD are presented.

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Hannover, Hanover, Federal Republic of Germany, Apr. 8-12, 1990, Reports

NASA Astrophysics Data System (ADS)

Various papers on applied mathematics and mechanics are presented. Among the individual topics addressed are: dynamical systems with time-varying or unsteady structure, micromechanical modeling of creep rupture, forced vibrations of elastic sandwich plates with thick surface layers, postbuckling of a complete spherical shell under a line load, differential-geometric approach to the multibody system dynamics, stability of an oscillator with stochastic parametric excitation, identification strategies for crack-formation in rotors, identification of physical parameters of FEMs, impact model for elastic and partly plastic impacts on objects, varying delay and stability in dynamical systems. Also discussed are: parameter identification of a hybrid model for vibration analysis using the FEM, vibration behavior of a labyrinth seal with through-flow, similarities in the boundary layer of fiber composite materials, distortion parameter in shell theories, elastoplastic crack problem at finite strain, algorithm for computing effective stiffnesses of plates with periodic structure, plasticity of metal-matrix composites in a mixed stress-strain space formation, constitutive equations in directly formulated plate theories, microbuckling and homogenization for long fiber composites.

Analytical and scale model research aimed at improved hangglider design

NASA Technical Reports Server (NTRS)

Kroo, I.; Chang, L. S.

1979-01-01

Research consisted of a theoretical analysis which attempts to predict aerodynamic characteristics using lifting surface theory and finite-element structural analysis as well as an experimental investigation using 1/5 scale elastically similar models in the NASA Ames 2m x 3m (7' x 10') wind tunnel. Experimental data were compared with theoretical results in the development of a computer program which may be used in the design and evaluation of ultralight gliders.

Curvature Forces in Membrane Lipid-Protein Interactions

PubMed Central

Brown, Michael F.

2012-01-01

Membrane biochemists are becoming increasingly aware of the role of lipid-protein interactions in diverse cellular functions. This review describes how conformational changes of membrane proteins—involving folding, stability, and membrane shape transitions—potentially involve elastic remodeling of the lipid bilayer. Evidence suggests that membrane lipids affect proteins through interactions of a relatively long-range nature, extending beyond a single annulus of next-neighbor boundary lipids. It is assumed the distance scale of the forces is large compared to the molecular range of action. Application of the theory of elasticity to flexible soft surfaces derives from classical physics, and explains the polymorphism of both detergents and membrane phospholipids. A flexible surface model (FSM) describes the balance of curvature and hydrophobic forces in lipid-protein interactions. Chemically nonspecific properties of the lipid bilayer modulate the conformational energetics of membrane proteins. The new biomembrane model challenges the standard model (the fluid mosaic model) found in biochemistry texts. The idea of a curvature force field based on data first introduced for rhodopsin gives a bridge between theory and experiment. Influences of bilayer thickness, nonlamellar-forming lipids, detergents, and osmotic stress are all explained by the FSM. An increased awareness of curvature forces suggests that research will accelerate as structural biology becomes more closely entwined with the physical chemistry of lipids in explaining membrane structure and function. PMID:23163284

Theory of activated glassy dynamics in randomly pinned fluids.

PubMed

Phan, Anh D; Schweizer, Kenneth S

2018-02-07

We generalize the force-level, microscopic, Nonlinear Langevin Equation (NLE) theory and its elastically collective generalization [elastically collective nonlinear Langevin equation (ECNLE) theory] of activated dynamics in bulk spherical particle liquids to address the influence of random particle pinning on structural relaxation. The simplest neutral confinement model is analyzed for hard spheres where there is no change of the equilibrium pair structure upon particle pinning. As the pinned fraction grows, cage scale dynamical constraints are intensified in a manner that increases with density. This results in the mobile particles becoming more transiently localized, with increases of the jump distance, cage scale barrier, and NLE theory mean hopping time; subtle changes of the dynamic shear modulus are predicted. The results are contrasted with recent simulations. Similarities in relaxation behavior are identified in the dynamic precursor regime, including a roughly exponential, or weakly supra-exponential, growth of the alpha time with pinning fraction and a reduction of dynamic fragility. However, the increase of the alpha time with pinning predicted by the local NLE theory is too small and severely so at very high volume fractions. The strong deviations are argued to be due to the longer range collective elasticity aspect of the problem which is expected to be modified by random pinning in a complex manner. A qualitative physical scenario is offered for how the three distinct aspects that quantify the elastic barrier may change with pinning. ECNLE theory calculations of the alpha time are then presented based on the simplest effective-medium-like treatment for how random pinning modifies the elastic barrier. The results appear to be consistent with most, but not all, trends seen in recent simulations. Key open problems are discussed with regard to both theory and simulation.

Theory of activated glassy dynamics in randomly pinned fluids

NASA Astrophysics Data System (ADS)

Phan, Anh D.; Schweizer, Kenneth S.

2018-02-01

We generalize the force-level, microscopic, Nonlinear Langevin Equation (NLE) theory and its elastically collective generalization [elastically collective nonlinear Langevin equation (ECNLE) theory] of activated dynamics in bulk spherical particle liquids to address the influence of random particle pinning on structural relaxation. The simplest neutral confinement model is analyzed for hard spheres where there is no change of the equilibrium pair structure upon particle pinning. As the pinned fraction grows, cage scale dynamical constraints are intensified in a manner that increases with density. This results in the mobile particles becoming more transiently localized, with increases of the jump distance, cage scale barrier, and NLE theory mean hopping time; subtle changes of the dynamic shear modulus are predicted. The results are contrasted with recent simulations. Similarities in relaxation behavior are identified in the dynamic precursor regime, including a roughly exponential, or weakly supra-exponential, growth of the alpha time with pinning fraction and a reduction of dynamic fragility. However, the increase of the alpha time with pinning predicted by the local NLE theory is too small and severely so at very high volume fractions. The strong deviations are argued to be due to the longer range collective elasticity aspect of the problem which is expected to be modified by random pinning in a complex manner. A qualitative physical scenario is offered for how the three distinct aspects that quantify the elastic barrier may change with pinning. ECNLE theory calculations of the alpha time are then presented based on the simplest effective-medium-like treatment for how random pinning modifies the elastic barrier. The results appear to be consistent with most, but not all, trends seen in recent simulations. Key open problems are discussed with regard to both theory and simulation.

Determination of Elastic Moduli of Fiber-Resin Composites Using an Impulse Excitation Technique

NASA Technical Reports Server (NTRS)

Viens, Michael J.; Johnson, Jeffrey J.

1996-01-01

The elastic moduli of graphite/epoxy and graphite/cyanate ester composite specimens with various laminate lay-ups was determined using an impulse excitation/acoustic resonance technique and compared to those determined using traditional strain gauge and extensometer techniques. The stiffness results were also compared to those predicted from laminate theory using uniaxial properties. The specimen stiffnesses interrogated ranged from 12 to 30 Msi. The impulse excitation technique was found to be a relatively quick and accurate method for determining elastic moduli with minimal specimen preparation and no requirement for mechanical loading frames. The results of this investigation showed good correlation between the elastic modulus determined using the impulse excitation technique, strain gauge and extensometer techniques, and modulus predicted from laminate theory. The flexural stiffness determined using the impulse excitation was in good agreement with that predicted from laminate theory. The impulse excitation/acoustic resonance interrogation technique has potential as a quality control test.

The complete process of large elastic-plastic deflection of a cantilever

NASA Astrophysics Data System (ADS)

Wu, Xiaoqiang; Yu, Tongxi

1986-11-01

An extension of the Elastica theory is developed to study the large deflection of an elastic-perfectly plastic horizontal cantilever beam subjected to a vertical concentrated force at its tip. The entire process is divided into four stages: I.elastic in the whole cantilever; II.loading and developing of the plastic region; III.unloading in the plastic region; and IV.reverse loading. Solutions for stages I and II are presented in a closed form. A combination of closed-form solution and numerical integration is presented for stage III. Finally, stage IV is qualitatively studied. Computed results are given and compared with those from small-deflection theory and from the Elastica theory.

Sex Ratio Elasticity Influences the Selection of Sex Ratio Strategy.

PubMed

Wang, Yaqiang; Wang, Ruiwu; Li, Yaotang; Sam Ma, Zhanshan

2016-12-23

There are three sex ratio strategies (SRS) in nature-male-biased sex ratio, female-biased sex ratio and, equal sex ratio. It was R. A. Fisher who first explained why most species in nature display a sex ratio of ½. Consequent SRS theories such as Hamilton's local mate competition (LMC) and Clark's local resource competition (LRC) separately explained the observed deviations from the seemingly universal 1:1 ratio. However, to the best of our knowledge, there is not yet a unified theory that accounts for the mechanisms of the three SRS. Here, we introduce the price elasticity theory in economics to define sex ratio elasticity (SRE), and present an analytical model that derives three SRSs based on the following assumption: simultaneously existing competitions for both resources A and resources B influence the level of SRE in both sexes differently. Consequently, it is the difference (between two sexes) in the level of their sex ratio elasticity that leads to three different SRS. Our analytical results demonstrate that the elasticity-based model not only reveals a highly plausible mechanism that explains the evolution of SRS in nature, but also offers a novel framework for unifying two major classical theories (i.e., LMC &LRC) in the field of SRS research.

Sex Ratio Elasticity Influences the Selection of Sex Ratio Strategy

NASA Astrophysics Data System (ADS)

Wang, Yaqiang; Wang, Ruiwu; Li, Yaotang; (Sam) Ma, Zhanshan

2016-12-01

There are three sex ratio strategies (SRS) in nature—male-biased sex ratio, female-biased sex ratio and, equal sex ratio. It was R. A. Fisher who first explained why most species in nature display a sex ratio of ½. Consequent SRS theories such as Hamilton’s local mate competition (LMC) and Clark’s local resource competition (LRC) separately explained the observed deviations from the seemingly universal 1:1 ratio. However, to the best of our knowledge, there is not yet a unified theory that accounts for the mechanisms of the three SRS. Here, we introduce the price elasticity theory in economics to define sex ratio elasticity (SRE), and present an analytical model that derives three SRSs based on the following assumption: simultaneously existing competitions for both resources A and resources B influence the level of SRE in both sexes differently. Consequently, it is the difference (between two sexes) in the level of their sex ratio elasticity that leads to three different SRS. Our analytical results demonstrate that the elasticity-based model not only reveals a highly plausible mechanism that explains the evolution of SRS in nature, but also offers a novel framework for unifying two major classical theories (i.e., LMC & LRC) in the field of SRS research.

Application of the line-spring model to a cylindrical shell containing a circumferential or axial part-through crack

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

An approximate solution was obtained for a cylindrical shell containing a part-through surface crack. It was assumed that the shell contains a circumferential or axial semi-elliptic internal or external surface crack and was subjected to a uniform membrane loading or a uniform bending moment away from the crack region. A Reissner type theory was used to account for the effects of the transverse shear deformations. The stress intensity factor at the deepest penetration point of the crack was tabulated for bending and membrane loading by varying three dimensionless length parameters of the problem formed from the shell radius, the shell thickness, the crack length, and the crack depth. The upper bounds of the stress intensity factors are provided by the results of the elasticity solution obtained from the axisymmetric crack problem for the circumferential crack, and that found from the plane strain problem for a circular ring having a radial crack for the axial crack. The line-spring model gives the expected results in comparison with the elasticity solutions. Results also compare well with the existing finite element solution of the pressurized cylinder containing an internal semi-elliptic surface crack.

Derivation of Nonlinear Wave Equation for Flexural Motions of AN Elastic Beam Travelling in AN Air-Filled Tube

NASA Astrophysics Data System (ADS)

Sugimoto, N.; Kugo, K.; Watanabe, Y.

2002-07-01

Asymptotic analysis is carried out to derive a nonlinear wave equation for flexural motions of an elastic beam of circular cross-section travelling along the centre-axis of an air-filled, circular tube placed coaxially. Both the beam and tube are assumed to be long enough for end-effects to be ignored and the aerodynamic loading on the lateral surface of the beam is considered. Assuming a compressible inviscid fluid, the velocity potential of the air is sought systematically in the form of power series in terms of the ratios of the tube radius to a wavelength and of a typical deflection to the radius. Evaluating the pressure force acting on the lateral surface of the beam, the aerodynamic loading including the effects of finite deflection as well as of air's compressibility and axial curvature of the beam are obtained. Although the nonlinearity arises from the kinematical condition on the beam surface, it may be attributed to the presence of the tube wall. With the aerodynamic loading thus obtained, a nonlinear wave equation is derived, whereas linear theory is assumed for the flexural motions of the beam. Some discussions are given on the results.

On contact problems of elasticity theory

NASA Technical Reports Server (NTRS)

Kalandiya, A. I.

1986-01-01

Certain contact problems are reviewed in the two-dimensional theory of elasticity when round bodies touch without friction along most of the boundary and, therefore, Herz' hypothesis on the smallness of the contact area cannot be used. Fundamental equations were derived coinciding externally with the equation in the theory of a finite-span wing with unkown parameter. These equations are solved using Multhopp's well-known technique, and numerical calculations are performed in specific examples.

Kinetic Theories for Biofilms (Preprint)

DTIC Science & Technology

2011-01-01

2011 2. REPORT TYPE 3. DATES COVERED 00-00-2011 to 00-00-2011 4. TITLE AND SUBTITLE Kinetic Theories for Biofilms 5a. CONTRACT NUMBER 5b...binary complex fluids to develop a set of hydrodynamic models for the two-phase mixture of biofilms and solvent (water). It is aimed to model...kinetics along with the intrinsic molecular elasticity of the EPS network strand modeled as an elastic dumbbell. This theory is valid in both the biofilm

A high-order boundary integral method for surface diffusions on elastically stressed axisymmetric rods.

PubMed

Li, Xiaofan; Nie, Qing

2009-07-01

Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratures along with an extrapolation technique, leading to an arbitrarily high-order quadrature; in addition, a high-order (temporal) integration factor method, based on explicit representation of the mean curvature, is used to reduce the stability constraint on time-step. To apply this method to a periodic (in axial direction) and axi-symmetric elastically stressed cylinder, we also present a fast and accurate summation method for the periodic Green's functions of isotropic elasticity. Using the high-order boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a self-similar assumption. In the presence of elastic stress, we show that a finite time, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated.

Exact solutions for laminated composite cylindrical shells in cylindrical bending

NASA Technical Reports Server (NTRS)

Yuan, F. G.

1992-01-01

Analytic elasticity solutions for laminated composite cylindrical shells under cylindrical bending are presented. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity, coupled governing partial differential equations are developed. The general expressions for the stresses and displacements in the laminated composite cylinders are discussed. The closed form solutions based on Classical Shell Theory (CST) and Donnell's (1933) theory are also derived for comparison purposes. Three examples illustrate the effect of radius-to-thickness ratio, coupling and stacking sequence. The results show that, in general, CST yields poor stress and displacement distributions for thick-section composite shells, but converges to the exact elasticity solution as the radius-to-thickness ratio increases. It is also shown that Donnell's theory significantly underestimates the stress and displacement response.

Line-spring model for surface cracks in a Reissner plate

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

In this paper the line-spring model developed by Rice and Levy for a surface crack in elastic plates is reconsidered. The problem is formulated by using Reissner's plate bending theory. For the plane strain problem of a strip containing an edge crack and subjected to tension and bending new expressions for stress intensity factors are used which are valid up to a depth-to-thickness ratio of 0.8. The stress intensity factors for a semi-elliptic and a rectangular crack are calculated. Considering the simplicity of the technique and the severity of the underlying assumptions, the results compare rather well with the existing finite element solutions.

Some aspects of the stability of the plane deformation mode of filaments of finite stiffness beyond the elasticity limits

NASA Astrophysics Data System (ADS)

Shimanovskii, A. V.

A method for calculating the plane bending of elastic-plastic filaments of finite stiffness is proposed on the basis of plastic flow theory. The problem considered is shown to reduce to relations similar to Kirchhoff equations for elastic work. Expressions are obtained for determining the normalized stiffness characteristics for the cross section of a filament with plastic regions containing beam theory equations as a particular case. A study is made of the effect of the plastic region size on the position of the elastic deformation-unloading interface and on the normalized stiffness of the filament cross section. Calculation results are presented in graphic form.

Investigation of structural, electronic, elastic and optical properties of Cd{sub 1-x-y}Zn{sub x}Hg{sub y}Te alloys

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

Tamer, M., E-mail: mehmet.tamer@zirve.edu.tr

2016-06-15

Structural, optical and electronic properties and elastic constants of Cd1{sub -x-y}Zn{sub x} Hg{sub y}Te alloys have been studied by employing the commercial code Castep based on density functional theory. The generalized gradient approximation and local density approximation were utilized as exchange correlation. Using elastic constants for compounds, bulk modulus, band gap, Fermi energy and Kramers–Kronig relations, dielectric constants and the refractive index have been found through calculations. Apart from these, X-ray measurements revealed elastic constants and Vegard’s law. It is seen that results obtained from theory and experiments are all in agreement.

Solution of Eshelby's inclusion problem with a bounded domain and Eshelby's tensor for a spherical inclusion in a finite spherical matrix based on a simplified strain gradient elasticity theory

NASA Astrophysics Data System (ADS)

Gao, X.-L.; Ma, H. M.

2010-05-01

A solution for Eshelby's inclusion problem of a finite homogeneous isotropic elastic body containing an inclusion prescribed with a uniform eigenstrain and a uniform eigenstrain gradient is derived in a general form using a simplified strain gradient elasticity theory (SSGET). An extended Betti's reciprocal theorem and an extended Somigliana's identity based on the SSGET are proposed and utilized to solve the finite-domain inclusion problem. The solution for the disturbed displacement field is expressed in terms of the Green's function for an infinite three-dimensional elastic body in the SSGET. It contains a volume integral term and a surface integral term. The former is the same as that for the infinite-domain inclusion problem based on the SSGET, while the latter represents the boundary effect. The solution reduces to that of the infinite-domain inclusion problem when the boundary effect is not considered. The problem of a spherical inclusion embedded concentrically in a finite spherical elastic body is analytically solved by applying the general solution, with the Eshelby tensor and its volume average obtained in closed forms. This Eshelby tensor depends on the position, inclusion size, matrix size, and material length scale parameter, and, as a result, can capture the inclusion size and boundary effects, unlike existing Eshelby tensors. It reduces to the classical Eshelby tensor for the spherical inclusion in an infinite matrix if both the strain gradient and boundary effects are suppressed. Numerical results quantitatively show that the inclusion size effect can be quite large when the inclusion is very small and that the boundary effect can dominate when the inclusion volume fraction is very high. However, the inclusion size effect is diminishing as the inclusion becomes large enough, and the boundary effect is vanishing as the inclusion volume fraction gets sufficiently low.

Liquid-assisted tunable metasurface for simultaneous manipulation of surface elastic and acoustic waves

NASA Astrophysics Data System (ADS)

Yuan, Si-Min; Ma, Tian-Xue; Chen, A.-Li; Wang, Yue-Sheng

2018-03-01

A tunable and multi-functional one-dimensional metasurface, which is formed by engraving periodic semi-ellipse grooves on the surface of an aluminum half-space, is proposed in this paper. One characteristic of the metasurface is the manipulation of multi-physical fields, i.e. it could be utilized to manipulate surface elastic and acoustic waves simultaneously. The dispersion curves of the elastic and acoustic waves can be effectively tuned by adding liquids into the grooves. Based on the tunability different applications can be realized by adding different volumes of different liquids into the grooves. As an example, simultaneous rainbow trapping of the surface elastic and acoustic waves is demonstrated in the metasurface. Moreover, a resonant cavity where the elastic and acoustic waves are highly confined is reported. The proposed metasurface paves the way to the design of multi-functional devices for simultaneous control of elastic and acoustic waves.

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

PubMed

Miehe, C; Teichtmeister, S; Aldakheel, F

2016-04-28

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

Sound transmission through stiffened double-panel structures lined with elastic porous materials

NASA Astrophysics Data System (ADS)

Mathur, Gopal P.; Tran, Boi N.; Bolton, J. S.; Shiau, Nae-Ming

This paper presents transmission loss prediction models for a periodically stiffened panel and stiffened double-panel structures using the periodic structure theory. The inter-panel cavity in the double-panels structures can be modeled as being separated by an airspace or filled with an elastic porous layer in various configurations. The acoustic behavior of elastic porous layer is described by a theory capable of accounting fully for multi-dimensional wave propagation in such materials. The predicted transmission loss of a single stiffened panel is compared with the measured data.

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.

The limits of hamiltonian structures in three-dimensional elasticity, shells, and rods

NASA Astrophysics Data System (ADS)

Ge, Z.; Kruse, H. P.; Marsden, J. E.

1996-01-01

This paper uses Hamiltonian structures to study the problem of the limit of three-dimensional (3D) elastic models to shell and rod models. In the case of shells, we show that the Hamiltonian structure for a three-dimensional elastic body converges, in a sense made precise, to that for a shell model described by a one-director Cosserat surface as the thickness goes to zero. We study limiting procedures that give rise to unconstrained as well as constrained Cosserat director models. The case of a rod is also considered and similar convergence results are established, with the limiting model being a geometrically exact director rod model (in the framework developed by Antman, Simo, and coworkers). The resulting model may or may not have constraints, depending on the nature of the constitutive relations and their behavior under the limiting procedure. The closeness of Hamiltonian structures is measured by the closeness of Poisson brackets on certain classes of functions, as well as the Hamiltonians. This provides one way of justifying the dynamic one-director model for shells. Another way of stating the convergence result is that there is an almost-Poisson embedding from the phase space of the shell to the phase space of the 3D elastic body, which implies that, in the sense of Hamiltonian structures, the dynamics of the elastic body is close to that of the shell. The constitutive equations of the 3D model and their behavior as the thickness tends to zero dictates whether the limiting 2D model is a constrained or an unconstrained director model. We apply our theory in the specific case of a 3D Saint Venant-Kirchhoff material and derive the corresponding limiting shell and rod theories. The limiting shell model is an interesting Kirchhoff-like shell model in which the stored energy function is explicitly derived in terms of the shell curvature. For rods, one gets (with an additional inextensibility constraint) a one-director Kirchhoff elastic rod model, which reduces to the well-known Euler elastica if one adds an additional single constraint that the director lines up with the Frenet frame.

Effective-medium theory of elastic waves in random networks of rods.

PubMed

Katz, J I; Hoffman, J J; Conradi, M S; Miller, J G

2012-06-01

We formulate an effective medium (mean field) theory of a material consisting of randomly distributed nodes connected by straight slender rods, hinged at the nodes. Defining wavelength-dependent effective elastic moduli, we calculate both the static moduli and the dispersion relations of ultrasonic longitudinal and transverse elastic waves. At finite wave vector k the waves are dispersive, with phase and group velocities decreasing with increasing wave vector. These results are directly applicable to networks with empty pore space. They also describe the solid matrix in two-component (Biot) theories of fluid-filled porous media. We suggest the possibility of low density materials with higher ratios of stiffness and strength to density than those of foams, aerogels, or trabecular bone.

Homogenization theory for designing graded viscoelastic sonic crystals

NASA Astrophysics Data System (ADS)

Qu, Zhao-Liang; Ren, Chun-Yu; Pei, Yong-Mao; Fang, Dai-Ning

2015-02-01

In this paper, we propose a homogenization theory for designing graded viscoelastic sonic crystals (VSCs) which consist of periodic arrays of elastic scatterers embedded in a viscoelastic host material. We extend an elastic homogenization theory to VSC by using the elastic-viscoelastic correspondence principle and propose an analytical effective loss factor of VSC. The results of VSC and the equivalent structure calculated by using the finite element method are in good agreement. According to the relation of the effective loss factor to the filling fraction, a graded VSC plate is easily and quickly designed. Then, the graded VSC may have potential applications in the vibration absorption and noise reduction fields. Project supported by the National Basic Research Program of China (Grant No. 2011CB610301).

Thermodynamic stability in elastic systems: Hard spheres embedded in a finite spherical elastic solid.

PubMed

Solano-Altamirano, J M; Goldman, Saul

2015-12-01

We determined the total system elastic Helmholtz free energy, under the constraints of constant temperature and volume, for systems comprised of one or more perfectly bonded hard spherical inclusions (i.e. "hard spheres") embedded in a finite spherical elastic solid. Dirichlet boundary conditions were applied both at the surface(s) of the hard spheres, and at the outer surface of the elastic solid. The boundary conditions at the surface of the spheres were used to describe the rigid displacements of the spheres, relative to their initial location(s) in the unstressed initial state. These displacements, together with the initial positions, provided the final shape of the strained elastic solid. The boundary conditions at the outer surface of the elastic medium were used to ensure constancy of the system volume. We determined the strain and stress tensors numerically, using a method that combines the Neuber-Papkovich spherical harmonic decomposition, the Schwartz alternating method, and Least-squares for determining the spherical harmonic expansion coefficients. The total system elastic Helmholtz free energy was determined by numerically integrating the elastic Helmholtz free energy density over the volume of the elastic solid, either by a quadrature, or a Monte Carlo method, or both. Depending on the initial position of the hard sphere(s) (or equivalently, the shape of the un-deformed stress-free elastic solid), and the displacements, either stationary or non-stationary Helmholtz free energy minima were found. The non-stationary minima, which involved the hard spheres nearly in contact with one another, corresponded to lower Helmholtz free energies, than did the stationary minima, for which the hard spheres were further away from one another.

The trampoline aftereffect: the motor and sensory modulations associated with jumping on an elastic surface.

PubMed

Márquez, Gonzalo; Aguado, Xavier; Alegre, Luis M; Lago, Angel; Acero, Rafael M; Fernández-del-Olmo, Miguel

2010-08-01

After repeated jumps over an elastic surface (e.g. a trampoline), subjects usually report a strange sensation when they jump again overground (e.g. they feel unable to jump because their body feels heavy). However, the motor and sensory effects of exposure to an elastic surface are unknown. In the present study, we examined the motor and perceptual effects of repeated jumps over two different surfaces (stiff and elastic), measuring how this affected maximal countermovement vertical jump (CMJ). Fourteen subjects participated in two counterbalanced sessions, 1 week apart. Each experimental session consisted of a series of maximal CMJs over a force plate before and after 1 min of light jumping on an elastic or stiff surface. We measured actual motor performance (height jump and leg stiffness during CMJ) and how that related to perceptual experience (jump height estimation and subjective sensation). After repeated jumps on an elastic surface, the first CMJ showed a significant increase in leg stiffness (P < or = 0.01), decrease in jump height (P < or = 0.01) increase in perceptual misestimation (P < or = 0.05) and abnormal subjective sensation (P < or = 0.001). These changes were not observed after repeated jumps on a rigid surface. In a complementary experiment, continuous surface transitions show that the effects persist across cycles, and the effects over the leg stiffness and subjective experience are minimized (P < or = 0.05). We propose that these aftereffects could be the consequence of an erroneous internal model resulting from the high vertical forces produced by the elastic surface.

The effect of transverse shear in a cracked plate under skew-symmetric loading

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1979-01-01

The problem of an elastic plate containing a through crack and subjected to twisting moments or transverse shear loads is considered. By using a bending theory which allows the satisfaction of the boundary conditions on the crack surface regarding the normal and the twisting moments and the transverse shear load separately, it is found that the resulting asymptotic stress field around the crack tip becomes identical to that given by the elasticity solutions of the plane strain and antiplane shear problems. The problem is solved for uniformly distributed or concentrated twisting moment or transverse shear load and the normalized Mode II and Mode III stress-intensity factors are tabulated. The results also include the effect of the Poisson's ratio and material orthotropy for specially orthotropic materials on the stress-intensity factors.

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.

Tactile mapping system: a novel imaging technology for surface topography and elasticity of tissues or organs.

PubMed

Oie, Tomonori; Suzuki, Hisato; Fukuda, Toru; Murayama, Yoshinobu; Omata, Sadao; Kanda, Keiichi; Nakayama, Yasuhide

2009-11-01

: We demonstrated that the tactile mapping system (TMS) has a high degree of spatial precision in the distribution mapping of surface elasticity of tissues or organs. : Samples used were a circumferential section of a small-caliber porcine artery (diameter: ∼3 mm) and an elasticity test pattern with a line and space configuration for the distribution mapping of elasticity, prepared by regional micropatterning of a 14-μm thick gelatin hydrogel coating on a polyurethane sheet. Surface topography and elasticity in normal saline were simultaneously investigated by TMS using a probe with a diameter of 5 or 12 μm, a spatial interval of 1 to 5 μm, and an indentation depth of 4 μm. : In the test pattern, a spatial resolution in TMS of <5 μm was acquired under water with a minimal probe diameter and spatial interval of the probe movement. TMS was used for the distribution mapping of surface elasticity in a flat, circumferential section (thickness: ∼0.5 mm) of a porcine artery, and the concentric layers of the vascular wall, including the collagen-rich and elastin-rich layers, could be clearly differentiated in terms of surface elasticity at the spatial resolution of <2 μm. : TMS is a simple and inexpensive technique for the distribution mapping of the surface elasticity in vascular tissues at the spatial resolution <2 μm. TMS has the ability to analyze a complex structure of the tissue samples under normal saline.

A Reformulation of Nonlinear Anisotropic Elasticity for Impact Physics

DTIC Science & Technology

2014-02-01

aluminum, copper, and magnesium . 15. SUBJECT TERMS impact physics, shock compression, elasticity, plasticity 16. SECURITY CLASSIFICATION OF: 17... deformation wave propagation code accounting for dissipative inelastic mechanisms. • Accuracy of the new nonlinear elastic- plastic model(s) will be...gradient and its transpose. A new general thermomechanical theory accounting for both elastic and plastic deformations has been briefly outlined in

Elastic S-matrices in (1 + 1) dimensions and Toda field theories

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

Christe, P.; Mussardo, G.

Particular deformations of 2-D conformal field theory lead to integrable massive quantum field theories. These can be characterized by the relative scattering data. This paper proposes a general scheme for classifying the elastic nondegenerate S-matrix in (1 + 1) dimensions starting from the possible boot-strap processes and the spins of the conserved currents. Their identification with the S-matrix coming from the Toda field theory is analyzed. The authors discuss both cases of Toda field theory constructed with the simply-laced Dynkin diagrams and the nonsimply-laced ones. The authors present the results of the perturbative analysis and their geometrical interpretations.

Single-crystal-material-based induced-shear actuation for vibration reduction of helicopters with composite rotor system

NASA Astrophysics Data System (ADS)

Pawar, Prashant M.; Jung, Sung Nam

2008-12-01

In this study, an assessment is made for the helicopter vibration reduction of composite rotor blades using an active twist control concept. Special focus is given to the feasibility of implementing the benefits of the shear actuation mechanism along with elastic couplings of composite blades for achieving maximum vibration reduction. The governing equations of motion for composite rotor blades with surface bonded piezoceramic actuators are obtained using Hamilton's principle. The equations are then solved for dynamic response using finite element discretization in the spatial and time domains. A time domain unsteady aerodynamic theory with free wake model is used to obtain the airloads. A newly developed single-crystal piezoceramic material is introduced as an actuator material to exploit its superior shear actuation authority. Seven rotor blades with different elastic couplings representing stiffness properties similar to stiff-in-plane rotor blades are used to investigate the hub vibration characteristics. The rotor blades are modeled as a box beam with actuator layers bonded on the outer surface of the top and bottom of the box section. Numerical results show that a notable vibration reduction can be achieved for all the combinations of composite rotor blades. This investigation also brings out the effect of different elastic couplings on various vibration-reduction-related parameters which could be useful for the optimal design of composite helicopter blades.

An exact stiffness theory for unidirectional xFRP composites

NASA Astrophysics Data System (ADS)

Klasztorny, M.; Konderla, P.; Piekarski, R.

2009-01-01

UD xFRP composites, i.e., isotropic plastics reinforced with long transversely isotropic fibres packed unidirectionally according to the hexagonal scheme are considered. The constituent materials are geometrically and physically linear. The previous formulations of the exact stiffness theory of such composites are revised, and the theory is developed further based on selected boundary-value problems of elasticity theory. The numerical examples presented are focussed on testing the theory with account of previous variants of this theory and experimental values of the effective elastic constants. The authors have pointed out that the exact stiffness theory of UD xFRP composites, with the modifications proposed in our study, will be useful in the engineering practice and in solving the current problems of the mechanics of composite materials.

Effective Medium Theories for Multicomponent Poroelastic Composites

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

Berryman, J G

2005-02-08

In Biot's theory of poroelasticity, elastic materials contain connected voids or pores and these pores may be filled with fluids under pressure. The fluid pressure then couples to the mechanical effects of stress or strain applied externally to the solid matrix. Eshelby's formula for the response of a single ellipsoidal elastic inclusion in an elastic whole space to a strain imposed at a distant boundary is a very well-known and important result in elasticity. Having a rigorous generalization of Eshelby's results valid for poroelasticity means that the hard part of Eshelby's work (in computing the elliptic integrals needed to evaluatemore » the fourth-rank tensors for inclusions shaped like spheres, oblate and prolate spheroids, needles and disks) can be carried over from elasticity to poroelasticity--and also thermoelasticity--with only relatively minor modifications. Effective medium theories for poroelastic composites such as rocks can then be formulated easily by analogy to well-established methods used for elastic composites. An identity analogous to Eshelby's classic result has been derived [Physical Review Letters 79:1142-1145 (1997)] for use in these more complex and more realistic problems in rock mechanics analysis. Descriptions of the application of this result as the starting point for new methods of estimation are presented, including generalizations of the coherent potential approximation (CPA), differential effective medium (DEM) theory, and two explicit schemes. Results are presented for estimating drained shear and bulk modulus, the Biot-Willis parameter, and Skempton's coefficient. Three of the methods considered appear to be quite reliable estimators, while one of the explicit schemes is found to have some undesirable characteristics.« less

Rotational elasticity

NASA Astrophysics Data System (ADS)

Vassiliev, Dmitri

2017-04-01

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

Nonlinear Acoustic Landmine Detection: Profiling Soil Surface Vibrations and Modeling Mesoscopic Elastic Behavior

DTIC Science & Technology

2007-05-04

TITLE AND SUBTITLE Nonlinear Acoustic Landmine Detection: Profiling Soil Surface Vibrations and Modeling Mesoscopic Elastic Behavior 6. AUTHOR(S...project report; no. 352 (2007) NONLINEAR ACOUSTIC LANDMINE DETECTION: PROFILING SOIL SURFACE VIBRATIONS AND MODELING MESOSCOPIC ELASTIC... model (Caughey 1966). Nonlinear acoustic landmine detection experiments are performed in the anechoic chamber facility using both a buried acrylic

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

Snap-buckling in asymmetrically constrained elastic strips

NASA Astrophysics Data System (ADS)

Sano, Tomohiko G.; Wada, Hirofumi

2018-01-01

When a flat elastic strip is compressed along its axis, it is bent in one of two possible directions via spontaneous symmetry breaking, forming a cylindrical arc. This is a phenomenon well known as Euler buckling. When this cylindrical section is pushed in the other direction, the bending direction can suddenly reverse. This instability is called "snap-through buckling" and is one of the elementary shape transitions in a prestressed thin structure. Combining experiments and theory, we study snap-buckling of an elastic strip with one end hinged and the other end clamped. These asymmetric boundary constraints break the intrinsic symmetry of the strip, generating mechanical behaviors, including largely hysteretic but reproducible force responses and switchlike discontinuous shape changes. We establish the set of exact analytical solutions to fully explain all our major experimental and numerical findings. Asymmetric boundary conditions arise naturally in diverse situations when a thin object is in contact with a solid surface at one end. The introduction of asymmetry through boundary conditions yields new insight into complex and programmable functionalities in material and industrial design.

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

Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two-temperature

NASA Astrophysics Data System (ADS)

Lotfy, K.; Sarkar, N.

2017-11-01

In this work, a novel generalized model of photothermal theory with two-temperature thermoelasticity theory based on memory-dependent derivative (MDD) theory is performed. A one-dimensional problem for an elastic semiconductor material with isotropic and homogeneous properties has been considered. The problem is solved with a new model (MDD) under the influence of a mechanical force with a photothermal excitation. The Laplace transform technique is used to remove the time-dependent terms in the governing equations. Moreover, the general solutions of some physical fields are obtained. The surface taken into consideration is free of traction and subjected to a time-dependent thermal shock. The numerical Laplace inversion is used to obtain the numerical results of the physical quantities of the problem. Finally, the obtained results are presented and discussed graphically.

Polarized electron beams elastically scattered by atoms as a tool for testing fundamental predictions of quantum mechanics.

PubMed

Dapor, Maurizio

2018-03-29

Quantum information theory deals with quantum noise in order to protect physical quantum bits (qubits) from its effects. A single electron is an emblematic example of a qubit, and today it is possible to experimentally produce polarized ensembles of electrons. In this paper, the theory of the polarization of electron beams elastically scattered by atoms is briefly summarized. Then the POLARe program suite, a set of computer programs aimed at the calculation of the spin-polarization parameters of electron beams elastically interacting with atomic targets, is described. Selected results of the program concerning Ar, Kr, and Xe atoms are presented together with the comparison with experimental data about the Sherman function for low kinetic energy of the incident electrons (1.5eV-350eV). It is demonstrated that the quantum-relativistic theory of the polarization of electron beams elastically scattered by atoms is in good agreement with experimental data down to energies smaller than a few eV.

On some problems in a theory of thermally and mechanically interacting continuous media. Ph.D. Thesis; [linearized theory of interacting mixture of elastic solid and viscous fluid

NASA Technical Reports Server (NTRS)

Lee, Y. M.

1971-01-01

Using a linearized theory of thermally and mechanically interacting mixture of linear elastic solid and viscous fluid, we derive a fundamental relation in an integral form called a reciprocity relation. This reciprocity relation relates the solution of one initial-boundary value problem with a given set of initial and boundary data to the solution of a second initial-boundary value problem corresponding to a different initial and boundary data for a given interacting mixture. From this general integral relation, reciprocity relations are derived for a heat-conducting linear elastic solid, and for a heat-conducting viscous fluid. An initial-boundary value problem is posed and solved for the mixture of linear elastic solid and viscous fluid. With the aid of the Laplace transform and the contour integration, a real integral representation for the displacement of the solid constituent is obtained as one of the principal results of the analysis.

Peeling without precursors

NASA Astrophysics Data System (ADS)

Lister, John; Skinner, Dominic; Large, Tim

2017-11-01

The peeling by fluid injection of an elastic sheet away from a substrate is often regularised by invoking a thin prewetting film or a low-viscosity phase in the tip. Here we analyse fluid-driven peeling without such precursors, and consider an elastic sheet either bonded to, or simply laid on, an elastic substrate. To resolve the `elastic contact-line problem' that arises from viscous flow and beam theory, we determine the near-tip behaviour from lubrication theory coupled to the full equations of elasticity and fracture. The result is a law for the tip propagation speed in terms of the remote loading and the toughness of the sheet-substrate bonding (which might be zero). There are distinct modes of failure, according to whether there is slip ahead of the fluid front. The propagation-speed law gives rise to new similarity solutions for the spread of a fluid-filled blister in different regimes.

Effect of surface-related Rayleigh and multiple waves on velocity reconstruction with time-domain elastic FWI

NASA Astrophysics Data System (ADS)

Fang, Jinwei; Zhou, Hui; Zhang, Qingchen; Chen, Hanming; Wang, Ning; Sun, Pengyuan; Wang, Shucheng

2018-01-01

It is critically important to assess the effectiveness of elastic full waveform inversion (FWI) algorithms when FWI is applied to real land seismic data including strong surface and multiple waves related to the air-earth boundary. In this paper, we review the realization of the free surface boundary condition in staggered-grid finite-difference (FD) discretization of elastic wave equation, and analyze the impact of the free surface on FWI results. To reduce inputs/outputs (I/O) operations in gradient calculation, we adopt the boundary value reconstruction method to rebuild the source wavefields during the backward propagation of the residual data. A time-domain multiscale inversion strategy is conducted by using a convolutional objective function, and a multi-GPU parallel programming technique is used to accelerate our elastic FWI further. Forward simulation and elastic FWI examples without and with considering the free surface are shown and analyzed, respectively. Numerical results indicate that no free surface incorporated elastic FWI fails to recover a good inversion result from the Rayleigh wave contaminated observed data. By contrast, when the free surface is incorporated into FWI, the inversion results become better. We also discuss the dependency of the Rayleigh waveform incorporated FWI on the accuracy of initial models, especially the accuracy of the shallow part of the initial models.

Elastic instabilities in rubber

NASA Astrophysics Data System (ADS)

Gent, Alan

2009-03-01

Materials that undergo large elastic deformations can exhibit novel instabilities. Several examples are described: development of an aneurysm on inflating a rubber tube; non-uniform stretching on inflating a spherical balloon; formation of internal cracks in rubber blocks at a critical level of triaxial tension or when supersaturated with a dissolved gas; surface wrinkling of a block at a critical amount of compression; debonding or fracture of constrained films on swelling, and formation of ``knots'' on twisting stretched cylindrical rods. These various deformations are analyzed in terms of a simple strain energy function, using Rivlin's theory of large elastic deformations, and the results are compared with experimental measurements of the onset of unstable states. Such comparisons provide new tests of Rivlin's theory and, at least in principle, critical tests of proposed strain energy functions for rubber. Moreover the onset of highly non-uniform deformations has serious implications for the fatigue life and fracture resistance of rubber components. [4pt] References: [0pt] R. S. Rivlin, Philos. Trans. Roy. Soc. Lond. Ser. A241 (1948) 379--397. [0pt] A. Mallock, Proc. Roy. Soc. Lond. 49 (1890--1891) 458--463. [0pt] M. A. Biot, ``Mechanics of Incremental Deformations'', Wiley, New York, 1965. [0pt] A. N. Gent and P. B. Lindley, Proc. Roy. Soc. Lond. A 249 (1958) 195--205. [0pt] A. N. Gent, W. J. Hung and M. F. Tse, Rubb. Chem. Technol. 74 (2001) 89--99. [0pt] A. N. Gent, Internatl. J. Non-Linear Mech. 40 (2005) 165--175.

Nonclassical models of the theory of plates and shells

NASA Astrophysics Data System (ADS)

Annin, Boris D.; Volchkov, Yuri M.

2017-11-01

Publications dealing with the study of methods of reducing a three-dimensional problem of the elasticity theory to a two-dimensional problem of the theory of plates and shells are reviewed. Two approaches are considered: the use of kinematic and force hypotheses and expansion of solutions of the three-dimensional elasticity theory in terms of the complete system of functions. Papers where a three-dimensional problem is reduced to a two-dimensional problem with the use of several approximations of each of the unknown functions (stresses and displacements) by segments of the Legendre polynomials are also reviewed.

Theory of liquid crystal elastomers and polymer networks : Connection between neoclassical theory and differential geometry.

PubMed

Nguyen, Thanh-Son; Selinger, Jonathan V

2017-09-01

In liquid crystal elastomers and polymer networks, the orientational order of liquid crystals is coupled with elastic distortions of crosslinked polymers. Previous theoretical research has described these materials through two different approaches: a neoclassical theory based on the liquid crystal director and the deformation gradient tensor, and a geometric elasticity theory based on the difference between the actual metric tensor and a reference metric. Here, we connect those two approaches using a formalism based on differential geometry. Through this connection, we determine how both the director and the geometry respond to a change of temperature.

Reaction paths of alane dissociation on the Si(0 0 1) surface

NASA Astrophysics Data System (ADS)

Smith, Richard; Bowler, David R.

2018-03-01

Building on our earlier study, we examine the kinetic barriers to decomposition of alane, AlH3, on the Si(0 0 1) surface, using the nudged elastic band approach within density functional theory. We find that the initial decomposition to AlH with two H atoms on the surface proceeds without a significant barrier. There are several pathways available to lose the final hydrogen, though these present barriers of up to 1 eV. Incorporation is more challenging, with the initial structures less stable in several cases than the starting structures, just as was found for phosphorus. We identify a stable route for Al incorporation following selective surface hydrogen desorption (e.g. by scanning tunneling microscope tip). The overall process parallels PH3, and indicates that atomically precise acceptor doping should be possible.

Elasticity of smectic liquid crystals with in-plane orientational order and dispiration asymmetry

NASA Astrophysics Data System (ADS)

Alageshan, Jaya Kumar; Chakrabarti, Buddhapriya; Hatwalne, Yashodhan

2017-02-01

The Nelson-Peliti formulation of the elasticity theory of isolated fluid membranes with orientational order emphasizes the interplay between geometry, topology, and thermal fluctuations. Fluid layers of lamellar liquid crystals such as smectic-C , hexatic smectics, and smectic-C* are endowed with in-plane orientational order. We extend the Nelson-Peliti formulation so as to bring these smectics within its ambit. Using the elasticity theory of smectics-C*, we show that positive and negative dispirations (topological defects in Smectic-C* liquid crystals) with strengths of equal magnitude have disparate energies—a result that is amenable to experimental tests.

Elasticity and Fluctuations of Frustrated Nanoribbons

NASA Astrophysics Data System (ADS)

Grossman, Doron; Sharon, Eran; Diamant, Haim

2016-06-01

We derive a reduced quasi-one-dimensional theory of geometrically frustrated elastic ribbons. Expressed in terms of geometric properties alone, it applies to ribbons over a wide range of scales, allowing the study of their elastic equilibrium, as well as thermal fluctuations. We use the theory to account for the twisted-to-helical transition of ribbons with spontaneous negative curvature and the effect of fluctuations on the corresponding critical exponents. The persistence length of such ribbons changes nonmonotonically with the ribbon's width, dropping to zero at the transition. This and other statistical properties qualitatively differ from those of nonfrustrated fluctuating filaments.

Fermi surfaces and electronic topological transitions in metallic solid solutions

NASA Astrophysics Data System (ADS)

Bruno, E.; Ginatempo, B.; Guiliano, E. S.; Ruban, A. V.; Vekilov, Yu. Kh.

1994-12-01

Notwithstanding the substitutional disorder, the Fermi surface of metallic alloys can be measured and computed. We show that, from the theoretical point of view, it is defined as the locus of the peaks of the Bloch Spectral Function (BSF). Such Fermi surfaces, on varying the atomic concentrations, may undergo changes of their topology, known as Electronic Topological Transitions (ETT). Thus, for instance, pockets of electrons or holes may appear or disappear, necks may open or close. ETTs cause anomalous behaviours of thermodynamic, transport and elastic properties of metals and constitute a fascinating field in the study of Fermi liquid systems. Although ETTs could be studied on pure systems as a function of the thermodynamic variables, nevertheless such a study would often require extreme conditions, and would lead to experimental difficulties. On the other hand, it is possible to explore the variations of atomic concentration, i.e. the valence electron per atom ratio, in metallic solid solutions with a relative experimental ease. In this paper we review the theoretical techniques for the determination of Fermi surfaces in metallic solid solutions and discuss some examples of ETTs, namely LiMg, ZrNb, NbMo, MoRe, AgPd, CdMg, NiW and NiTi alloys, also in connection with experimental data as thermoelectric power, resistivity, elastic constants and electron-phonon coupling and with the determinations of the electron momentum distribution function from Compton scattering and positron annihilation experiments. We show that the ab initio calculations of the electronic structure for the quoted systems, together with a careful determination of the BSF, are able to predict quantitatively ETTs at those concentrations where physical quantities display anomalies, so confirming directly ETT theory. Although it is not the purpose of the present review to give a full account of electronic structure calculation schemes, however, we briefly discuss the ideas and the main physical approximations underlying theories of substitutional disorder in alloys. We shall pay some more attention to the Coherent Potential Approximation (CPA) in the Korringa-Kohn-Rostoker (KKR) multiple scattering framework and the Hohenberg and Kohn Density Functional Theory in the Local Density Approximation (LDA) for the exchange-correlation potential. The above choice is supported by the numerical versatility of the LDAKKRCPA theory, and, more important, by the a fortiori evidence that essentially equivalent results are obtained from different theoretical frameworks, provided the same basic physical approximations are used. Accordingly, when convenient, we present new LDAKKRCPA determinations of the Fermi surfaces, as for the ZrNbMoRe series.

Coseismic Gravity and Displacement Signatures Induced by the 2013 Okhotsk Mw8.3 Earthquake.

PubMed

Zhang, Guoqing; Shen, Wenbin; Xu, Changyi; Zhu, Yiqing

2016-09-01

In this study, Gravity Recovery and Climate Experiment (GRACE) RL05 data from January 2003 to October 2014 were used to extract the coseismic gravity changes induced by the 24 May 2013 Okhotsk Mw8.3 deep-focus earthquake using the difference and least square fitting methods. The gravity changes obtained from GRACE data agreed well with those from dislocation theory in both magnitude and spatial pattern. Positive and negative gravity changes appeared on both sides of the epicenter. The positive signature appeared on the western side, and the peak value was approximately 0.4 microgal (1 microgal = 10(-8) m/s²), whereas on the eastern side, the gravity signature was negative, and the peak value was approximately -1.1 microgal. It demonstrates that deep-focus earthquakes Mw ≤ 8.5 are detectable by GRACE observations. Moreover, the coseismic displacements of 20 Global Positioning System (GPS) stations on the Earth's surface were simulated using an elastic dislocation theory in a spherical earth model, and the results are consistent with the GPS results, especially the near-field results. We also estimated the gravity contributions from the coseismic vertical displacements and density changes, analyzed the proportion of these two gravity change factors (based on an elastic dislocation theory in a spherical earth model) in this deep-focus earthquake. The gravity effect from vertical displacement is four times larger than that caused by density redistribution.

Delamination growth in composite materials

NASA Technical Reports Server (NTRS)

Gillespie, J. W., Jr.; Carlsson, L. A.; Pipes, R. B.; Rothschilds, R.; Trethewey, B.; Smiley, A.

1986-01-01

The Double Cantilever Beam (DCB) and the End Notched Flexure (ENF) specimens are employed to characterize MODE I and MODE II interlaminar fracture resistance of graphite/epoxy (CYCOM 982) and graphite/PEEK (APC2) composites. Sizing of test specimen geometries to achieve crack growth in the linear elastic regime is presented. Data reduction schemes based upon beam theory are derived for the ENF specimen and include the effects of shear deformation and friction between crack surfaces on compliance, C, and strain energy release rate, G sub II. Finite element (FE) analyses of the ENF geometry including the contact problem with friction are presented to assess the accuracy of beam theory expressions for C and G sub II. Virtual crack closure techniques verify that the ENF specimen is a pure Mode II test. Beam theory expressions are shown to be conservative by 20 to 40 percent for typical unidirectional test specimen geometries. A FE parametric study investigating the influence of delamination length and depth, span, thickness and material properties on G sub II is presented. Mode I and II interlaminar fracture test results are presented. Important experimental parameters are isolated, such as precracking techniques, rate effects, and nonlinear load-deflection response. It is found that subcritical crack growth and inelastic materials behavior, responsible for the observed nonlinearities, are highly rate-dependent phenomena with high rates generally leading to linear elastic response.

Lithospheric Flexural Modeling of Iapetus' Equatorial Ridge

NASA Astrophysics Data System (ADS)

Zheng, W.; Ip, W.-H.; Teng, L. S.

2012-04-01

Iapetus, which is one of Saturn's ball-shaped satellites, has some unique features in the Solar System. This satellite has a mean radius of 735 km, and there is an approximately 20-kilometer-high mountain lying precisely on its equator. The mountain is known as an "equatorial ridge" since it makes Iapetus appear walnut shaped. The origin of the equatorial ridge is attributed to several hypotheses, including different endogenesis and exogenesis processes. In this work, we attempted to construct a flexural model of the equatorial ridge using elastic lithosphere theory. The equatorial ridge is treated as a linear load which exerts uniform force on Iapetus' hard shell (i.e. elastic lithosphere of Iapetus). To calculate the deflection of surface, we use the Digital Terrain Model (DTM) data of Iapetus' leading side published by Giese et al. (2008). Giese et al. also pointed out that the elastic lithospheric thickness of Iapetus must exceed 100 km to support the ridge without deflecting. However, we found possible evidence in the DTM data that implied deflection. There are two sites of surface depression on the northern side of the equatorial ridge. The few-kilometer deflection implies a thinner lithosphere than previous suggested. Assume that the thickness of elastic lithosphere is only 5% below of the radius of Iapetus, so the flat-Earth and one-plate condition could adapt to the flexure model of Iapetus. Based on analysis of the distance between a bulge and the ridge, the calculated lithospheric thickness is 6-10 km. The new result seems controversial, but the modeled surface profile is highly consistent with numerical ridge DTM profile extracted from Giese et al. (2008). Thinner lithosphere also supports the contraction model proposed by Sandwell and Schubert (2010) since the bucking harmonic degree increases. In the other hand, the transformation layer between hard shell and plastic inner core may need constraint on thermal history or crystal form of ice. In conclusion, The flexural model of Iapetus' equatorial ridge reveals the possibility of thinner hard shell, fits the surface profile, and supplies more clues to the origin of Iapetus, the interesting satellite in the Solar System.

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

Reliability assessment of different plate theories for elastic wave propagation analysis in functionally graded plates.

PubMed

Mehrkash, Milad; Azhari, Mojtaba; Mirdamadi, Hamid Reza

2014-01-01

The importance of elastic wave propagation problem in plates arises from the application of ultrasonic elastic waves in non-destructive evaluation of plate-like structures. However, precise study and analysis of acoustic guided waves especially in non-homogeneous waveguides such as functionally graded plates are so complicated that exact elastodynamic methods are rarely employed in practical applications. Thus, the simple approximate plate theories have attracted much interest for the calculation of wave fields in FGM plates. Therefore, in the current research, the classical plate theory (CPT), first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT) are used to obtain the transient responses of flexural waves in FGM plates subjected to transverse impulsive loadings. Moreover, comparing the results with those based on a well recognized hybrid numerical method (HNM), we examine the accuracy of the plate theories for several plates of various thicknesses under excitations of different frequencies. The material properties of the plate are assumed to vary across the plate thickness according to a simple power-law distribution in terms of volume fractions of constituents. In all analyses, spatial Fourier transform together with modal analysis are applied to compute displacement responses of the plates. A comparison of the results demonstrates the reliability ranges of the approximate plate theories for elastic wave propagation analysis in FGM plates. Furthermore, based on various examples, it is shown that whenever the plate theories are used within the appropriate ranges of plate thickness and frequency content, solution process in wave number-time domain based on modal analysis approach is not only sufficient but also efficient for finding the transient waveforms in FGM plates. Copyright © 2013 Elsevier B.V. All rights reserved.

Theory of activated glassy relaxation, mobility gradients, surface diffusion, and vitrification in free standing thin films

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

Mirigian, Stephen, E-mail: kschweiz@illinois.edu, E-mail: smirigian@gmail.com; Schweizer, Kenneth S., E-mail: kschweiz@illinois.edu, E-mail: smirigian@gmail.com

2015-12-28

We have constructed a quantitative, force level, statistical mechanical theory for how confinement in free standing thin films introduces a spatial mobility gradient of the alpha relaxation time as a function of temperature, film thickness, and location in the film. The crucial idea is that relaxation speeds up due to the reduction of both near-surface barriers associated with the loss of neighbors in the local cage and the spatial cutoff and dynamical softening near the vapor interface of the spatially longer range collective elasticity cost for large amplitude hopping. These two effects are fundamentally coupled. Quantitative predictions are made formore » how an apparent glass temperature depends on the film thickness and experimental probe technique, the emergence of a two-step decay and mobile layers in time domain measurements, signatures of confinement in frequency-domain dielectric loss experiments, the dependence of film-averaged relaxation times and dynamic fragility on temperature and film thickness, surface diffusion, and the relationship between kinetic experiments and pseudo-thermodynamic measurements such as ellipsometry.« less

Theory of activated glassy relaxation, mobility gradients, surface diffusion, and vitrification in free standing thin films.

PubMed

Mirigian, Stephen; Schweizer, Kenneth S

2015-12-28

We have constructed a quantitative, force level, statistical mechanical theory for how confinement in free standing thin films introduces a spatial mobility gradient of the alpha relaxation time as a function of temperature, film thickness, and location in the film. The crucial idea is that relaxation speeds up due to the reduction of both near-surface barriers associated with the loss of neighbors in the local cage and the spatial cutoff and dynamical softening near the vapor interface of the spatially longer range collective elasticity cost for large amplitude hopping. These two effects are fundamentally coupled. Quantitative predictions are made for how an apparent glass temperature depends on the film thickness and experimental probe technique, the emergence of a two-step decay and mobile layers in time domain measurements, signatures of confinement in frequency-domain dielectric loss experiments, the dependence of film-averaged relaxation times and dynamic fragility on temperature and film thickness, surface diffusion, and the relationship between kinetic experiments and pseudo-thermodynamic measurements such as ellipsometry.

A rotational ablation tool for calcified atherosclerotic plaque removal.

PubMed

Kim, Min-Hyeng; Kim, Hyung-Jung; Kim, Nicholas N; Yoon, Hae-Sung; Ahn, Sung-Hoon

2011-12-01

Atherosclerosis is a major cardiovascular disease involving accumulations of lipids, white blood cells, and other materials on the inside of artery walls. Since the calcification found in the advanced stage of atherosclerosis dramatically enhances the mechanical properties of the plaque, restoring the original lumen of the artery remains a challenge. High-speed rotational atherectomy, when performed with an ablating grinder to remove the plaque, produces much better results in the treatment of calcified plaque compared to other methods. However, the high-speed rotation of the Rotablator commercial rotational atherectomy device produces microcavitation, which should be avoided because of the serious complications it can cause. This research involves the development of a high-speed rotational ablation tool that does not generate microcavitation. It relies on surface modification to achieve the required surface roughness. The surface roughness of the tool for differential cutting was designed based on lubrication theory, and the surface of the tool was modified using Nd:YAG laser beam engraving. Electron microscope images and profiles indicated that the engraved surface of the tool had approximately 1 μm of root mean square surface roughness. The ablation experiment was performed on hydroxyapatite/polylactide composite with an elastic modulus similar to that of calcified plaque. In addition, differential cutting was verified on silicone rubber with an elastic modulus similar to that of a normal artery. The tool performance and reliability were evaluated by measuring the ablation force exerted, the size of the debris generated during ablation, and through visual inspection of the silicone rubber surface.

Elastic wave generated by granular impact on rough and erodible surfaces

NASA Astrophysics Data System (ADS)

Bachelet, Vincent; Mangeney, Anne; de Rosny, Julien; Toussaint, Renaud; Farin, Maxime

2018-01-01

The elastic waves generated by impactors hitting rough and erodible surfaces are studied. For this purpose, beads of variable materials, diameters, and velocities are dropped on (i) a smooth PMMA plate, (ii) stuck glass beads on the PMMA plate to create roughness, and (iii) the rough plate covered with layers of free particles to investigate erodible beds. The Hertz model validity to describe impacts on a smooth surface is confirmed. For rough and erodible surfaces, an empirical scaling law that relates the elastic energy to the radius Rb and normal velocity Vz of the impactor is deduced from experimental data. In addition, the radiated elastic energy is found to decrease exponentially with respect to the bed thickness. Lastly, we show that the variability of the elastic energy among shocks increases from some percents to 70% between smooth and erodible surfaces. This work is a first step to better quantify seismic emissions of rock impacts in natural environment, in particular on unconsolidated soils.

Assessing exchange-correlation functionals for elasticity and thermodynamics of α -ZrW2O8 : A density functional perturbation theory study

NASA Astrophysics Data System (ADS)

Weck, Philippe F.; Kim, Eunja; Greathouse, Jeffery A.; Gordon, Margaret E.; Bryan, Charles R.

2018-04-01

Elastic and thermodynamic properties of negative thermal expansion (NTE) α -ZrW2O8 have been calculated using PBEsol and PBE exchange-correlation functionals within the framework of density functional perturbation theory (DFPT). Measured elastic constants are reproduced within ∼ 2 % with PBEsol and ∼ 6 % with PBE. The thermal evolution of the Grüneisen parameter computed within the quasi-harmonic approximation exhibits negative values below the Debye temperature, consistent with observation. The standard molar heat capacity is predicted to be CP0 = 192.2 and 193.8 J mol-1K-1 with PBEsol and PBE, respectively. These results suggest superior accuracy of DFPT/PBEsol for studying the lattice dynamics, elasticity and thermodynamics of NTE materials.

Propagation of ultrasonic Love waves in nonhomogeneous elastic functionally graded materials.

PubMed

Kiełczyński, P; Szalewski, M; Balcerzak, A; Wieja, K

2016-02-01

This paper presents a theoretical study of the propagation behavior of ultrasonic Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in the mechanics of solids. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved by using two methods: i.e., (1) Finite Difference Method, and (2) Haskell-Thompson Transfer Matrix Method. The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The effect of elastic non-homogeneities on the dispersion curves of Love waves is discussed. Two Love wave waveguide structures are analyzed: (1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and (2) a semi-infinite nonhomogeneous elastic half-space. Obtained in this work, the phase and group velocity dispersion curves of Love waves propagating in the considered nonhomogeneous elastic waveguides have not previously been reported in the scientific literature. The results of this paper may give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials, and can provide theoretical guidance for the design and optimization of Love wave based devices. Copyright © 2015 Elsevier B.V. All rights reserved.

Modeling elasto-viscoplasticity in a consistent phase field framework

DOE PAGES

Cheng, Tian -Le; Wen, You -Hai; Hawk, Jeffrey A.

2017-05-19

Existing continuum level phase field plasticity theories seek to solve plastic strain by minimizing the shear strain energy. However, rigorously speaking, for thermodynamic consistency it is required to minimize the total strain energy unless there is proof that hydrostatic strain energy is independent of plastic strain which is unfortunately absent. In this work, we extend the phase-field microelasticity theory of Khachaturyan et al. by minimizing the total elastic energy with constraint of incompressibility of plastic strain. We show that the flow rules derived from the Ginzburg-Landau type kinetic equation can be in line with Odqvist's law for viscoplasticity and Prandtl-Reussmore » theory. Free surfaces (external surfaces or internal cracks/voids) are treated in the model. Deformation caused by a misfitting spherical precipitate in an elasto-plastic matrix is studied by large-scale three-dimensional simulations in four different regimes in terms of the matrix: (a) elasto-perfectly-plastic, (b) elastoplastic with linear hardening, (c) elastoplastic with power-law hardening, and (d) elasto-perfectly-plastic with a free surface. The results are compared with analytical/numerical solutions of Lee et al. for (a-c) and analytical solution derived in this work for (d). Additionally, the J integral of a fixed crack is calculated in the phase-field model and discussed in the context of fracture mechanics.« less

Modeling elasto-viscoplasticity in a consistent phase field framework

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

Cheng, Tian -Le; Wen, You -Hai; Hawk, Jeffrey A.

Existing continuum level phase field plasticity theories seek to solve plastic strain by minimizing the shear strain energy. However, rigorously speaking, for thermodynamic consistency it is required to minimize the total strain energy unless there is proof that hydrostatic strain energy is independent of plastic strain which is unfortunately absent. In this work, we extend the phase-field microelasticity theory of Khachaturyan et al. by minimizing the total elastic energy with constraint of incompressibility of plastic strain. We show that the flow rules derived from the Ginzburg-Landau type kinetic equation can be in line with Odqvist's law for viscoplasticity and Prandtl-Reussmore » theory. Free surfaces (external surfaces or internal cracks/voids) are treated in the model. Deformation caused by a misfitting spherical precipitate in an elasto-plastic matrix is studied by large-scale three-dimensional simulations in four different regimes in terms of the matrix: (a) elasto-perfectly-plastic, (b) elastoplastic with linear hardening, (c) elastoplastic with power-law hardening, and (d) elasto-perfectly-plastic with a free surface. The results are compared with analytical/numerical solutions of Lee et al. for (a-c) and analytical solution derived in this work for (d). Additionally, the J integral of a fixed crack is calculated in the phase-field model and discussed in the context of fracture mechanics.« less

Influence of carbon nanotubes on the buckling of microtubule bundles in viscoelastic cytoplasm using nonlocal strain gradient theory

NASA Astrophysics Data System (ADS)

Farajpour, A.; Rastgoo, A.

Carbon nanotubes are a new class of microtubule-stabilizing agents since they interact with protein microtubules in living cells, interfering with cell division and inducing apoptosis. In the present work, a modified beam model is developed to investigate the effect of carbon nanotubes on the buckling of microtubule bundles in living cell. A realistic interaction model is employed using recent experimental data on the carbon nanotube-stabilized microtubules. Small scale and surface effects are taken into account applying the nonlocal strain gradient theory and surface elasticity theory. Pasternak model is used to describe the normal and shearing effects of enclosing filament matrix on the buckling behavior of the system. An exact solution is obtained for the buckling growth rates of the mixed bundle in viscoelastic surrounding cytoplasm. The present results are compared with those reported in the open literature for single microtubules and an excellent agreement is found. Finally, the effects of different parameters such as the size, chirality, position and surface energy of carbon nanotubes on the buckling growth rates of microtubule bundles are studied. It is found that the buckling growth rate may increase or decrease by adding carbon nanotubes, depending on the diameter and chirality of carbon nanotubes.

Spacetime representation of topological phononics

NASA Astrophysics Data System (ADS)

Deymier, Pierre A.; Runge, Keith; Lucas, Pierre; Vasseur, Jérôme O.

2018-05-01

Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein–Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.

Flutter and divergence instability of supported piezoelectric nanotubes conveying fluid

NASA Astrophysics Data System (ADS)

Bahaadini, Reza; Hosseini, Mohammad; Jamali, Behnam

2018-01-01

In this paper, divergence and flutter instabilities of supported piezoelectric nanotubes containing flowing fluid are investigated. To take the size effects into account, the nonlocal elasticity theory is implemented in conjunction with the Euler-Bernoulli beam theory incorporating surface stress effects. The Knudsen number is applied to investigate the slip boundary conditions between the flow and wall of nanotube. The nonlocal governing equations of nanotube are obtained using Newtonian method, including the influence of piezoelectric voltage, surface effects, Knudsen number and nonlocal parameter. Applying Galerkin approach to transform resulting equations into a set of eigenvalue equations under the simple-simple (S-S) and clamped-clamped (C-C) boundary conditions. The effects of the piezoelectric voltage, surface effects, Knudsen number, nonlocal parameter and boundary conditions on the divergence and flutter boundaries of nanotubes are discussed. It is observed that the fluid-conveying nanotubes with both ends supported lose their stability by divergence first and then by flutter with increase in fluid velocity. Results indicate the importance of using piezoelectric voltage, nonlocal parameter and Knudsen number in decrease of critical flow velocities of system. Moreover, the surface effects have a significant role on the eigenfrequencies and critical fluid velocity.

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

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

Feng, Lu; Wang, Jing; Wang, Shibin

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

Multiparameter elastic full waveform inversion with facies-based constraints

NASA Astrophysics Data System (ADS)

Zhang, Zhen-dong; Alkhalifah, Tariq; Naeini, Ehsan Zabihi; Sun, Bingbing

2018-06-01

Full waveform inversion (FWI) incorporates all the data characteristics to estimate the parameters described by the assumed physics of the subsurface. However, current efforts to utilize FWI beyond improved acoustic imaging, like in reservoir delineation, faces inherent challenges related to the limited resolution and the potential trade-off between the elastic model parameters. Some anisotropic parameters are insufficiently updated because of their minor contributions to the surface collected data. Adding rock physics constraints to the inversion helps mitigate such limited sensitivity, but current approaches to add such constraints are based on including them as a priori knowledge mostly valid around the well or as a global constraint for the whole area. Since similar rock formations inside the Earth admit consistent elastic properties and relative values of elasticity and anisotropy parameters (this enables us to define them as a seismic facies), utilizing such localized facies information in FWI can improve the resolution of inverted parameters. We propose a novel approach to use facies-based constraints in both isotropic and anisotropic elastic FWI. We invert for such facies using Bayesian theory and update them at each iteration of the inversion using both the inverted models and a priori information. We take the uncertainties of the estimated parameters (approximated by radiation patterns) into consideration and improve the quality of estimated facies maps. Four numerical examples corresponding to different acquisition, physical assumptions and model circumstances are used to verify the effectiveness of the proposed method.

Closed system of coupling effects in generalized thermo-elastoplasticity

NASA Astrophysics Data System (ADS)

Śloderbach, Z.

2016-05-01

In this paper, the field equations of the generalized coupled thermoplasticity theory are derived using the postulates of classical thermodynamics of irreversible processses. Using the Legendre transformations two new thermodynamics potentials P and S depending upon internal thermodynamic forces Π are introduced. The most general form for all the thermodynamics potentials are assumed instead of the usually used additive form. Due to this assumption, it is possible to describe all the effects of thermomechanical couples and also the elastic-plastic coupling effects observed in such materials as rocks, soils, concretes and in some metalic materials. In this paper not only the usual postulate of existence of a dissipation qupotential (the Gyarmati postulate) is used to derive the velocity equation. The plastic flow constitutive equations have the character of non-associated flow laws even when the Gyarmati postulate is assumed. In general formulation, the plastic strain rate tensor is normal to the surface of the generalized function of plastic flow defined in the the space of internal thermodynamic forces Π but is not normal to the yield surface. However, in general formulation and after the use the Gyarmati postulate, the direction of the sum of the plastic strain rate tensor and the coupled elastic strain rate tensor is normal to the yield surface.

Finger-Shaped GelForce: Sensor for Measuring Surface Traction Fields for Robotic Hand.

PubMed

Sato, K; Kamiyama, K; Kawakami, N; Tachi, S

2010-01-01

It is believed that the use of haptic sensors to measure the magnitude, direction, and distribution of a force will enable a robotic hand to perform dexterous operations. Therefore, we develop a new type of finger-shaped haptic sensor using GelForce technology. GelForce is a vision-based sensor that can be used to measure the distribution of force vectors, or surface traction fields. The simple structure of the GelForce enables us to develop a compact finger-shaped GelForce for the robotic hand. GelForce that is developed on the basis of an elastic theory can be used to calculate surface traction fields using a conversion equation. However, this conversion equation cannot be analytically solved when the elastic body of the sensor has a complicated shape such as the shape of a finger. Therefore, we propose an observational method and construct a prototype of the finger-shaped GelForce. By using this prototype, we evaluate the basic performance of the finger-shaped GelForce. Then, we conduct a field test by performing grasping operations using a robotic hand. The results of this test show that using the observational method, the finger-shaped GelForce can be successfully used in a robotic hand.

Marangoni and Gibbs elasticity of flowing soap films

NASA Astrophysics Data System (ADS)

Kim, Ildoo; Sane, Aakash; Mandre, Shreyas

2017-11-01

A flowing soap film has two elasticities. Marangoni elasticity dynamically stabilizes the film from sudden disturbance, and Gibbs elasticity is an equilibrium property that influences the film's persistence over time. In our experimental investigation, we find that Marangoni elasticity is 22 mN/m independent of the film thickness. On the other hand, Gibbs elasticity depends both on the film thickness and the soap concentration. Interestingly, the soap film made of dilute soap solution has the greater Gibbs elasticity, which is not consistent to the existing theory. Such discrepancy is originated from the flowing nature of our soap films, in which surfactants are continuously replenished.

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.

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.

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.

Elastic moduli of a smectic membrane: a rod-level scaling analysis

NASA Astrophysics Data System (ADS)

Wensink, H. H.; Morales Anda, L.

2018-02-01

Chiral rodlike colloids exposed to strong depletion attraction may self-assemble into chiral membranes whose twisted director field differs from that of a 3D bulk chiral nematic. We formulate a simple microscopic variational theory to determine the elastic moduli of rods assembled into a bidimensional smectic membrane. The approach is based on a simple Onsager-Straley theory for a non-uniform director field that we apply to describe rod twist within the membrane. A microscopic approach enables a detailed estimate of the individual Frank elastic moduli (splay, twist and bend) as well as the twist penetration depth of the smectic membrane in relation to the rod density and shape. We find that the elastic moduli are distinctly different from those of a bulk nematic fluid, with the splay elasticity being much stronger and the curvature elasticity much weaker than for rods assembled in a three-dimensional nematic fluid. We argue that the use of the simplistic one-constant approximation in which all moduli are assumed to be of equal magnitude is not appropriate for modelling the structure-property relation of smectic membranes.

Seismic transmission operator reciprocity - II: impedance-operator symmetry via elastic lateral modes

NASA Astrophysics Data System (ADS)

Thomson, C. J.

2015-08-01

The properties of the overburden transmission response are of particular interest for the analysis of reflectivity illumination or blurring in seismic depth imaging. The first step to showing a transmission-operator reciprocity property is to identify the symmetry of the so-called displacement-to-traction operators. The latter are analogous to Dirichlet-to-Neumann operators and they may also be called impedance operators. Their symmetry is deduced here after development of a formal spectral or modal theory of lateral wavefunctions in a laterally heterogeneous generally anisotropic elastic medium. The elastic lateral modes are displacement-traction 6-vectors and they are built from two auxiliary 3-vector lateral-mode bases. These auxiliary modes arise from Hermitian and anti-Hermitian operators, so they have familiar properties such as orthogonality. There is no assumption of down/up symmetry of the elasticity tensor, but basic assumptions are made about the existence and completeness of the elastic modes. A point-symmetry property appears and plays a central role. The 6-vector elastic modes have a symplectic orthogonality property, which facilitates the development of modal expansions for 6-vector functions of the lateral coordinates when completeness is assumed. While the elastic modal theory is consistent with the laterally homogeneous case, numerical work would provide confidence that it is correct in general. An appendix contains an introductory overview of acoustic lateral modes that were studied by other authors, given from the perspective of this new work. A distinction is drawn between unit normalization of scalar auxiliary modes and a separate energy-flux normalization of 2-vector acoustic modes. Neither is crucial to the form of acoustic pressure-to-velocity or impedance operators. This statement carries over to the elastic case for the 3-vector auxiliary- and 6-vector elastic-mode normalizations. The modal theory is used to construct the kernel of the elastic displacement-to-traction or impedance operator. Symmetry properties of this operator are then deduced, which is the main goal of this paper. The implications of elastic impedance-operator symmetry and the symplectic property for the transmission and reflection responses of finite regions are described in a companion paper.

The Khachaturyan theory of elastic inclusions: Recollections and results

NASA Astrophysics Data System (ADS)

Morris, J. W.

2010-01-01

In keeping with the assignment, this paper has two parts. The first is a personal recollection of my interactions with Professor Armen Khachaturyan since he first visited Berkeley in the 1970s. The second part is a review of the Khachaturyan formulation of the theory of elastic inclusions, with emphasis on results found since his classic monograph on the Theory of Structural Transformations in Solids [Wiley, New York, 1983]. The focus here is on the shapes and habits of coherent inclusions. The basic theory is presented, briefly, to exhibit Khachaturyan's results for the strain and energy within a coherent inclusion and show that the elastic energy is minimal for a thin-plate morphology with a definite habit. The preferred habit of the thin-plate inclusion is then discussed and computed for inclusions with dyadic strain (including the dislocation loop) and coherent inclusions with orthorhombic or simpler symmetry. This is followed by a discussion of the evolution of precipitate shape during coarsening, including the theory of the spontaneous splitting of coarsening precipitates and the development of octahedral or tetrahedral shapes.

Out-of-plane electron transport in finite layer MoS2

NASA Astrophysics Data System (ADS)

Holzapfel, R.; Weber, J.; Lukashev, P. V.; Stollenwerk, A. J.

2018-05-01

Ballistic electron emission microscopy (BEEM) has been used to study the processes affecting electron transport along the [0001] direction of finite layer MoS2 flakes deposited onto the surface of Au/Si(001) Schottky diodes. Prominent features present in the differential spectra from the MoS2 flakes are consistent with the density of states of finite layer MoS2 calculated using density functional theory. The ability to observe the electronic structure of the MoS2 appears to be due to the relatively smooth density of states of Si in this energy range and a substantial amount of elastic or quasi-elastic scattering along the MoS2/Au/Si(001) path. Demonstration of these measurements using BEEM suggests that this technique could potentially be used to study electron transport through van der Waals heterostructures, with applications in a number of electronic devices.

Structure, Energetics, and Dynamics of Screw Dislocations in Even n-Alkane Crystals.

PubMed

Olson, Isabel A; Shtukenberg, Alexander G; Hakobyan, Gagik; Rohl, Andrew L; Raiteri, Paolo; Ward, Michael D; Kahr, Bart

2016-08-18

Spiral hillocks on n-alkane crystal surfaces were observed immediately after Frank recognized the importance of screw dislocations for crystal growth, yet their structures and energies in molecular crystals remain ill-defined. To illustrate the structural chemistry of screw dislocations that are responsible for plasticity in organic crystals and upon which the organic electronics and pharmaceutical industries depend, molecular dynamics was used to examine heterochiral dislocation pairs with Burgers vectors along [001] in n-hexane, n-octane, and n-decane crystals. The cores were anisotropic and elongated in the (110) slip plane, with significant local changes in molecular position, orientation, conformation, and energy. This detailed atomic level picture produced a distribution of strain consistent with linear elastic theory, giving confidence in the simulations. Dislocations with doubled Burgers vectors split into pairs with elementary displacements. These results suggest a pathway to understanding the mechanical properties and failure associated with elastic and plastic deformation in soft crystals.

Engineered unique elastic modes at a BaTiO 3/2x1-Ge(001) interface

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

Kumah, D. P.; Dogan, M.; Ngai, J. H.

Here, the strong interaction at an interface between a substrate and thin film leads to epitaxy and provides a means of inducing structural changes in the epitaxial film. These induced material phases often exhibit technologically relevant electronic, magnetic, and functional properties. The 2×1 surface of a Ge(001) substrate applies a unique type of epitaxial constraint on thin films of the perovskite oxide BaTiO 3 where a change in bonding and symmetry at the interface leads to a non-bulk-like crystal structure of the BaTiO 3. While the complex crystal structure is predicted using first-principles theory, it is further shown that themore » details of the structure are a consequence of hidden phases found in the bulk elastic response of the BaTiO 3 induced by the symmetry of forces exerted by the germanium substrate.« less

Engineered Unique Elastic Modes at a BaTiO 3 / ( 2 × 1 ) - Ge ( 001 ) Interface

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

Kumah, D. P.; Dogan, M.; Ngai, J. H.

The strong interaction at an interface between a substrate and thin film leads to epitaxy and provides a means of inducing structural changes in the epitaxial film. These induced material phases often exhibit technologically relevant electronic, magnetic, and functional properties. The 2×1 surface of a Ge(001) substrate applies a unique type of epitaxial constraint on thin films of the perovskite oxide BaTiO3 where a change in bonding and symmetry at the interface leads to a non-bulk-like crystal structure of the BaTiO3. While the complex crystal structure is predicted using first-principles theory, it is further shown that the details of themore » structure are a consequence of hidden phases found in the bulk elastic response of the BaTiO3 induced by the symmetry of forces exerted by the germanium substrate.« less

Engineered unique elastic modes at a BaTiO 3/2x1-Ge(001) interface

DOE PAGES

Kumah, D. P.; Dogan, M.; Ngai, J. H.; ...

2016-03-07

Here, the strong interaction at an interface between a substrate and thin film leads to epitaxy and provides a means of inducing structural changes in the epitaxial film. These induced material phases often exhibit technologically relevant electronic, magnetic, and functional properties. The 2×1 surface of a Ge(001) substrate applies a unique type of epitaxial constraint on thin films of the perovskite oxide BaTiO 3 where a change in bonding and symmetry at the interface leads to a non-bulk-like crystal structure of the BaTiO 3. While the complex crystal structure is predicted using first-principles theory, it is further shown that themore » details of the structure are a consequence of hidden phases found in the bulk elastic response of the BaTiO 3 induced by the symmetry of forces exerted by the germanium substrate.« less

Interface stresses in fiber-reinforced materials with regular fiber arrangements

NASA Astrophysics Data System (ADS)

Mueller, W. H.; Schmauder, S.

The theory of linear elasticity is used here to analyze the stresses inside and at the surface of fiber-reinforced composites. Plane strain, plane stress, and generalized plane strain are analyzed using the shell model and the BHE model and are numerically studied using finite element analysis. Interface stresses are shown to depend weakly on Poisson's ratio. For equal values of the ratio, generalized plane strain and plane strain results are identical. For small volume fractions up to 40 vol pct of fibers, the shell and the BHE models predict the interface stresses very well over a wide range of elastic mismatches and for different fiber arrangements. At higher volume fractions the stresses are influenced by interactions with neighboring fibers. Introducing an external pressure into the shell model allows the prediction of interface stresses in real composite with isolated or regularly arranged fibers.

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.

Holographic Phonons

NASA Astrophysics Data System (ADS)

Alberte, Lasma; Ammon, Martin; Jiménez-Alba, Amadeo; Baggioli, Matteo; Pujolàs, Oriol

2018-04-01

We present a class of holographic massive gravity models that realize a spontaneous breaking of translational symmetry—they exhibit transverse phonon modes whose speed relates to the elastic shear modulus according to elasticity theory. Massive gravity theories thus emerge as versatile and convenient theories to model generic types of translational symmetry breaking: explicit, spontaneous, and a mixture of both. The nature of the breaking is encoded in the radial dependence of the graviton mass. As an application of the model, we compute the temperature dependence of the shear modulus and find that it features a glasslike melting transition.

Influence of surface roughness and waviness on film thickness and pressure distribution in elastohydrodynamic contacts

NASA Technical Reports Server (NTRS)

Chow, L. S. H.; Cheng, H. S.

1976-01-01

The Christensen theory of a stochastic model for hydrodynamic lubrication of rough surfaces was extended to elastohydrodynamic lubrication between two rollers. Solutions for the reduced pressure at the entrance as a function of the ratio of the average nominal film thickness to the rms surface roughness, were obtained numerically. Results were obtained for purely transverse as well as purely longitudinal surface roughness for cases with or without slip. The reduced pressure was shown to decrease slightly by considering longitudinal surface roughness. The same approach was used to study the effect of surface roughness on lubrication between rigid rollers and lubrication of an infinitely wide slider bearing. Using the flow balance concept, the perturbed Reynolds equation, was derived and solved for the perturbed pressure distribution. In addition, Cheng's numerical scheme was modified to incorporate a single two-dimensional elastic asperity on the stationary surface. The perturbed pressures obtained by these three different models were compared.

Stress Related Surface Tension Effects in Hard Elastic Polymers.

DTIC Science & Technology

1982-08-19

tension 4, and viscosity and the ,_;.rain imposed csn the materials. Results indicate that these microfi-r! Slated polymers contain a substantia- surface...modulus, 2) large recoverability (up to 98%), 3) ’energetic’ elasticity, and 4) high porosity. This field was thoroughly reviewed by Cannon, McKenna, and...influenced ’N load bearing microfibrils, open to the environment. The stress sensitivity of hard elastic polymers to changes in environmental surface

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

NASA Technical Reports Server (NTRS)

Lakes, R.

1991-01-01

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

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.

Effects of long-range interactions on curvature energies of viral shells

NASA Astrophysics Data System (ADS)

Shojaei, Hamid R.; Božič, Anže Lošdorfer; Muthukumar, Murugappan; Podgornik, Rudolf

2016-05-01

We formulate a theory of the effects of long-range interactions on the surface tension and spontaneous curvature of proteinaceous shells based on the general Deryaguin-Landau-Verwey-Overbeek mesoscale approach to colloid stability. We derive the full renormalization formulas for the elastic properties of the shell and consider in detail the renormalization of the spontaneous curvature as a function of the corresponding Hamaker coefficient, inner and outer capsid charges, and bathing solution properties. The renormalized spontaneous curvature is found to be a nonmonotonic function of several parameters describing the system.

Mechanical and Thermophysical Properties of Cubic Rock-Salt AlN Under High Pressure

NASA Astrophysics Data System (ADS)

Lebga, Noudjoud; Daoud, Salah; Sun, Xiao-Wei; Bioud, Nadhira; Latreche, Abdelhakim

2018-03-01

Density functional theory, density functional perturbation theory, and the Debye model have been used to investigate the structural, elastic, sound velocity, and thermodynamic properties of AlN with cubic rock-salt structure under high pressure, yielding the equilibrium structural parameters, equation of state, and elastic constants of this interesting material. The isotropic shear modulus, Pugh ratio, and Poisson's ratio were also investigated carefully. In addition, the longitudinal, transverse, and average elastic wave velocities, phonon contribution to the thermal conductivity, and interesting thermodynamic properties were predicted and analyzed in detail. The results demonstrate that the behavior of the elastic wave velocities under increasing hydrostatic pressure explains the hardening of the corresponding phonons. Based on the elastic stability criteria under pressure, it is found that AlN with cubic rock-salt structure is mechanically stable, even at pressures up to 100 GPa. Analysis of the Pugh ratio and Poisson's ratio revealed that AlN with cubic rock-salt structure behaves in brittle manner.

Heterogeneous shear elasticity of glasses: the origin of the boson peak.

PubMed

Marruzzo, Alessia; Schirmacher, Walter; Fratalocchi, Andrea; Ruocco, Giancarlo

2013-01-01

The local elasticity of glasses is known to be inhomogeneous on a microscopic scale compared to that of crystalline materials. Their vibrational spectrum strongly deviates from that expected from Debye's elasticity theory: The density of states deviates from Debye's law, the sound velocity shows a negative dispersion in the boson-peak frequency regime and there is a strong increase of the sound attenuation near the boson-peak frequency. By comparing a mean-field theory of shear-elastic heterogeneity with a large-scale simulation of a soft-sphere glass we demonstrate that the observed anomalies in glasses are caused by elastic heterogeneity. By observing that the macroscopic bulk modulus is frequency independent we show that the boson-peak-related vibrational anomalies are predominantly due to the spatially fluctuating microscopic shear stresses. It is demonstrated that the boson-peak arises from the steep increase of the sound attenuation at a frequency which marks the transition from wave-like excitations to disorder-dominated ones.

Elasticity of microscale volumes of viscoelastic soft matter by cavitation rheometry

NASA Astrophysics Data System (ADS)

Pavlovsky, Leonid; Ganesan, Mahesh; Younger, John G.; Solomon, Michael J.

2014-09-01

Measurement of the elastic modulus of soft, viscoelastic liquids with cavitation rheometry is demonstrated for specimens as small as 1 μl by application of elasticity theory and experiments on semi-dilute polymer solutions. Cavitation rheometry is the extraction of the elastic modulus of a material, E, by measuring the pressure necessary to create a cavity within it [J. A. Zimberlin, N. Sanabria-DeLong, G. N. Tew, and A. J. Crosby, Soft Matter 3, 763-767 (2007)]. This paper extends cavitation rheometry in three ways. First, we show that viscoelastic samples can be approximated with the neo-Hookean model provided that the time scale of the cavity formation is measured. Second, we extend the cavitation rheometry method to accommodate cases in which the sample size is no longer large relative to the cavity dimension. Finally, we implement cavitation rheometry to show that the theory accurately measures the elastic modulus of viscoelastic samples with volumes ranging from 4 ml to as low as 1 μl.

Noncontact viscoelastic measurement of polymer thin films in a liquid medium using a long-needle AFM

NASA Astrophysics Data System (ADS)

Guan, Dongshi; Barraud, Chloe; Charlaix, Elisabeth; Tong, Penger

We report noncontact measurement of the viscoelastic property of polymer thin films in a liquid medium using frequency-modulation atomic force microscopy (FM-AFM) with a newly developed long-needle probe. The probe contains a long vertical glass fiber with one end adhered to a cantilever beam and the other end with a sharp tip placed near the liquid-film interface. The nanoscale flow generated by the resonant oscillation of the needle tip provides a precise hydrodynamic force acting on the soft surface of the thin film. By accurately measuring the mechanical response of the thin film, we obtain the elastic and loss moduli of the thin film using the linear response theory of elasto-hydrodynamics. The experiment verifies the theory and demonstrates its applications. The technique can be used to accurately measure the viscoelastic property of soft surfaces, such as those made of polymers, nano-bubbles, live cells and tissues. This work was supported by the Research Grants Council of Hong Kong SAR.

Shape design sensitivity analysis and optimization of three dimensional elastic solids using geometric modeling and automatic regridding. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Yao, Tse-Min; Choi, Kyung K.

1987-01-01

An automatic regridding method and a three dimensional shape design parameterization technique were constructed and integrated into a unified theory of shape design sensitivity analysis. An algorithm was developed for general shape design sensitivity analysis of three dimensional eleastic solids. Numerical implementation of this shape design sensitivity analysis method was carried out using the finite element code ANSYS. The unified theory of shape design sensitivity analysis uses the material derivative of continuum mechanics with a design velocity field that represents shape change effects over the structural design. Automatic regridding methods were developed by generating a domain velocity field with boundary displacement method. Shape design parameterization for three dimensional surface design problems was illustrated using a Bezier surface with boundary perturbations that depend linearly on the perturbation of design parameters. A linearization method of optimization, LINRM, was used to obtain optimum shapes. Three examples from different engineering disciplines were investigated to demonstrate the accuracy and versatility of this shape design sensitivity analysis method.

Fluid Mechanics of Capillary-Elastic Instabilities in Microgravity Environment

NASA Technical Reports Server (NTRS)

Grotberg, James B.

2002-01-01

The aim of this project is to investigate the closure and reopening of lung airways due to surface tension forces, coupled with airway elasticity. Airways are liquid-lined, flexible tubes and closure of airways can occur by a Rayleigh instability of the liquid lining, or an instability of the elastic support for the airway as the surface tension of the air-liquid interface pulls the tube shut, or both. Regardless of the mechanism, the airway is closed because the liquid lining has created a plug that prevents axial gas exchange. In the microgravity environment, surface tension forces dominate lung mechanics and would lead to more prevalent, and more uniformly distributed air-way closure, thereby creating a potential for respiratory problems for astronauts. Once closed the primary option for reopening an airway is by deep inspiration. This maneuver will pull the flexible airways open and force the liquid plug to flow distally by the incoming air stream. Airway reopening depends to a large extent on this plug flow and how it may lead to plug rupture to regain the continuity of gas between the environment and the alveoli. In addition to mathematical modeling of plug flows in liquid-lined, flexible tubes, this work has involved benchtop studies of propagating liquid plugs down tube networks that mimic the human airway tree. We have extended the work to involve animal models of liquid plug propagation in rat lungs. The liquid is radio-opaque and x-ray video imaging is used to ascertain the movement and distribution of the liquid plugs so that comparisons to theory may be made. This research has other uses, such as the delivery of liquids or drugs into the lung that may be used for surfactant replacement therapy or for liquid ventilation.

Assessing exchange-correlation functionals for elasticity and thermodynamics of α - ZrW 2 O 8 : A density functional perturbation theory study

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

Weck, Philippe F.; Kim, Eunja; Greathouse, Jeffery A.

Elastic and thermodynamic properties of negative thermal expansion (NTE) αα-ZrW2O8 have been calculated using PBEsol and PBE exchange-correlation functionals within the framework of density functional perturbation theory (DFPT). Measured elastic constants are reproduced within ~2% with PBEsol and 6% with PBE. The thermal evolution of the Grüneisen parameter computed within the quasi-harmonic approximation exhibits negative values below the Debye temperature, consistent with observation. The standard molar heat capacity is predicted to be Cmore » $$O\\atop{P}$$=192.2 and 193.8 J mol -1K -1 with PBEsol and PBE, respectively. These results suggest superior accuracy of DFPT/PBEsol for studying the lattice dynamics, elasticity and thermodynamics of NTE materials.« less

Assessing exchange-correlation functionals for elasticity and thermodynamics of α - ZrW 2 O 8 : A density functional perturbation theory study

DOE PAGES

Weck, Philippe F.; Kim, Eunja; Greathouse, Jeffery A.; ...

2018-03-15

Elastic and thermodynamic properties of negative thermal expansion (NTE) αα-ZrW2O8 have been calculated using PBEsol and PBE exchange-correlation functionals within the framework of density functional perturbation theory (DFPT). Measured elastic constants are reproduced within ~2% with PBEsol and 6% with PBE. The thermal evolution of the Grüneisen parameter computed within the quasi-harmonic approximation exhibits negative values below the Debye temperature, consistent with observation. The standard molar heat capacity is predicted to be Cmore » $$O\\atop{P}$$=192.2 and 193.8 J mol -1K -1 with PBEsol and PBE, respectively. These results suggest superior accuracy of DFPT/PBEsol for studying the lattice dynamics, elasticity and thermodynamics of NTE materials.« less

Elastic anomalies in Fe-Cr alloys

NASA Astrophysics Data System (ADS)

Zhang, Hualei; Wang, Guisheng; Punkkinen, Marko P. J.; Hertzman, Staffan; Johansson, Börje; Vitos, Levente

2013-05-01

Using ab initio alloy theory, we determine the elastic parameters of ferromagnetic and paramagnetic Fe1-cCrc (0 ≤ c ≤ 1) alloys in the body centered cubic crystallographic phase. Comparison with the experimental data demonstrates that the employed theoretical approach accurately describes the observed composition dependence of the polycrystalline elastic moduli. The predicted single-crystal elastic constants follow complex anomalous trends, which are shown to originate from the interplay between magnetic and chemical effects. The nonmonotonic composition dependence of the elastic parameters has marked implications on the micro-mechanical properties of ferrite stainless steels.

Modeling of a piezoelectric/piezomagnetic nano energy harvester based on two dimensional theory

NASA Astrophysics Data System (ADS)

Yan, Zhi

2018-01-01

This work presents a two dimensional theory for a piezoelectric/piezomagnetic bilayer nanoplate in coupled extensional and flexural vibrations with both flexoelectric and surface effects. The magneto-electro-elastic (MEE) coupling equations are derived from three-dimensional equations and Kirchhoff plate theory. Based on the developed theory, a piezoelectric/piezomagnetic nano energy harvester is proposed, which can generate electricity under time-harmonic applied magnetic field. The approximate solutions for the mechanical responses and voltage of the energy harvester are obtained using the weighted residual method. Results show that the properties of the proposed energy harvester are size-dependent due to the flexoelectric and surface effects, and such effects are more pronounced when the bilayer thickness is reduced to dozens of nanometers. It is also found that the magnetoelectric coupling coefficient and power density of the energy harvester are sensitive to the load resistance, the thickness fraction of the piezoelectric or the piezomagnetic layer and damping ratios. Moreover, results indicate that the flexoelectric effect could be made use to build a dielectric/piezomagnetic nano energy harvester. This work provides modeling techniques and numerical methods for investigating the size-dependent properties of MEE nanoplate-based energy harvester and could be helpful for designing nano energy harvesters using the principle of flexoelectricity.

A multiscale coupled finite-element and phase-field framework to modeling stressed grain growth in polycrystalline thin films

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

Jamshidian, M., E-mail: jamshidian@cc.iut.ac.ir; Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstrasse 15, 99423 Weimar; Thamburaja, P., E-mail: prakash.thamburaja@gmail.com

A previously-developed finite-deformation- and crystal-elasticity-based constitutive theory for stressed grain growth in cubic polycrystalline bodies has been augmented to include a description of excess surface energy and grain-growth stagnation mechanisms through the use of surface effect state variables in a thermodynamically-consistent manner. The constitutive theory was also implemented into a multiscale coupled finite-element and phase-field computational framework. With the material parameters in the constitutive theory suitably calibrated, our three-dimensional numerical simulations show that the constitutive model is able to accurately predict the experimentally-determined evolution of crystallographic texture and grain size statistics in polycrystalline copper thin films deposited on polyimide substratemore » and annealed at high-homologous temperatures. In particular, our numerical analyses show that the broad texture transition observed in the annealing experiments of polycrystalline thin films is caused by grain growth stagnation mechanisms. - Graphical abstract: - Highlights: • Developing a theory for stressed grain growth in polycrystalline thin films. • Implementation into a multiscale coupled finite-element and phase-field framework. • Quantitative reproduction of the experimental grain growth data by simulations. • Revealing the cause of texture transition to be due to the stagnation mechanisms.« less

Soliton-like defects in nematic liquid crystal thin layers

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

Chuvyrov, A. N.; Krekhov, A. P.; Lebedev, Yu. A., E-mail: lebedev@anrb.ru

The nonsingular soliton-like defects in plane nematic liquid crystal (NLC) layers and spherical NLC drops are experimentally detected and studied when the interaction of NLC molecules with a bounding surface is varied. The dynamics and the annihilation of nonsingular defects of opposite signs on a plane surface are investigated. Periodic transformations of the soliton-like defects in NLC drops in an electric field are detected. The theory of elasticity is used to show that the surface energy taken into account in the total free energy of NLC in the case of weak anchoring leads to the possibility of nonsingular solutions ofmore » a director equilibrium equation. The calculated pictures of director distribution in a plane NLC layer and in a spherical NLC drop characterized by weak surface anchoring agree well with the results of polarized light optical observations.« less

Segregation Phenomena on the Crystal Surface of Chemical Compounds

NASA Astrophysics Data System (ADS)

Tomashpol'skii, Yu. Ya.

2018-06-01

The current state of the theoretical and experimental studies of changes in the chemical structure and composition caused by segregation phenomena on the surface of chemical compounds was reviewed. The review considers the experimental data obtained exclusively on single crystals, which were studied by modern instrumental methods, including in situ Auger electron spectrometry, X-ray spectral microanalysis, high-resolution scanning and transmission electron microscopy, secondary electron emission, and atomic force microscopy. The models that suggest the crystal-chemical diffusion and liquid-phase mechanisms of segregation were described. The parameters of the theory include the type of chemical bond, elastic constants, and crystal-chemical characteristics of substances. The models make it possible to predict the nature of changes in the surface composition: segregation tendency, segregant type, and degree of nonstoichiometry. A new direction in surface segregation was considered, which is promising for nanoelectronics and emission electronics.

Elastic properties of spherically anisotropic piezoelectric composites

NASA Astrophysics Data System (ADS)

Wei, En-Bo; Gu, Guo-Qing; Poon, Ying-Ming

2010-09-01

Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezoelectric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed.

Bulk solitary waves in elastic solids

NASA Astrophysics Data System (ADS)

Samsonov, A. M.; Dreiden, G. V.; Semenova, I. V.; Shvartz, A. G.

2015-10-01

A short and object oriented conspectus of bulk solitary wave theory, numerical simulations and real experiments in condensed matter is given. Upon a brief description of the soliton history and development we focus on bulk solitary waves of strain, also known as waves of density and, sometimes, as elastic and/or acoustic solitons. We consider the problem of nonlinear bulk wave generation and detection in basic structural elements, rods, plates and shells, that are exhaustively studied and widely used in physics and engineering. However, it is mostly valid for linear elasticity, whereas dynamic nonlinear theory of these elements is still far from being completed. In order to show how the nonlinear waves can be used in various applications, we studied the solitary elastic wave propagation along lengthy wave guides, and remarkably small attenuation of elastic solitons was proven in physical experiments. Both theory and generation for strain soliton in a shell, however, remained unsolved problems until recently, and we consider in more details the nonlinear bulk wave propagation in a shell. We studied an axially symmetric deformation of an infinite nonlinearly elastic cylindrical shell without torsion. The problem for bulk longitudinal waves is shown to be reducible to the one equation, if a relation between transversal displacement and the longitudinal strain is found. It is found that both the 1+1D and even the 1+2D problems for long travelling waves in nonlinear solids can be reduced to the Weierstrass equation for elliptic functions, which provide the solitary wave solutions as appropriate limits. We show that the accuracy in the boundary conditions on free lateral surfaces is of crucial importance for solution, derive the only equation for longitudinal nonlinear strain wave and show, that the equation has, amongst others, a bidirectional solitary wave solution, which lead us to successful physical experiments. We observed first the compression solitary wave in the duct-like polymer shell and proved, that there is no tensile area behind the wave, the bulk soliton propagates on a distance many times longer than its wave length, while both its shape and amplitude remain unchanged. We demonstrated recently how the strain solitons can be used for non-destructive testing (NDT) of laminated composites, used nowadays for various applications, e.g., in microelectronics, aerospace and automotive industries, and bulk strain solitons are among prospective instruments for NDT. Being aimed to propose the bulk strain solitons as an instrument for NDT in solids, we studied numerically the evolution of them in various wave guides with local defects, and shown that the strain soliton undergoes changes in amplitude, phase shift and the shape, that are distinctive and can be estimated. To sum up, now we are able to propose a new NDT technique, based on bulk strain soliton propagation in structural elements.

Surface energy effect on nonlinear buckling and postbuckling behavior of functionally graded piezoelectric cylindrical nanoshells under lateral pressure

NASA Astrophysics Data System (ADS)

Fang, Xue-Qian; Zhu, Chang-Song; Liu, Jin-Xi; Zhao, Jing

2018-04-01

In this paper, the surface energy effect on the nonlinear buckling and postbuckling behavior of functionally graded piezoelectric (FGP) cylindrical nanoshells subjected to lateral pressure is studied based on the electro-elastic surface/interface theory together with von-Kármán-Donnell-type kinematics of nonlinearity. The total strain energy of the FGP nanoshell, including surface energy, is derived by considering the constitutive formulations of surface phase. The principle of minimum potential energy is utilized to establish the nonlinear governing differential equations, and the singular perturbation technique is employed to obtain the asymptotic solutions. Then, two sets of comparison are conducted to validate the present work, and some numerical examples are given to study the effects of surface parameters, power law index and aspect ratio on the buckling and postbuckling behavior of FGP nanoshells. The results show that the critical buckling load and postbuckling path of FGP nanoshell are significantly size-dependent.

Shaping through buckling in elastic gridshells: from camping tents to architectural roofs

NASA Astrophysics Data System (ADS)

Reis, Pedro

Elastic gridshells comprise an initially planar network of elastic rods that is actuated into a 3D shell-like structure by loading its extremities. This shaping results from elastic buckling and the subsequent geometrically nonlinear deformation of the grid structure. Architectural elastic gridshells first appeared in the 1970's. However, to date, only a limited number of examples have been constructed around the world, primarily due to the challenges involved in their structural design. Yet, elastic gridshells are highly appealing: they can cover wide spans with low self-weight, they allow for aesthetically pleasing shapes and their construction is typically simple and rapid. We study the mechanics of elastic gridshells by combining precision model experiments that explore their scale invariance, together with computer simulations that employ the Discrete Elastic Rods method. Excellent agreement is found between the two. Upon validation, the numerics are then used to systematically explore parameter space and identify general design principles for specific target final shapes. Our findings are rationalized using the theory of discrete Chebyshev nets, together with the group theory for crystals. Higher buckling modes occur for some configurations due to geometric incompatibility at the boundary and result in symmetry breaking. Along with the systematic classification of the various possible modes of deformation, we provide a reduced model that rationalizes form-finding in elastic gridshells. This work was done in collaboration with Changyeob Baek, Khalid Jawed and Andrew Sageman-Furnas. We are grateful to the NSF for funding (CAREER, CMMI-1351449).

First-principles calculations for elastic properties of OsB 2 under pressure

NASA Astrophysics Data System (ADS)

Yang, Jun-Wei; Chen, Xiang-Rong; Luo, Fen; Ji, Guang-Fu

2009-11-01

The structure, elastic properties and elastic anisotropy of orthorhombic OsB 2 are investigated by density functional theory method with the ultrasoft pseudopotential scheme in the frame of the generalized gradient approximation (GGA) as well as local density approximation (LDA). The obtained structural parameters, elastic constants, elastic anisotropy and Debye temperature for OsB 2 under pressure are consistent with the available experimental data and other theoretical results. It is found that the elastic constants, bulk modulus and Debye temperature of OsB 2 tend to increase with increasing pressure. It is predicted that OsB 2 is not a superhard material from our calculations.

Nano and micro mechanical properties of uncross-linked and cross-linked chitosan films

PubMed Central

Aryaei, Ashkan; Jayatissa, Ahalapitiya H.; Jayasuriya, A. Champa

2016-01-01

The aim of this study is to determine the nano and micro mechanical properties for uncross-linked and cross-linked chitosan films. Specifically, we looked at nanoindentation hardness, microhardness, and elastic modulus. It is important to study the nano and microscale mechanical properties of chitosan since chitosan has been widely used for biomedical applications. Using the solvent-cast method, the chitosan films were prepared at room temperature on the cleaned glass plates. The chitosan solution was prepared by dissolving chitosan in acetic acid 1% (v/v). Tripolyphosphate (TPP) was used to create the cross-links between amine groups in chitosan and phosphate groups in TPP. In this study, atomic force microscopy was used to measure the nanoindentation hardness and surface topography of the uncross-linked and cross-linked chitosan films. Elastic modulus was then calculated from the nanoindentation results. The effective elastic modulus was determined by microhardness with some modifications to previous theories. The microhardness of the chitosan films were measured using Vicker’s hardness meter under three different loads. Our results show that the microhardness and elastic modulus for cross-linked chitosan films are higher than the uncross-linked films. However, the cross-linked chitosan films show increased brittleness when compared to uncross-linked films. By increasing the load magnitude, the microhardness increases for both uncross-linked and cross-linked chitosan films. PMID:22100082

Deformation of compound shells under action of internal shock wave loading

NASA Astrophysics Data System (ADS)

Chernobryvko, Marina; Kruszka, Leopold; Avramov, Konstantin

2015-09-01

The compound shells under the action of internal shock wave loading are considered. The compound shell consists of a thin cylindrical shell and two thin parabolic shells at the edges. The boundary conditions in the shells joints satisfy the equality of displacements. The internal shock wave loading is modelled as the surplus pressure surface. This pressure is a function of the shell coordinates and time. The strain rate deformation of compound shell takes place in both the elastic and in plastic stages. In the elastic stage the equations of the structure motions are obtained by the assumed-modes method, which uses the kinetic and potential energies of the cylindrical and two parabolic shells. The dynamic behaviour of compound shells is treated. In local plastic zones the 3-D thermo-elastic-plastic model is used. The deformations are described by nonlinear model. The stress tensor elements are determined using dynamic deformation theory. The deformation properties of materials are influenced by the strain rate behaviour, the influence of temperature parameters, and the elastic-plastic properties of materials. The dynamic yield point of materials and Pisarenko-Lebedev's criterion of destruction are used. The modified adaptive finite differences method of numerical analysis is suggested for those simulations. The accuracy of the numerical simulation is verified on each temporal step of calculation and in the case of large deformation gradients.

The role of surface elasticity in liquid film formation

NASA Astrophysics Data System (ADS)

Champougny, Lorene; Scheid, Benoit; Restagno, Frederic; Rio, Emmanuelle; Laboratoire de Physique des Solides Team; TIPS-Fluid Physics Unit Team

2014-11-01

The formation of thin liquid films, either free standing (soap films) or deposited on a solid substrate (coated films), is of utmost importance for many applications, ranging from the control of foam stability to surface functionalization. In this work, the behavior of thin liquid films during their generation from a surfactant solution is investigated through comparison between a hydrodynamic model including surface elasticity and experiments. ``Twin'' models are proposed to describe the coating of films onto a solid plate (Landau-Levich-Derjaguin configuration) as well as soap film pulling (Frankel configuration) in a single framework. Experimental data are successfully fitted using the models, surface elasticity being the only adjustable parameter. For a given surfactant solution, the analyses of soap and coated films both yield the same value for the effective surface elasticity, showing that it is an intrinsic parameter of a surfactant solution. Conversely, we demonstrate that Frankel- or Landau-Levich-like experiments can be used in practice as surface rheometers to determine the numerical value of the (effective) surface elasticity of a solution, especially for values lower than those measurable by classical devices. L.C. was supported by ANR F2F. B.S. thanks the F.R.S.-FNRS for funding as well as the IAP-MicroMAST project.

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.

Stable elastic knots with no self-contact

NASA Astrophysics Data System (ADS)

Moulton, Derek E.; Grandgeorge, Paul; Neukirch, Sébastien

2018-07-01

We study an elastic rod bent into an open trefoil knot and clamped at both ends. The question we consider is whether there are stable configurations for which there are no points of self-contact. This idea can be fairly easily replicated with a thin strip of paper, but is more difficult or even impossible with a flexible wire. We search for such configurations within the space of three tuning parameters related to the degrees of freedom in a simple experiment. Mathematically, we show, both within standard Kirchhoff theory as well within an elastic strip theory, that stable and contact-free knotted configurations can be found, and we classify the corresponding parametric regions. Numerical results are complemented with an asymptotic analysis that demonstrates the presence of knots near the doubly-covered ring. In the case of the strip model, quantitative experiments of the region of good knots are also provided to validate the theory.

Proton behaviour, structure and elasticity of serpentine at high-pressure

NASA Astrophysics Data System (ADS)

Mookherjee, Mainak; Stixrude, Lars

2007-03-01

Serpentine occurs in oceanic crust as the alteration product of ultramafic rocks and is a possible candidate for carrying water to the deep earth. The presence of sub-surface serpentine may be manifested by mud volcanoes, high electrical conductivities, and seismic anomalies. Using density functional theory, we predict a phase transition in serpentine near 22 GPa. The phase transition is caused by a re-orientation of the hydroxyl vector coupled with changes in the di-trigonal rings of SiO4 tetrahedra. The symmetry of the crystal-structure remains unaffected. Evidence of pressure-induced hydrogen bonding is absent in serpentine, as evident from the reduction of O-H bond length upon compression. Results of compression for the low-pressure phase is well represented by a fourth order Birch-Murnaghan finite strain expression with KO= 63 GPa, K'O= 10.2 and KOK''O = -120, where K is the bulk modulus, prime indicates pressure derivatives, and O refers to zero pressure. At low pressures, the elastic constant tensor is highly anisotropic with C11^o ˜2.4xC33^o , and becomes more isotropic with compression. We find an elastic instability near 36 GPa that may be related to experimentally observed amorphization.

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.

Solvated dissipative electro-elastic network model of hydrated proteins

NASA Astrophysics Data System (ADS)

Martin, Daniel

2013-03-01

Elastic network models coarse grain proteins into a network of residue beads connected by springs. We add dissipative dynamics to this mechanical system by applying overdamped Langevin equations of motion to normal-mode vibrations of the network. In addition, the network is made heterogeneous and softened at the protein surface by accounting for hydration of the ionized residues. Solvation changes the network Hessian in two ways. Diagonal solvation terms soften the spring constants and off-diagonal dipole-dipole terms correlate displacements of the ionized residues. The model is used to formulate the response functions of the electrostatic potential and electric field appearing in theories of redox reactions and spectroscopy. We also formulate the dielectric response of the protein and find that solvation of the surface ionized residues leads to a slow relaxation peak in the dielectric loss spectrum, about two orders of magnitude slower than the main peak of protein relaxation. Finally, the solvated network is used to formulate the allosteric response of the protein to ion binding. The global thermodynamics of ion binding is not strongly affected by the network solvation, but it dramatically enhances conformational changes in response to placing a charge at the a the active site.

Solvated dissipative electro-elastic network model of hydrated proteins

NASA Astrophysics Data System (ADS)

Martin, Daniel R.; Matyushov, Dmitry V.

2012-10-01

Elastic network models coarse grain proteins into a network of residue beads connected by springs. We add dissipative dynamics to this mechanical system by applying overdamped Langevin equations of motion to normal-mode vibrations of the network. In addition, the network is made heterogeneous and softened at the protein surface by accounting for hydration of the ionized residues. Solvation changes the network Hessian in two ways. Diagonal solvation terms soften the spring constants and off-diagonal dipole-dipole terms correlate displacements of the ionized residues. The model is used to formulate the response functions of the electrostatic potential and electric field appearing in theories of redox reactions and spectroscopy. We also formulate the dielectric response of the protein and find that solvation of the surface ionized residues leads to a slow relaxation peak in the dielectric loss spectrum, about two orders of magnitude slower than the main peak of protein relaxation. Finally, the solvated network is used to formulate the allosteric response of the protein to ion binding. The global thermodynamics of ion binding is not strongly affected by the network solvation, but it dramatically enhances conformational changes in response to placing a charge at the active site of the protein.

Scalar model for frictional precursors dynamics

PubMed Central

Taloni, Alessandro; Benassi, Andrea; Sandfeld, Stefan; Zapperi, Stefano

2015-01-01

Recent experiments indicate that frictional sliding occurs by nucleation of detachment fronts at the contact interface that may appear well before the onset of global sliding. This intriguing precursory activity is not accounted for by traditional friction theories but is extremely important for friction dominated geophysical phenomena as earthquakes, landslides or avalanches. Here we simulate the onset of slip of a three dimensional elastic body resting on a surface and show that experimentally observed frictional precursors depend in a complex non-universal way on the sample geometry and loading conditions. Our model satisfies Archard's law and Amontons' first and second laws, reproducing with remarkable precision the real contact area dynamics, the precursors' envelope dynamics prior to sliding, and the normal and shear internal stress distributions close to the interfacial surface. Moreover, it allows to assess which features can be attributed to the elastic equilibrium, and which are attributed to the out-of-equilibrium dynamics, suggesting that precursory activity is an intrinsically quasi-static physical process. A direct calculation of the evolution of the Coulomb stress before and during precursors nucleation shows large variations across the sample, explaining why earthquake forecasting methods based only on accumulated slip and Coulomb stress monitoring are often ineffective. PMID:25640079

Scalar model for frictional precursors dynamics.

PubMed

Taloni, Alessandro; Benassi, Andrea; Sandfeld, Stefan; Zapperi, Stefano

2015-02-02

Recent experiments indicate that frictional sliding occurs by nucleation of detachment fronts at the contact interface that may appear well before the onset of global sliding. This intriguing precursory activity is not accounted for by traditional friction theories but is extremely important for friction dominated geophysical phenomena as earthquakes, landslides or avalanches. Here we simulate the onset of slip of a three dimensional elastic body resting on a surface and show that experimentally observed frictional precursors depend in a complex non-universal way on the sample geometry and loading conditions. Our model satisfies Archard's law and Amontons' first and second laws, reproducing with remarkable precision the real contact area dynamics, the precursors' envelope dynamics prior to sliding, and the normal and shear internal stress distributions close to the interfacial surface. Moreover, it allows to assess which features can be attributed to the elastic equilibrium, and which are attributed to the out-of-equilibrium dynamics, suggesting that precursory activity is an intrinsically quasi-static physical process. A direct calculation of the evolution of the Coulomb stress before and during precursors nucleation shows large variations across the sample, explaining why earthquake forecasting methods based only on accumulated slip and Coulomb stress monitoring are often ineffective.

First-principles study of molecular NO dissociation on Ir(100) surface

NASA Astrophysics Data System (ADS)

Erikat, I. A.; Hamad, B. A.; Khalifeh, J. M.

2014-02-01

The dissociation of NO on Ir(100) surface is investigated using density functional theory (DFT). The pathway and transition state (TS) of the dissociation of NO molecule are determined using climbing image nudge elastic band (CI-NEB). The prerequisite state of NO dissociation is determining the most stable sites of the reactant and products. We found that the most energetically stable sites are the hollow for N atom and the bridge for NO molecule as well as O atom. We found that the bending of NO is the first step of the dissociation reaction due to the increase of the back-donation from the d-band of Ir to 2 π ∗ orbital of NO, which causes the weakening of NO bond. The dissociation energy barrier of NO molecule on Ir(100) surface is 0.49 eV.

Estimation of critical thickness of Stranski-Krastanow transition in GeSi/Sn/Si system

NASA Astrophysics Data System (ADS)

Lozovoy, K. A.; Pishchagin, A. A.; Kokhanenko, A. P.; Voitsekhovskii, A. V.

2017-11-01

In this paper Stranski-Krastanow growth of Ge x Si1-x epitaxial layers on the Si(001) surface with pre-deposited tin layer with the thickness less than 1 ML is considered. For the calculations of critical thickness of transition from 2D to 3D growth in this paper a theoretical model based on general nucleation theory is used. This model is specified by taking into account dependencies of elastic modulus, lattices mismatch and surface energy of side facet on the composition x, as well as change in the adatoms diffusion coefficient and surface energy of the substrate in the presence of tin. As a result, dependencies of critical thickness of Stranski-Krastanow transition on compositon x and temperature are obtained. The simulated results are in a good agreement with experimentally observed results.

On residual stresses and homeostasis: an elastic theory of functional adaptation in living matter.

PubMed

Ciarletta, P; Destrade, M; Gower, A L

2016-04-26

Living matter can functionally adapt to external physical factors by developing internal tensions, easily revealed by cutting experiments. Nonetheless, residual stresses intrinsically have a complex spatial distribution, and destructive techniques cannot be used to identify a natural stress-free configuration. This work proposes a novel elastic theory of pre-stressed materials. Imposing physical compatibility and symmetry arguments, we define a new class of free energies explicitly depending on the internal stresses. This theory is finally applied to the study of arterial remodelling, proving its potential for the non-destructive determination of the residual tensions within biological materials.

Theory of fiber reinforced materials

NASA Technical Reports Server (NTRS)

Hashin, Z.

1972-01-01

A unified and rational treatment of the theory of fiber reinforced composite materials is presented. Fundamental geometric and elasticity considerations are throughly covered, and detailed derivations of the effective elastic moduli for these materials are presented. Biaxially reinforced materials which take the form of laminates are then discussed. Based on the fundamentals presented in the first portion of this volume, the theory of fiber-reinforced composite materials is extended to include viscoelastic and thermoelastic properties. Thermal and electrical conduction, electrostatics and magnetostatics behavior of these materials are discussed. Finally, a brief statement of the very difficult subject of physical strength is included.

Fractonic line excitations: An inroad from three-dimensional elasticity theory

NASA Astrophysics Data System (ADS)

Pai, Shriya; Pretko, Michael

2018-06-01

We demonstrate the existence of a fundamentally new type of excitation, fractonic lines, which are linelike excitations with the restricted mobility properties of fractons. These excitations, described using an amalgamation of higher-form gauge theories with symmetric tensor gauge theories, see direct physical realization as the topological lattice defects of ordinary three-dimensional quantum crystals. Starting with the more familiar elasticity theory, we show how theory maps onto a rank-4 tensor gauge theory, with phonons corresponding to gapless gauge modes and disclination defects corresponding to linelike charges. We derive flux conservation laws which lock these linelike excitations in place, analogous to the higher moment charge conservation laws of fracton theories. This way of encoding mobility restrictions of lattice defects could shed light on melting transitions in three dimensions. This new type of extended object may also be a useful tool in the search for improved quantum error-correcting codes in three dimensions.

The dielectric function of weakly ionized dusty plasmas

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

Li, Hui; China Research Institute of Radio wave Propagation; Wu, Jian

2016-07-15

Using classical Boltzmann kinetic theory, the dielectric function of weakly ionized unmagnetized dusty plasma is derived. The elastic Coulomb collision and inelastic charging collision of electrons with charged dust particle as well as charge variation on dust surface are taken into account. The theoretical result is applied to analyze the propagation of electromagnetic wave in a dusty plasma. It is demonstrated that the additional collision mechanism provided by charged dust particle can significantly increase the absorbed power of electromagnetic wave. These increases are mainly determined by the dust radius, density, and the charge numbers on the dust surface. The obtainedmore » results will support an enhanced understanding of the wave propagation processes in space and laboratory dusty plasmas.« less

On computing the geoelastic response to a disk load

NASA Astrophysics Data System (ADS)

Bevis, M.; Melini, D.; Spada, G.

2016-06-01

We review the theory of the Earth's elastic and gravitational response to a surface disk load. The solutions for displacement of the surface and the geoid are developed using expansions of Legendre polynomials, their derivatives and the load Love numbers. We provide a MATLAB function called diskload that computes the solutions for both uncompensated and compensated disk loads. In order to numerically implement the Legendre expansions, it is necessary to choose a harmonic degree, nmax, at which to truncate the series used to construct the solutions. We present a rule of thumb (ROT) for choosing an appropriate value of nmax, describe the consequences of truncating the expansions prematurely and provide a means to judiciously violate the ROT when that becomes a practical necessity.

Two modes of grain boundary pinning by coherent precipitates

DOE PAGES

Wang, Nan; Ji, Yanzhou; Wang, Yongbiao; ...

2017-06-18

Here, we propose a two-mechanism theory to estimate the pinning effect of coherent precipitates on grain-boundary (GB) migration in grain growth, taking into account the important effect of elastic misfit strain at the coherent interface. Depending on the relative importance of the elastic and the GB contributions to the total free energy, Zener type stabilization or a novel elastic energy induced stabilization may occur. It is found that the pinning is most effective in the crossover region between these two mechanisms. Finally, a phase-field-crystal model is used to numerically validate the theory. Relevant experiments and potential impacts on alloy designmore » are also discussed.« less

Elastic Heterogeneity in Metallic Glasses

NASA Astrophysics Data System (ADS)

Dmowski, W.; Iwashita, T.; Chuang, C.-P.; Almer, J.; Egami, T.

2010-11-01

When a stress is applied on a metallic glass it deforms following Hook’s law. Therefore it may appear obvious that a metallic glass deforms elastically. Using x-ray diffraction and anisotropic pair-density function analysis we show that only about (3)/(4) in volume fraction of metallic glasses deforms elastically, whereas the rest of the volume is anelastic and in the experimental time scale deform without resistance. We suggest that this anelastic portion represents residual liquidity in the glassy state. Many theories, such as the free-volume theory, assume the density of defects in the glassy state to be of the order of 1%, but this result shows that it is as much as a quarter.

Validity of Binary Collision Theory in Ion-Surface Interactions at 50-500 eV

NASA Astrophysics Data System (ADS)

Gordon, Michael; Giapis, Kostas

2003-10-01

Ion-surface interactions in the 50-500 eV regime have become increasingly important in plasma processing. Concerns exist in literature about the validity of the binary collision approximation (BCA) at low impact energies because peculiarities are frequently seen in the scattered ion energy distribution. Sub-surface processes, multiple bouncing, and super-elastic phenomena have all been hypothesized. This talk will explore the usefulness of BCA theory in predicting energy transfer during ion-surface collisions in the 50-500 eV energy range. Well-defined beams of rare gas ions (Ne, Ar, Kr) were scattered off semiconductor (Si, Ge) and metal surfaces (Ag, Au, Ni, Nb) to measure energy loss upon impact. The ion beams were produced from a floating ICP reactor coupled to a small accelerator beamline for transport and mass filtering. Exit channel energies were measured using a 90 gegree electrostatic sector coupled to a quadrupole mass filter with single ion detection capability. Although the BCA presents an over-simplified picture of the collision process, our results demonstrate that it is remarkably accurate in the low energy range for a variety of projectile-target combinations. In addition, reactive ion scattering of O2+ and O+ on inert and reactive surfaces (Au vs. Ag, Pt) suggests there may be rather high energy threshold processes which determine exit channel selectivity.

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

PubMed

Bevzenko, Dmytro; Lubchenko, Vassiliy

2014-11-07

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

Equivalence between short-time biphasic and incompressible elastic material responses.

PubMed

Ateshian, Gerard A; Ellis, Benjamin J; Weiss, Jeffrey A

2007-06-01

Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response deltat

Solution of the Eshelby problem in gradient elasticity for multilayer spherical inclusions

NASA Astrophysics Data System (ADS)

Volkov-Bogorodskii, D. B.; Lurie, S. A.

2016-03-01

We consider gradient models of elasticity which permit taking into account the characteristic scale parameters of the material. We prove the Papkovich-Neuber theorems, which determine the general form of the gradient solution and the structure of scale effects. We derive the Eshelby integral formula for the gradient moduli of elasticity, which plays the role of the closing equation in the self-consistent three-phase method. In the gradient theory of deformations, we consider the fundamental Eshelby-Christensen problem of determining the effective elastic properties of dispersed composites with spherical inclusions; the exact solution of this problem for classical models was obtained in 1976. This paper is the first to present the exact analytical solution of the Eshelby-Christensen problem for the gradient theory, which permits estimating the influence of scale effects on the stress state and the effective properties of the dispersed composites under study.We also analyze the influence of scale factors.

Biot-Gassmann theory for velocities of gas hydrate-bearing sediments

USGS Publications Warehouse

Lee, M.W.

2002-01-01

Elevated elastic velocities are a distinct physical property of gas hydrate-bearing sediments. A number of velocity models and equations (e.g., pore-filling model, cementation model, effective medium theories, weighted equations, and time-average equations) have been used to describe this effect. In particular, the weighted equation and effective medium theory predict reasonably well the elastic properties of unconsolidated gas hydrate-bearing sediments. A weakness of the weighted equation is its use of the empirical relationship of the time-average equation as one element of the equation. One drawback of the effective medium theory is its prediction of unreasonably higher shear-wave velocity at high porosities, so that the predicted velocity ratio does not agree well with the observed velocity ratio. To overcome these weaknesses, a method is proposed, based on Biot-Gassmann theories and assuming the formation velocity ratio (shear to compressional velocity) of an unconsolidated sediment is related to the velocity ratio of the matrix material of the formation and its porosity. Using the Biot coefficient calculated from either the weighted equation or from the effective medium theory, the proposed method accurately predicts the elastic properties of unconsolidated sediments with or without gas hydrate concentration. This method was applied to the observed velocities at the Mallik 2L-39 well, Mackenzie Delta, Canada.

Bending analysis of embedded nanoplates based on the integral formulation of Eringen's nonlocal theory using the finite element method

NASA Astrophysics Data System (ADS)

Ansari, R.; Torabi, J.; Norouzzadeh, A.

2018-04-01

Due to the capability of Eringen's nonlocal elasticity theory to capture the small length scale effect, it is widely used to study the mechanical behaviors of nanostructures. Previous studies have indicated that in some cases, the differential form of this theory cannot correctly predict the behavior of structure, and the integral form should be employed to avoid obtaining inconsistent results. The present study deals with the bending analysis of nanoplates resting on elastic foundation based on the integral formulation of Eringen's nonlocal theory. Since the formulation is presented in a general form, arbitrary kernel functions can be used. The first order shear deformation plate theory is considered to model the nanoplates, and the governing equations for both integral and differential forms are presented. Finally, the finite element method is applied to solve the problem. Selected results are given to investigate the effects of elastic foundation and to compare the predictions of integral nonlocal model with those of its differential nonlocal and local counterparts. It is found that by the use of proposed integral formulation of Eringen's nonlocal model, the paradox observed for the cantilever nanoplate is resolved.

Selective scanning tunnelling microscope electron-induced reactions of single biphenyl molecules on a Si(100) surface.

PubMed

Riedel, Damien; Bocquet, Marie-Laure; Lesnard, Hervé; Lastapis, Mathieu; Lorente, Nicolas; Sonnet, Philippe; Dujardin, Gérald

2009-06-03

Selective electron-induced reactions of individual biphenyl molecules adsorbed in their weakly chemisorbed configuration on a Si(100) surface are investigated by using the tip of a low-temperature (5 K) scanning tunnelling microscope (STM) as an atomic size source of electrons. Selected types of molecular reactions are produced, depending on the polarity of the surface voltage during STM excitation. At negative surface voltages, the biphenyl molecule diffuses across the surface in its weakly chemisorbed configuration. At positive surface voltages, different types of molecular reactions are activated, which involve the change of adsorption configuration from the weakly chemisorbed to the strongly chemisorbed bistable and quadristable configurations. Calculated reaction pathways of the molecular reactions on the silicon surface, using the nudge elastic band method, provide evidence that the observed selectivity as a function of the surface voltage polarity cannot be ascribed to different activation energies. These results, together with the measured threshold surface voltages and the calculated molecular electronic structures via density functional theory, suggest that the electron-induced molecular reactions are driven by selective electron detachment (oxidation) or attachment (reduction) processes.

Theory of nonlinear elasticity, stress-induced relaxation, and dynamic yielding in dense fluids of hard nonspherical colloids

NASA Astrophysics Data System (ADS)

Zhang, Rui; Schweizer, Kenneth S.

2012-04-01

We generalize the microscopic naïve mode coupling and nonlinear Langevin equation theories of the coupled translation-rotation dynamics of dense suspensions of uniaxial colloids to treat the effect of applied stress on shear elasticity, cooperative cage escape, structural relaxation, and dynamic and static yielding. The key concept is a stress-dependent dynamic free energy surface that quantifies the center-of-mass force and torque on a moving colloid. The consequences of variable particle aspect ratio and volume fraction, and the role of plastic versus double glasses, are established in the context of dense, glass-forming suspensions of hard-core dicolloids. For low aspect ratios, the theory provides a microscopic basis for the recently observed phenomenon of double yielding as a consequence of stress-driven sequential unlocking of caging constraints via reduction of the distinct entropic barriers associated with the rotational and translational degrees of freedom. The existence, and breadth in volume fraction, of the double yielding phenomena is predicted to generally depend on both the degree of particle anisotropy and experimental probing frequency, and as a consequence typically occurs only over a window of (high) volume fractions where there is strong decoupling of rotational and translational activated relaxation. At high enough concentrations, a return to single yielding is predicted. For large aspect ratio dicolloids, rotation and translation are always strongly coupled in the activated barrier hopping event, and hence for all stresses only a single yielding process is predicted.

Coseismic Gravity and Displacement Signatures Induced by the 2013 Okhotsk Mw8.3 Earthquake

PubMed Central

Zhang, Guoqing; Shen, Wenbin; Xu, Changyi; Zhu, Yiqing

2016-01-01

In this study, Gravity Recovery and Climate Experiment (GRACE) RL05 data from January 2003 to October 2014 were used to extract the coseismic gravity changes induced by the 24 May 2013 Okhotsk Mw8.3 deep-focus earthquake using the difference and least square fitting methods. The gravity changes obtained from GRACE data agreed well with those from dislocation theory in both magnitude and spatial pattern. Positive and negative gravity changes appeared on both sides of the epicenter. The positive signature appeared on the western side, and the peak value was approximately 0.4 microgal (1 microgal = 10−8 m/s2), whereas on the eastern side, the gravity signature was negative, and the peak value was approximately −1.1 microgal. It demonstrates that deep-focus earthquakes Mw ≤ 8.5 are detectable by GRACE observations. Moreover, the coseismic displacements of 20 Global Positioning System (GPS) stations on the Earth’s surface were simulated using an elastic dislocation theory in a spherical earth model, and the results are consistent with the GPS results, especially the near-field results. We also estimated the gravity contributions from the coseismic vertical displacements and density changes, analyzed the proportion of these two gravity change factors (based on an elastic dislocation theory in a spherical earth model) in this deep-focus earthquake. The gravity effect from vertical displacement is four times larger than that caused by density redistribution. PMID:27598158

Deformation of Reservoir Sandstones by Elastic versus Inelastic Deformation Mechanisms

NASA Astrophysics Data System (ADS)

Pijnenburg, R.; Verberne, B. A.; Hangx, S.; Spiers, C. J.

2016-12-01

Hydrocarbon or groundwater production from sandstone reservoirs can result in surface subsidence and induced seismicity. Subsidence results from combined elastic and inelastic compaction of the reservoir due to a change in the effective stress state upon fluid extraction. The magnitude of elastic compaction can be accurately described using poroelasticity theory. However inelastic or time-dependent compaction is poorly constrained. Specifically, the underlying microphysical processes controlling sandstone compaction remain poorly understood. We use sandstones recovered by the field operator (NAM) from the Slochteren gas reservoir (Groningen, NE Netherlands) to study the importance of elastic versus inelastic deformation processes upon simulated pore pressure depletion. We conducted conventional triaxial tests under true in-situ conditions of pressure and temperature. To investigate the effect of applied differential stress (σ1 - σ3 = 0 - 50 MPa) and initial sample porosity (φi = 12 - 24%) on instantaneous and time-dependent inelastic deformation, we imposed multiple stages of axial loading and relaxation. The results show that inelastic strain develops at all stages of loading, and that its magnitude increases with increasing value of differential stress and initial porosity. The stress sensitivity of the axial creep strain rate and microstructural evidence suggest that inelastic compaction is controlled by a combination of intergranular slip and intragranular cracking. Intragranular cracking is shown to be more pervasive with increasing values of initial porosity. The results are consistent with a conceptual microphysical model, involving deformation by poro-elasticity combined with intergranular sliding and grain contact failure. This model aims to predict sandstone deformation behavior for a wide range of stress conditions.

University of Maryland MRSEC - Research

Science.gov Websites

-2012 Seed 3: Modeling Elastic Effects on Crystal Surfaces (Leader: Dionisios Margetis) 2009-2012 Seed 4 Rubloff & Sang Bok Lee) 2007-2009 Seed 3: Modeling Elastic Effects on Crystal Surfaces (Leader

High-temperature elastic properties of a nickel-based superalloy studied by surface Brillouin scattering

NASA Astrophysics Data System (ADS)

Zhang, X.; Stoddart, P. R.; Comins, J. D.; Every, A. G.

2001-03-01

Surface Brillouin scattering (SBS) has been used to study the thermally induced surface vibrations (phonons) and thereby obtain the elastic properties of the nickel-based superalloy CMSX-4. SBS spectra have been acquired for a range of wavevector directions in the (001) surface in the single-crystal specimen to determine the angular variation of SAW velocities and the nature of the various excitations. Rayleigh and pseudo-surface acoustic waves as well as the details of the Lamb shoulder are studied, and the elastic constants and engineering moduli are determined using different, but self-consistent, methods at ambient and high temperatures. Calculations of the SBS spectra using surface Green function methods are in good agreement with the experimental results.

Theory of bright-field scanning transmission electron microscopy for tomography

NASA Astrophysics Data System (ADS)

Levine, Zachary H.

2005-02-01

Radiation transport theory is applied to electron microscopy of samples composed of one or more materials. The theory, originally due to Goudsmit and Saunderson, assumes only elastic scattering and an amorphous medium dominated by atomic interactions. For samples composed of a single material, the theory yields reasonable parameter-free agreement with experimental data taken from the literature for the multiple scattering of 300-keV electrons through aluminum foils up to 25μm thick. For thin films, the theory gives a validity condition for Beer's law. For thick films, a variant of Molière's theory [V. G. Molière, Z. Naturforschg. 3a, 78 (1948)] of multiple scattering leads to a form for the bright-field signal for foils in the multiple-scattering regime. The signal varies as [tln(e1-2γt/τ)]-1 where t is the path length of the beam, τ is the mean free path for elastic scattering, and γ is Euler's constant. The Goudsmit-Saunderson solution interpolates numerically between these two limits. For samples with multiple materials, elemental sensitivity is developed through the angular dependence of the scattering. From the elastic scattering cross sections of the first 92 elements, a singular-value decomposition of a vector space spanned by the elastic scattering cross sections minus a delta function shows that there is a dominant common mode, with composition-dependent corrections of about 2%. A mathematically correct reconstruction procedure beyond 2% accuracy requires the acquisition of the bright-field signal as a function of the scattering angle. Tomographic reconstructions are carried out for three singular vectors of a sample problem with four elements Cr, Cu, Zr, and Te. The three reconstructions are presented jointly as a color image; all four elements are clearly identifiable throughout the image.

Bending analysis of a general cross-ply laminate using 3D elasticity solution and layerwise theory

NASA Astrophysics Data System (ADS)

Yazdani Sarvestani, H.; Naghashpour, A.; Heidari-Rarani, M.

2015-12-01

In this study, the analytical solution of interlaminar stresses near the free edges of a general (symmetric and unsymmetric layups) cross-ply composite laminate subjected to pure bending loading is presented based on Reddy's layerwise theory (LWT) for the first time. First, the reduced form of displacement field is obtained for a general cross-ply composite laminate subjected to a bending moment by elasticity theory. Then, first-order shear deformation theory of plates and LWT is utilized to determine the global and local deformation parameters appearing in the displacement fields, respectively. One of the main advantages of the developed solution based on the LWT is exact prediction of interlaminar stresses at the boundary layer regions. To show the accuracy of this solution, three-dimensional elasticity bending problem of a laminated composite is solved for special set of boundary conditions as well. Finally, LWT results are presented for edge-effect problems of several symmetric and unsymmetric cross-ply laminates under the bending moment. The obtained results indicate high stress gradients of interlaminar stresses near the edges of laminates.

Dynamics of elastic systems

NASA Astrophysics Data System (ADS)

Sankovich, Vladimir

1998-12-01

The goal of this paper is to build a consistent physical theory of the dynamics of the bat-ball interaction. This requires creating realistic models for both the softball bat and the softball. Some of the features of these models are known phenomenologically, from experiments conducted in our laboratory, others will be introduced and computed from first principles here for the first time. Both interacting objects are treated from the viewpoint of the theory of elasticity, and it is shown how a computer can be used to accurately calculate all the relevant characteristics of batball collisions. It is shown also how the major elastic parameters of the material constituting the interior of a softball can be determined using the existing experimental data. These parameters, such as the Young's modulus, the Poisson ratio and the damping coefficient are vital for the accurate description of the ball's dynamics. We are demonstrating how the existing theories of the elastic behavior of solid bars and hollow shells can be augmented to simplify the resulting equations and make the subsequent computer analysis feasible. The standard system of fourth-order PDE's is reduced to a system of the second order, because of the inclusion of the usually ignored effects of the shear forces in the bat.

Compatibility Conditions of Structural Mechanics

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.

1999-01-01

The theory of elasticity has camouflaged a deficiency in the compatibility formulation since 1860. In structures the ad hoc compatibility conditions through virtual "cuts" and closing "gaps" are not parallel to the strain formulation in elasticity. This deficiency in the compatibility conditions has prevented the development of a direct stress determination method in structures and in elasticity. We have addressed this deficiency and attempted to unify the theory of compatibility. This work has led to the development of the integrated force method for structures and the completed Beltrami-Michell formulation for elasticity. The improved accuracy observed in the solution of numerical examples by the integrated force method can be attributed to the compliance of the compatibility conditions. Using the compatibility conditions allows mapping of variables and facile movement among different structural analysis formulations. This paper reviews and illustrates the requirement of compatibility in structures and in elasticity. It also describes the generation of the conditions and quantifies the benefits of their use. The traditional analysis methods and available solutions (which have been obtained bypassing the missed conditions) should be verified for compliance of the compatibility conditions.

Collapse-driven formation of depressions on comet 67P/Churyumov-Gerasimenko

NASA Astrophysics Data System (ADS)

Leliwa-Kopystynski, J.

2018-03-01

The extremely diverse surface of comet 67P/Churyumov-Gerasimenko contains a large number of depressions or craters of very different scales. Among the most prominent are two large roughly circular depressions, each with radii of several hundred meters. In this work a model for the formation of the depressions is proposed. It is based on the theory of the deformation of a thin circular elastic plate under its own weight. The plate covers a circular cavity with a given radius. The resilience of the plate diminishes over time as a result of its thinning which is itself a consequence of sublimation. When the stress limit is achieved, a gravitational collapse occurs: the plate cracks and the remnants fall into the cavity bottom. A formula that links the radius of the plate corresponding to collapse with the plate thickness has been derived. The formula was discussed for the large intervals of the values of parameters that characterize surface layers of cometary nuclei. It was found that the surface above large cavities collapses sooner than one of a similar thickness that covers a smaller cavity. So, if the collapse mechanism theory works, that larger depressions are therefore older than smaller ones.

Retaining large and adjustable elastic strains of kilogram-scale Nb nanowires [Better Superconductor by Elastic Strain Engineering: Kilogram-scale Free-Standing Niobium Metal Composite with Large Retained Elastic Strains

DOE PAGES

Hao, Shijie; Cui, Lishan; Wang, Hua; ...

2016-02-10

Crystals held at ultrahigh elastic strains and stresses may exhibit exceptional physical and chemical properties. Individual metallic nanowires can sustain ultra-large elastic strains of 4-7%. However, retaining elastic strains of such magnitude in kilogram-scale nanowires is challenging. Here, we find that under active load, ~5.6% elastic strain can be achieved in Nb nanowires in a composite material. Moreover, large tensile (2.8%) and compressive (-2.4%) elastic strains can be retained in kilogram-scale Nb nanowires when the composite is unloaded to a free-standing condition. It is then demonstrated that the retained tensile elastic strains of Nb nanowires significantly increase their superconducting transitionmore » temperature and critical magnetic fields, corroborating ab initio calculations based on BCS theory. This free-standing nanocomposite design paradigm opens new avenues for retaining ultra-large elastic strains in great quantities of nanowires and elastic-strain-engineering at industrial scale.« less

Analytical formulation of 2-D aeroelastic model in weak ground effect

NASA Astrophysics Data System (ADS)

Dessi, Daniele; Mastroddi, Franco; Mancini, Simone

2013-10-01

This paper deals with the aeroelastic modeling and analysis of a 2-D oscillating airfoil in ground effect, elastically constrained by linear and torsional springs and immersed in an incompressible potential flow (typical section) at a finite distance from the ground. This work aims to extend Theodorsen theory, valid in an unbounded flow domain, to the case of weak ground effect, i.e., for clearances above half the airfoil chord. The key point is the determination of the aerodynamic loads, first in the frequency domain and then in the time domain, accounting for their dependence on the ground distance. The method of images is exploited in order to comply with the impermeability condition on the ground. The new integral equation in the unknown vortex distribution along the chord and the wake is solved using asymptotic expansions in the perturbation parameter defined as the inverse of the non-dimensional ground clearance of the airfoil. The mathematical model describing the aeroelastic system is transformed from the frequency domain into the time domain and then in a pure differential form using a finite-state aerodynamic approximation (augmented states). The typical section, which the developed theory is applied to, is obtained as a reduced model of a wing box finite element representation, thus allowing comparison with the corresponding aeroelastic analysis carried out by a commercial solver based on a 3-D lifting surface aerodynamic model. Stability (flutter margins) and response of the airfoil both in frequency and time domains are then investigated. In particular, within the developed theory, the solution of the Wagner problem can be directly achieved confirming an asymptotic trend of the aerodynamic coefficients toward the steady-state conditions different from that relative to the unbounded domain case. The dependence of flutter speed and the frequency response functions on ground clearance is highlighted, showing the usefulness of this approach in efficiently and robustly accounting for the presence of the ground when unsteady analysis of elastic lifting surfaces in weak ground effect is required.

Improving the estimate of the effective elastic modulus derived from three-point bending tests of long bones.

PubMed

Kourtis, Lampros C; Carter, Dennis R; Beaupre, Gary S

2014-08-01

Three-point bending tests are often used to determine the apparent or effective elastic modulus of long bones. The use of beam theory equations to interpret such tests can result in a substantial underestimation of the true effective modulus. In this study three-dimensional, nonlinear finite element analysis is used to quantify the errors inherent in beam theory and to create plots that can be used to correct the elastic modulus calculated from beam theory. Correction plots are generated for long bones representative of a variety of species commonly used in research studies. For a long bone with dimensions comparable to the mouse femur, the majority of the error in the effective elastic modulus results from deformations to the bone cross section that are not accounted for in the equations from beam theory. In some cases, the effective modulus calculated from beam theory can be less than one-third of the true effective modulus. Errors are larger: (1) for bones having short spans relative to bone length; (2) for bones with thin vs. thick cortices relative to periosteal diameter; and (3) when using a small radius or "knife-edge" geometry for the center loading ram and the outer supports in the three-point testing system. The use of these correction plots will enable researchers to compare results for long bones from different animal strains and to compare results obtained using testing systems that differ with regard to length between the outer supports and the radius used for the loading ram and outer supports.

Proposed moduli of dry rock and their application to predicting elastic velocities of sandstones

USGS Publications Warehouse

Lee, Myung W.

2005-01-01

Velocities of water-saturated isotropic sandstones under low frequency can be modeled using the Biot-Gassmann theory if the moduli of dry rocks are known. On the basis of effective medium theory by Kuster and Toksoz, bulk and shear moduli of dry sandstone are proposed. These moduli are related to each other through a consolidation parameter and provide a new way to calculate elastic velocities. Because this parameter depends on differential pressure and the degree of consolidation, the proposed moduli can be used to calculate elastic velocities of sedimentary rocks under different in-place conditions by varying the consolidation parameter. This theory predicts that the ratio of P-wave to S-wave velocity (Vp/Vs) of a dry rock decreases as differential pressure increases and porosity decreases. This pattern of behavior is similar to that of water-saturated sedimentary rocks. If microcracks are present in sandstones, the velocity ratio usually increases as differential pressure increases. This implies that this theory is optimal for sandstones having intergranular porosities. Even though the accurate behavior of the consolidation parameter with respect to differential pressure or the degree of consolidation is not known, this theory presents a new way to predict S-wave velocity from P-wave velocity and porosity and to calculate elastic velocities of gas-hydrate-bearing sediments. For given properties of sandstones such as bulk and shear moduli of matrix, only the consolidation parameter affects velocities, and this parameter can be estimated directly from the measurements; thus, the prediction of S-wave velocity is accurate, reflecting in-place conditions.

The magnitude of tissue cooling during cryotherapy with varied types of compression.

PubMed

Tomchuk, David; Rubley, Mack D; Holcomb, William R; Guadagnoli, Mark; Tarno, Jason M

2010-01-01

Certified athletic trainers can choose different types of external compression (none, Flex-i-Wrap, and elastic wrap) when applying an ice bag to the body. However, which type facilitates the greatest magnitude of tissue cooling is unclear. To compare the effects of 2 common types of external compression on the magnitude of surface and intramuscular cooling during an ice-bag treatment. Randomized controlled trial. University research laboratory. Fourteen college students (10 women, 4 men; age = 22.4 +/- 1.8 years, height = 169.1 +/- 8.2 cm, mass = 73.3 +/- 18.5 kg, skinfold = 13.14 +/- 1.61 mm) with previous cryotherapy experience and a posterior lower leg skinfold equal to or less than 15 mm. On 3 different days separated by 24 to 48 hours, an ice bag was applied to the posterior lower leg surface of each participant for 30 minutes with no compression, with elastic wrap, or with Flex-i-Wrap. Posterior lower leg surface and intramuscular (2 cm) temperatures were recorded for 95 minutes. At 15 minutes, the elastic wrap produced greater surface temperature reduction than no compression (P = .03); this difference remained throughout the protocol (P range, .03 to .04). At 30 minutes, surface temperatures were 14.95 degrees C, 11.55 degrees C, and 9.49 degrees C when an ice bag was applied with no external compression, Flex-i-Wrap, and elastic wrap, respectively. Surface temperatures between Flex-i-Wrap and elastic wrap and between Flex-i-Wrap and no compression were never different. At 10 minutes, Flex-i-Wrap (P = .006) and elastic wrap (P < .001) produced greater intramuscular temperature reduction than no compression produced; these differences remained throughout the protocol. At 10 minutes, no compression, Flex-i-Wrap, and elastic wrap decreased intramuscular temperature by 1.34 degrees C, 2.46 degrees C, and 2.73 degrees C, respectively. At 25 minutes, elastic wrap (8.03 degrees C) produced greater temperature reduction than Flex-i-Wrap (6.65 degrees C) (P = .03) or no compression (4.63 degrees C) (P < .001 ). These differences remained throughout ice application and until 50 minutes after ice-bag removal. During an ice-bag application, external compression with elastic wrap was more effective than Flex-i-Wrap at reducing intramuscular tissue temperature. Elastic wraps should be used for acute injury care.

The subtle interplay of elastic and inelastic collisions in the thermalization of the quark–gluon plasma

DOE PAGES

Blaizot, Jean-Paul; Liao, Jinfeng; Mehtar-Tani, Yacine

2016-12-01

We analyze the interplay of elastic and inelastic collisions in the thermalization of the quark-gluon plasma, using kinetic theory. Our main focus is the dynamics and equilibration of long wavelength modes.

Mechanics of plant fruit hooks

PubMed Central

Chen, Qiang; Gorb, Stanislav N.; Gorb, Elena; Pugno, Nicola

2013-01-01

Hook-like surface structures, observed in some plant species, play an important role in the process of plant growth and seed dispersal. In this study, we developed an elastic model and further used it to investigate the mechanical behaviour of fruit hooks in four plant species, previously measured in an experimental study. Based on Euler–Bernoulli beam theory, the force–displacement relationship is derived, and its Young's modulus is obtained. The result agrees well with the experimental data. The model aids in understanding the mechanics of hooks, and could be used in the development of new bioinspired Velcro-like materials. PMID:23365190

Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

NASA Technical Reports Server (NTRS)

Sidi, A.; Israeli, M.

1986-01-01

High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

Configuration interaction of hydropathic waves enables ubiquitin functionality

NASA Astrophysics Data System (ADS)

Allan, Douglas C.; Phillips, J. C.

2018-02-01

Ubiquitin, discovered less than 50 years ago, tags thousands of diseased proteins for destruction. It is small (only 76 amino acids), and is found unchanged in mammals, birds, fish and even worms. Key features of its functionality are identified here using critical point thermodynamic scaling theory. These include Fano interference between first- and second-order elements of correlated long-range globular surface shape transitions. Comparison with its closest relative, 76 amino acid Nedd8, shows that the latter lacks these features. A cracked elastic network model is proposed for the common target shared by many diseased proteins.

Localized Impact Damage in Ceramics.

DTIC Science & Technology

1982-08-31

are observed at several levels , all farther from the surface than the lateral crack at the comparable static site. The numbers and lengths of radial...8000- 6000 5000- 4000- 0 3000 2000 E C O* 1000 - 00 laterals first 0 A observed at a static sites o 600 500 o 0 0 400 0 300o radials and laterals first0...on elastic -plastic theory, eqvIO. 3, Zocr1/ 2 plotted on 1000 di CrI/2 scala. 800 0 z 6 0 0 - I 00 00 - - �o 1 0 200 0,, of 0 5.0 10.0 15.0 20.0

Local deformation for soft tissue simulation

PubMed Central

Omar, Nadzeri; Zhong, Yongmin; Smith, Julian; Gu, Chengfan

2016-01-01

ABSTRACT This paper presents a new methodology to localize the deformation range to improve the computational efficiency for soft tissue simulation. This methodology identifies the local deformation range from the stress distribution in soft tissues due to an external force. A stress estimation method is used based on elastic theory to estimate the stress in soft tissues according to a depth from the contact surface. The proposed methodology can be used with both mass-spring and finite element modeling approaches for soft tissue deformation. Experimental results show that the proposed methodology can improve the computational efficiency while maintaining the modeling realism. PMID:27286482

Mixed boundary value problems in mechanics

NASA Technical Reports Server (NTRS)

Erdogan, F.

1975-01-01

Certain boundary value problems were studied over a domain D which may contain the point at infinity and may be multiply connected. Contours forming the boundary are assumed to consist of piecewise smooth arcs. Mixed boundary value problems are those with points of flux singularity on the boundary; these are points on the surface, either side of which at least one of the differential operator has different behavior. The physical system was considered to be described by two quantities, the potential and the flux type quantities. Some of the examples that were illustrated included problems in potential theory and elasticity.

Analytical close-form solutions to the elastic fields of solids with dislocations and surface stress

NASA Astrophysics Data System (ADS)

Ye, Wei; Paliwal, Bhasker; Ougazzaden, Abdallah; Cherkaoui, Mohammed

2013-07-01

The concept of eigenstrain is adopted to derive a general analytical framework to solve the elastic field for 3D anisotropic solids with general defects by considering the surface stress. The formulation shows the elastic constants and geometrical features of the surface play an important role in determining the elastic fields of the solid. As an application, the analytical close-form solutions to the stress fields of an infinite isotropic circular nanowire are obtained. The stress fields are compared with the classical solutions and those of complex variable method. The stress fields from this work demonstrate the impact from the surface stress when the size of the nanowire shrinks but becomes negligible in macroscopic scale. Compared with the power series solutions of complex variable method, the analytical solutions in this work provide a better platform and they are more flexible in various applications. More importantly, the proposed analytical framework profoundly improves the studies of general 3D anisotropic materials with surface effects.

Residual stresses in cross-ply composite tubes

NASA Technical Reports Server (NTRS)

Cohen, D.; Hyer, M. W.

1984-01-01

The residual thermal stresses in 4-layer cross-ply tubes are studied. The tubes considered has a small radius to wall-thickness ratios and so elasticity solutions were used. The residual thermal stress problem was considered to be axisymmetric and three elasticity solutions were derived and the results compared with the results using classical lamination theory. The comparison illustrates the limitations of classical lamination theory. The three elasticity solutions derived were: plane stress, plane strain, and generalized plane strain, the latter being the most realistic. Residual stresses in both the hoop and axial direction is significant. Stacking arrangement effects the residual stress to some extent, as do the material properties of the individual lamina. The benefits of hybrid construction are briefly discussed.

The surface and through crack problems in layered orthotropic plates

NASA Technical Reports Server (NTRS)

Erdogan, Fazil; Wu, Binghua

1991-01-01

An analytical method is developed for a relatively accurate calculation of Stress Intensity Factors in a laminated orthotropic plate containing a through or part-through crack. The laminated plate is assumed to be under bending or membrane loading and the mode 1 problem is considered. First three transverse shear deformation plate theories (Mindlin's displacement based first-order theory, Reissner's stress-based first-order theory, and a simple-higher order theory due to Reddy) are reviewed and examined for homogeneous, laminated and heterogeneous orthotropic plates. Based on a general linear laminated plate theory, a method by which the stress intensity factors can be obtained in orthotropic laminated and heterogeneous plates with a through crack is developed. Examples are given for both symmetrically and unsymmetrically laminated plates and the effects of various material properties on the stress intensity factors are studied. In order to implement the line-spring model which is used later to study the surface crack problem, the corresponding plane elasticity problem of a two-bonded orthotropic plated containing a crack perpendicular to the interface is also considered. Three different crack profiles: an internal crack, an edge crack, and a crack terminating at the interface are considered. The effect of the different material combinations, geometries, and material orthotropy on the stress intensity factors and on the power of stress singularity for a crack terminating at the interface is fully examined. The Line Spring model of Rice and Levy is used for the part-through crack problem. The surface crack is assumed to lie in one of the two-layered laminated orthotropic plates due to the limitation of the available plane strain results. All problems considered are of the mixed boundary value type and are reduced to Cauchy type of singular integral equations which are then solved numerically.

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.

Prediction of Sliding Friction Coefficient Based on a Novel Hybrid Molecular-Mechanical Model.

PubMed

Zhang, Xiaogang; Zhang, Yali; Wang, Jianmei; Sheng, Chenxing; Li, Zhixiong

2018-08-01

Sliding friction is a complex phenomenon which arises from the mechanical and molecular interactions of asperities when examined in a microscale. To reveal and further understand the effects of micro scaled mechanical and molecular components of friction coefficient on overall frictional behavior, a hybrid molecular-mechanical model is developed to investigate the effects of main factors, including different loads and surface roughness values, on the sliding friction coefficient in a boundary lubrication condition. Numerical modelling was conducted using a deterministic contact model and based on the molecular-mechanical theory of friction. In the contact model, with given external loads and surface topographies, the pressure distribution, real contact area, and elastic/plastic deformation of each single asperity contact were calculated. Then asperity friction coefficient was predicted by the sum of mechanical and molecular components of friction coefficient. The mechanical component was mainly determined by the contact width and elastic/plastic deformation, and the molecular component was estimated as a function of the contact area and interfacial shear stress. Numerical results were compared with experimental results and a good agreement was obtained. The model was then used to predict friction coefficients in different operating and surface conditions. Numerical results explain why applied load has a minimum effect on the friction coefficients. They also provide insight into the effect of surface roughness on the mechanical and molecular components of friction coefficients. It is revealed that the mechanical component dominates the friction coefficient when the surface roughness is large (Rq > 0.2 μm), while the friction coefficient is mainly determined by the molecular component when the surface is relatively smooth (Rq < 0.2 μm). Furthermore, optimal roughness values for minimizing the friction coefficient are recommended.

An elastic-perfectly plastic analysis of the bending of the lithosphere at a trench

NASA Technical Reports Server (NTRS)

Turcotte, D. L.; Mcadoo, D. C.; Caldwell, J. G.

1978-01-01

A number of authors have modeled the flexure of the lithosphere at an oceanic trench using a thin elastic plate with a hydrostatic restoring force. In some cases good agreement with observed topography is obtained but in other cases the slope of the lithosphere within the trench is greater than that predicted by the elastic theory. In this paper the bending of a thin plate is considered using an elastic-perfectly plastic rheology. It is found that the lithosphere behaves elastically seaward of the trench, but that plasticity decreases the radius of curvature within the trench. The results are compared with a number of observed trench profiles. The elastic-perfectly plastic profiles are in excellent agreement with those profiles that deviate from elastic behavior.

Geometrically nonlinear analysis of laminated elastic structures

NASA Technical Reports Server (NTRS)

Reddy, J. N.

1984-01-01

Laminated composite plates and shells that can be used to model automobile bodies, aircraft wings and fuselages, and pressure vessels among many other were analyzed. The finite element method, a numerical technique for engineering analysis of structures, is used to model the geometry and approximate the solution. Various alternative formulations for analyzing laminated plates and shells are developed and their finite element models are tested for accuracy and economy in computation. These include the shear deformation laminate theory and degenerated 3-D elasticity theory for laminates.

Energy and Momentum Relaxation Times of 2D Electrons Due to Near Surface Deformation Potential Scattering

NASA Astrophysics Data System (ADS)

Pipa, Viktor; Vasko, Fedor; Mitin, Vladimir

1997-03-01

The low temperature energy and momentum relaxation rates of 2D electron gas placed near the free or clamped surface of a semi-infinit sample are calculated. To describe the electron-acoustic phonon interaction with allowance of the surface effect the method of elasticity theory Green functions was used. This method allows to take into account the reflection of acoustic waves from the surface and related mutual conversion of LA and TA waves. It is shown that the strength of the deformation potential scattering at low temperatures substantially depends on the mechanical conditions at the surface: relaxation rates are suppressed for the free surface while for the rigid one the rates are enhanced. The dependence of the conductivity on the distance between the 2D layer and the surface is discussed. The effect is most pronounced in the range of temperatures 2 sl pF < T < (2 hbar s_l)/d, where pF is the Fermi momentum, sl is the velocity of LA waves, d is the width of the quantum well.

Predicting elastic properties of β-HMX from first-principles calculations.

PubMed

Peng, Qing; Rahul; Wang, Guangyu; Liu, Gui-Rong; Grimme, Stefan; De, Suvranu

2015-05-07

We investigate the performance of van der Waals (vdW) functions in predicting the elastic constants of β cyclotetramethylene tetranitramine (HMX) energetic molecular crystals using density functional theory (DFT) calculations. We confirm that the accuracy of the elastic constants is significantly improved using the vdW corrections with environment-dependent C6 together with PBE and revised PBE exchange-correlation functionals. The elastic constants obtained using PBE-D3(0) calculations yield the most accurate mechanical response of β-HMX when compared with experimental stress-strain data. Our results suggest that PBE-D3 calculations are reliable in predicting the elastic constants of this material.

Surface folding-induced attraction and motion of particles in a soft elastic gel: cooperative effects of surface tension, elasticity, and gravity.

PubMed

Chakrabarti, Aditi; Chaudhury, Manoj K

2013-12-17

We report some experimental observations regarding a new type of long-range interaction between rigid particles that prevails when they are suspended in an ultrasoft elastic gel. A denser particle submerges itself to a considerable depth inside the gel and becomes elasto-buoyant by balancing its weight against the elastic force exerted by the surrounding medium. By virtue of a large elasto-capillary length, the surface of the gel wraps around the particle and closes to create a line singularity connecting the particle to the free surface of the gel. A substantial amount of tensile strain is thus developed in the gel network parallel to the free surface that penetrates to a significant depth inside the gel. The field of this tensile strain is rather long-range because of a large gravito-elastic correlation length and sufficiently strong to pull two submerged particles into contact. The particles move toward each other with an effective force following an inverse linear distance law. When more monomers or dimers of the particles are released inside the gel, they orient rather freely inside the capsules where they are located and attract each other to form closely packed clusters. Eventually, these clusters themselves interact and coalesce. This is an emergent phenomenon in which gravity, capillarity, and elasticity work in tandem to create a long-range interaction. We also present the results of a related experiment, in which a particle suspended inside a thickness-graded gel moves accompanied by the continuous folding and the relaxation of the gel's surface.

Durability and life prediction modeling in polyimide composites

NASA Technical Reports Server (NTRS)

Binienda, Wieslaw K.

1995-01-01

Sudden appearance of cracks on a macroscopically smooth surface of brittle materials due to cooling or drying shrinkage is a phenomenon related to many engineering problems. Although conventional strength theories can be used to predict the necessary condition for crack appearance, they are unable to predict crack spacing and depth. On the other hand, fracture mechanics theory can only study the behavior of existing cracks. The theory of crack initiation can be summarized into three conditions, which is a combination of a strength criterion and laws of energy conservation, the average crack spacing and depth can thus be determined. The problem of crack initiation from the surface of an elastic half plane is solved and compares quite well with available experimental evidence. The theory of crack initiation is also applied to concrete pavements. The influence of cracking is modeled by the additional compliance according to Okamura's method. The theoretical prediction by this structural mechanics type of model correlates very well with the field observation. The model may serve as a theoretical foundation for future pavement joint design. The initiation of interactive cracks of quasi-brittle material is studied based on a theory of cohesive crack model. These cracks may grow simultaneously, or some of them may close during certain stages. The concept of crack unloading of cohesive crack model is proposed. The critical behavior (crack bifurcation, maximum loads) of the cohesive crack model are characterized by rate equations. The post-critical behavior of crack initiation is also studied.

Surface cracks in a plate of finite width under tension or bending

NASA Technical Reports Server (NTRS)

Erdogan, F.; Boduroglu, H.

1984-01-01

The problem of a finite plate containing collinear surface cracks is considered and solved by using the line spring model with plane elasticity and Reissner's plate theory. The main focus is on the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors in an effort to provide extensive numerical results which may be useful in applications. Some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks, and two corner cracks for wide range of relative dimensions. Particularly in corner cracks, the agreement with the finite element solution is surprisingly very good. The results are obtained for semi-elliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

Surface cracks in a plate of finite width under extension or bending

NASA Technical Reports Server (NTRS)

Erdogan, F.; Boduroglu, H.

1984-01-01

In this paper the problem of a finite plate containing collinear surface cracks is considered. The problem is solved by using the line spring model with plane elasticity and Reissner's plate theory. The main purpose of the study is to investigate the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors and to provide extensive numerical results which may be useful in applications. First, some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks and two corner cracks for wide range of relative dimensions. Particularly in corner cracks the agreement with the finite element solution is surprisingly very good. The results are obtained for semielliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

P(P bar)P elastic scattering and cosmic ray data

NASA Technical Reports Server (NTRS)

FAZAL-E-ALEEM; Saleem, M.

1985-01-01

It is shown that the total cross section for pp elastic scattering at cosmic ray energies, as well as the total cross section, the slope parameter b(s,t) and the differential cross section for small momentum transfer at ISR and collider energies for p(p)p elastic scattering can be simultaneously fitted by using a simple Regge pole model. The results of this theory is discussed in detail.

EQUIVALENCE BETWEEN SHORT-TIME BIPHASIC AND INCOMPRESSIBLE ELASTIC MATERIAL RESPONSES

PubMed Central

Ateshian, Gerard A.; Ellis, Benjamin J.; Weiss, Jeffrey A.

2009-01-01

Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response δt≪Δ2/‖C4‖||K||, where Δ is a characteristic dimension, C4 is the elasticity tensor and K is the hydraulic permeability tensor of the solid matrix. Certain notes of caution are provided with regard to implementation issues, particularly when finite element formulations of incompressible elasticity employ an uncoupled strain energy function consisting of additive deviatoric and volumetric components. PMID:17536908

Emergent propagation modes of ferromagnetic swimmers in constrained geometries

NASA Astrophysics Data System (ADS)

Bryan, M. T.; Shelley, S. R.; Parish, M. J.; Petrov, P. G.; Winlove, C. P.; Gilbert, A. D.; Ogrin, F. Y.

2017-02-01

Magnetic microswimmers, composed of hard and soft ferromagnets connected by an elastic spring, are modelled under low Reynolds number conditions in the presence of geometrical boundaries. Approaching a surface, the magneto-elastic swimmer's velocity increases and its trajectory bends parallel to the surface contour. Further confinement to form a planar channel generates new propagation modes as the channel width narrows, altering the magneto-elastic swimmer's speed, orientation, and direction of travel. Our results demonstrate that constricted geometric environments, such as occuring in microfluidic channels or blood vessels, may influence the functionality of magneto-elastic microswimmers for applications such as drug delivery.

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

NASA Astrophysics Data System (ADS)

Becker, Leif E.; Shelley, Michael J.

2000-11-01

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

Quantitative elasticity measurement of urinary bladder wall using laser-induced surface acoustic waves.

PubMed

Li, Chunhui; Guan, Guangying; Zhang, Fan; Song, Shaozhen; Wang, Ruikang K; Huang, Zhihong; Nabi, Ghulam

2014-12-01

The maintenance of urinary bladder elasticity is essential to its functions, including the storage and voiding phases of the micturition cycle. The bladder stiffness can be changed by various pathophysiological conditions. Quantitative measurement of bladder elasticity is an essential step toward understanding various urinary bladder disease processes and improving patient care. As a nondestructive, and noncontact method, laser-induced surface acoustic waves (SAWs) can accurately characterize the elastic properties of different layers of organs such as the urinary bladder. This initial investigation evaluates the feasibility of a noncontact, all-optical method of generating and measuring the elasticity of the urinary bladder. Quantitative elasticity measurements of ex vivo porcine urinary bladder were made using the laser-induced SAW technique. A pulsed laser was used to excite SAWs that propagated on the bladder wall surface. A dedicated phase-sensitive optical coherence tomography (PhS-OCT) system remotely recorded the SAWs, from which the elasticity properties of different layers of the bladder were estimated. During the experiments, series of measurements were performed under five precisely controlled bladder volumes using water to estimate changes in the elasticity in relation to various urinary bladder contents. The results, validated by optical coherence elastography, show that the laser-induced SAW technique combined with PhS-OCT can be a feasible method of quantitative estimation of biomechanical properties.

A new problem in mathematical physics associated with the problem of coherent phase transformation

NASA Astrophysics Data System (ADS)

Grinfeld, M. A.

1985-06-01

The description of heterogeneous coherent phase equilibria in an elastic single component system is shown to lead, in the approximation of small intrinsic deformation, to a new problem in mathematical physics with an unknown bound. The low order terms of the resulting system of equilibrium equations coincide with the equations of the classical linear theory of elasticity (generally speaking, anisotropic); however, the problem remains strongly nonlinear overall, inasmuch as it contains an unknown bound and a boundary condition on it which is quadratic with respect to translation. The formulas obtained are used to find certain explicit solutions to the boundary problems. As an example, the problem of heterogeneous equilibria in an infinite rectangular isotropic beam with free faces and constant loading on the surfaces x squared = const can be examined. A modeling problem for the asymptote of small intrinsic deformation during coherent phase transformation is presented as a scalar analog of the vector problem considered initially.

The advancement of the high precision stress polishing

NASA Astrophysics Data System (ADS)

Li, Chaoqiang; Lei, Baiping; Han, Yu

2016-10-01

The stress polishing is a kind of large-diameter aspheric machining technology with high efficiency. This paper focuses on the principle, application in the processing of large aspheric mirror, and the domestic and foreign research status of stress polishing, aimed at the problem of insufficient precision of mirror surface deformation calculated by some traditional theories and the problem that the output precision and stability of the support device in stress polishing cannot meet the requirements. The improvement methods from these three aspects are put forward, the characterization method of mirror's elastic deformation in stress polishing, the deformation theory of influence function and the calculation of correction force, the design of actuator's mechanical structure. These improve the precision of stress polishing and provide theoretical basis for the further application of stress polishing in large-diameter aspheric machining.

Quantification of dislocation nucleation stress in TiN through high-resolution in situ indentation experiments and first principles calculations

DOE PAGES

Li, N.; Yadav, S. K.; Liu, X. -Y.; ...

2015-11-05

Using the in situ indentation of TiN in a high-resolution transmission electron microscope, the nucleation of full as well as partial dislocations has been observed from {001} and {111} surfaces, respectively. The critical elastic strains associated with the nucleation of the dislocations were analyzed from the recorded atomic displacements, and the nucleation stresses corresponding to the measured critical strains were computed using density functional theory. The resolved shear stress was estimated to be 13.8 GPa for the partial dislocation 1/6 <110> {111} and 6.7 GPa for the full dislocation ½ <110> {110}. Moreover, such an approach of quantifying nucleation stressesmore » for defects via in situ high-resolution experiment coupled with density functional theory calculation may be applied to other unit processes.« less

Improvement of the relaxation time and the order parameter of nematic liquid crystal using a hybrid alignment mixture of carbon nanotube and polyimide

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

Lee, Hyojin; Yang, Seungbin; Lee, Ji-Hoon, E-mail: jihoonlee@jbnu.ac.kr

2014-05-12

We examined the electrooptical properties of a nematic liquid crystal (LC) sample whose substrates were coated with a mixture of carbon nanotube (CNT) and polyimide (PI). The relaxation time of the sample coated with 1.5 wt. % CNT mixture was about 35% reduced compared to the pure polyimide sample. The elastic constant and the order parameter of the CNT-mixture sample were increased and the fast relaxation of LC could be approximated to the mean-field theory. We found the CNT-mixed polyimide formed more smooth surface than the pure PI from atomic force microscopy images, indicating the increased order parameter is related to themore » smooth surface topology of the CNT-polyimide mixture.« less

On the curvature effect of thin membranes

NASA Astrophysics Data System (ADS)

Wang, Duo; Jiao, Xiangmin; Conley, Rebecca; Glimm, James

2013-01-01

We investigate the curvature effect of a thin, curved elastic interface that separates two subdomains and exerts a pressure due to a curvature effect. This pressure, which we refer to as interface pressure, is similar to the surface tension in fluid mechanics. It is important in some applications, such as the canopy of parachutes, biological membranes of cells, balloons, airbags, etc., as it partially balances a pressure jump between the two sides of an interface. In this paper, we show that the interface pressure is equal to the trace of the matrix product of the curvature tensor and the Cauchy stress tensor in the tangent plane. We derive the theory for interfaces in both 2-D and 3-D, and present numerical discretizations for computing the quality over triangulated surfaces.

Thermodynamics, kinetics, and catalytic effect of dehydrogenation from MgH2 stepped surfaces and nanocluster: a DFT study

NASA Astrophysics Data System (ADS)

Reich, Jason; Wang, Linlin; Johnson, Duane

2013-03-01

We detail the results of a Density Functional Theory (DFT) based study of hydrogen desorption, including thermodynamics and kinetics with(out) catalytic dopants, on stepped (110) rutile and nanocluster MgH2. We investigate competing configurations (optimal surface and nanoparticle configurations) using simulated annealing with additional converged results at 0 K, necessary for finding the low-energy, doped MgH2 nanostructures. Thermodynamics of hydrogen desorption from unique dopant sites will be shown, as well as activation energies using the Nudged Elastic Band algorithm. To compare to experiment, both stepped structures and nanoclusters are required to understanding and predict the effects of ball milling. We demonstrate how these model systems relate to the intermediary sized structures typically seen in ball milling experiments.

Block Copolymer Adhesion Measured by Contact Mechanics Methods

NASA Astrophysics Data System (ADS)

Falsafi, A.; Bates, S.; Tirrell, M.; Pocius, A. V.

1997-03-01

Adhesion measurements for a series of polyolefin diblocks and triblocks are presented. These materials have poly(ethylene-propylene) or poly(ethyl-ethylene) rubbery block, and semicrystalline polyethylene block as physical crosslinker. The experiments consist of compression and decompression profiles of contact area between the samples as a function of normal load, analyzed by the JKR Theory. The samples are prepared either by formation of caps from the bulk material in melting and subsequent cooling, and/or coating them in thin films on surface modified elastic foundations of polydimethylsiloxane caps. The latter minimizes the viscoelastic losses which are dominant in the bulk of material. The effect of molecular architecture and microstructure on adhesion energy and dynamics of separation, obtained from decompression experiments, is discussed in view of their influence on molecular arrangements at the contacting surfaces.

Active Optics: stress polishing of toric mirrors for the VLT SPHERE adaptive optics system.

PubMed

Hugot, Emmanuel; Ferrari, Marc; El Hadi, Kacem; Vola, Pascal; Gimenez, Jean Luc; Lemaitre, Gérard R; Rabou, Patrick; Dohlen, Kjetil; Puget, Pascal; Beuzit, Jean Luc; Hubin, Norbert

2009-05-20

The manufacturing of toric mirrors for the Very Large Telescope-Spectro-Polarimetric High-Contrast Exoplanet Research instrument (SPHERE) is based on Active Optics and stress polishing. This figuring technique allows minimizing mid and high spatial frequency errors on an aspherical surface by using spherical polishing with full size tools. In order to reach the tight precision required, the manufacturing error budget is described to optimize each parameter. Analytical calculations based on elasticity theory and finite element analysis lead to the mechanical design of the Zerodur blank to be warped during the stress polishing phase. Results on the larger (366 mm diameter) toric mirror are evaluated by interferometry. We obtain, as expected, a toric surface within specification at low, middle, and high spatial frequencies ranges.

Slow dynamics and strength recovery in unconsolidated granular earth materials: a mechanistic theory

DOE PAGES

Lieou, Charles Ka Cheong; Daub, Eric G.; Ecke, Robert E.; ...

2017-09-08

Rock materials often display long-time relaxation, commonly termed aging or “slow dynamics”, after the cessation of acoustic perturbations. In this paper, we focus on unconsolidated rock materials and propose to explain such nonlinear relaxation through the Shear-Transformation-Zone (STZ) theory of granular media, adapted for small stresses and strains. The theory attributes the observed relaxation to the slow, irreversible change of positions of constituent grains, and posits that the aging process can be described in three stages: fast recovery before some characteristic time associated with the subset of local plastic events or grain rearrangements with a short time scale, log-linear recoverymore » of the elastic modulus at intermediate times, and gradual turnover to equilibrium steady-state behavior at long times. Here we demonstrate good agreement with experiments on aging in granular materials such as simulated fault gouge after an external disturbance. These results may provide insights into observed modulus recovery after strong shaking in the near surface region of earthquake zones.« less

Slow Dynamics and Strength Recovery in Unconsolidated Granular Earth Materials: A Mechanistic Theory

NASA Astrophysics Data System (ADS)

Lieou, Charles K. C.; Daub, Eric G.; Ecke, Robert E.; Johnson, Paul A.

2017-10-01

Rock materials often display long-time relaxation, commonly termed aging or "slow dynamics," after the cessation of acoustic perturbations. In this paper, we focus on unconsolidated rock materials and propose to explain such nonlinear relaxation through the shear-transformation-zone theory of granular media, adapted for small stresses and strains. The theory attributes the observed relaxation to the slow, irreversible change of positions of constituent grains and posits that the aging process can be described in three stages: fast recovery before some characteristic time associated with the subset of local plastic events or grain rearrangements with a short time scale, log linear recovery of the elastic modulus at intermediate times, and gradual turnover to equilibrium steady state behavior at long times. We demonstrate good agreement with experiments on aging in granular materials such as simulated fault gouge after an external disturbance. These results may provide insights into observed modulus recovery after strong shaking in the near surface region of earthquake zones.

Active optics: off axis aspherics generation for high contrast imaging

NASA Astrophysics Data System (ADS)

Hugot, E.; Laslandes, M.; Ferrari, M.; Vives, S.; Moindrot, S.; El Hadi, K.; Dohlen, K.

2017-11-01

Active Optics methods, based on elasticity theory, allow the aspherisation of optical surfaces by stress polishing but also active aspherisation in situ. Researches in this field will impact the final performance and the final cost of any telescope or instrument. The stress polishing method is well suited for the superpolishing of aspheric components for astronomy. Its principle relies on spherical polishing with a full-sized tool of a warped substrate, which becomes aspherical once unwarped. The main advantage of this technique is the very high optical quality obtained either on form or on high spatial frequency errors. Furthermore, the roughness can be decreased down to a few angstroms, thanks the classical polishing with a large pitch tool, providing a substantial gain on the final scientific performance, for instance on the contrast on coronagraphic images, but also on the polishing time and cost. Stress polishing is based on elasticity theory, and requires an optimised deformation system able to provide the right aspherical form on the optical surface during polishing. The optical quality of the deformation is validated using extensive Finite Element Analysis, allowing an estimation of residuals and an optimisation of the warping harness. We describe here the work realised on stress polishing of toric mirrors for VLT-SPHERE and then our actual work on off axis aspherics (OAA) for the ASPIICS-Proba3 mission for solar coronagraphy. The ASPIICS optical design made by Vives et al is a three mirrors anastigmat including a concave off axis hyperboloid and a convex off axis parabola (OAP). We are developing a prototype in order to demonstrate the feasibility of this type of surface, using a multi-mode warping harness (Lemaitre et al). Furthermore, we present our work on variable OAP, meaning the possibility to adjust the shape of a simple OAP in situ with a minimal number of actuators, typically one actuator per optical mode (Focus, Coma and Astigmatism). Applications for future space telescopes and instrumentation are discussed.

Measuring strain and rotation fields at the dislocation core in graphene

NASA Astrophysics Data System (ADS)

Bonilla, L. L.; Carpio, A.; Gong, C.; Warner, J. H.

2015-10-01

Strain fields, dislocations, and defects may be used to control electronic properties of graphene. By using advanced imaging techniques with high-resolution transmission electron microscopes, we have measured the strain and rotation fields about dislocations in monolayer graphene with single-atom sensitivity. These fields differ qualitatively from those given by conventional linear elasticity. However, atom positions calculated from two-dimensional (2D) discrete elasticity and three-dimensional discrete periodized Föppl-von Kármán equations (dpFvKEs) yield fields close to experiments when determined by geometric phase analysis. 2D theories produce symmetric fields whereas those from experiments exhibit asymmetries. Numerical solutions of dpFvKEs provide strain and rotation fields of dislocation dipoles and pairs that also exhibit asymmetries and, compared with experiments, may yield information on out-of-plane displacements of atoms. While discrete theories need to be solved numerically, analytical formulas for strains and rotation about dislocations can be obtained from 2D Mindlin's hyperstress theory. These formulas are very useful for fitting experimental data and provide a template to ascertain the importance of nonlinear and nonplanar effects. Measuring the parameters of this theory, we find two characteristic lengths between three and four times the lattice spacings that control dilatation and rotation about a dislocation. At larger distances from the dislocation core, the elastic fields decay to those of conventional elasticity. Our results may be relevant for strain engineering in graphene and other 2D materials of current interest.

Free vibration analysis of a cracked shear deformable beam on a two-parameter elastic foundation using a lattice spring model

NASA Astrophysics Data System (ADS)

Attar, M.; Karrech, A.; Regenauer-Lieb, K.

2014-05-01

The free vibration of a shear deformable beam with multiple open edge cracks is studied using a lattice spring model (LSM). The beam is supported by a so-called two-parameter elastic foundation, where normal and shear foundation stiffnesses are considered. Through application of Timoshenko beam theory, the effects of transverse shear deformation and rotary inertia are taken into account. In the LSM, the beam is discretised into a one-dimensional assembly of segments interacting via rotational and shear springs. These springs represent the flexural and shear stiffnesses of the beam. The supporting action of the elastic foundation is described also by means of normal and shear springs acting on the centres of the segments. The relationship between stiffnesses of the springs and the elastic properties of the one-dimensional structure are identified by comparing the homogenised equations of motion of the discrete system and Timoshenko beam theory.

Elastic constants from microscopic strain fluctuations

PubMed

Sengupta; Nielaba; Rao; Binder

2000-02-01

Fluctuations of the instantaneous local Lagrangian strain epsilon(ij)(r,t), measured with respect to a static "reference" lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse-grained by averaging them within subsystems (of size L(b)) of a system (of total size L) in the canonical ensemble. Using a simple finite size scaling theory we predict the behavior of the fluctuations as a function of L(b)/L and extract elastic constants of the system in the thermodynamic limit at nonzero temperature. Our method is simple to implement, efficient, and general enough to be able to handle a wide class of model systems, including those with singular potentials without any essential modification. We illustrate the technique by computing isothermal elastic constants of "hard" and "soft" disk triangular solids in two dimensions from Monte Carlo and molecular dynamics simulations. We compare our results with those from earlier simulations and theory.

Thermal expansion compensator having an elastic conductive element bonded to two facing surfaces

NASA Technical Reports Server (NTRS)

Determan, William (Inventor); Matejczyk, Daniel Edward (Inventor)

2012-01-01

A thermal expansion compensator is provided and includes a first electrode structure having a first surface, a second electrode structure having a second surface facing the first surface and an elastic element bonded to the first and second surfaces and including a conductive element by which the first and second electrode structures electrically and/or thermally communicate, the conductive element having a length that is not substantially longer than a distance between the first and second surfaces.

Surface self-organization in multilayer film coatings

NASA Astrophysics Data System (ADS)

Shuvalov, Gleb M.; Kostyrko, Sergey A.

2017-12-01

It is a recognized fact that during film deposition and subsequent thermal processing the film surface evolves into an undulating profile. Surface roughness affects many important aspects in the engineering application of thin film materials such as wetting, heat transfer, mechanical, electromagnetic and optical properties. To accurately control the morphological surface modifications at the micro- and nanoscale and improve manufacturing techniques, we design a mathematical model of the surface self-organization process in multilayer film materials. In this paper, we consider a solid film coating with an arbitrary number of layers under plane strain conditions. The film surface has a small initial perturbation described by a periodic function. It is assumed that the evolution of the surface relief is governed by surface and volume diffusion. Based on Gibbs thermodynamics and linear theory of elasticity, we present a procedure for constructing a governing equation that gives the amplitude change of the surface perturbation with time. A parametric study of the evolution equation leads to the definition of a critical undulation wavelength that stabilizes the surface. As a numerical result, the influence of geometrical and physical parameters on the morphological stability of an isotropic two-layered film coating is analyzed.

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.

An equilibrium method for prediction of transverse shear stresses in a thick laminated plate

NASA Technical Reports Server (NTRS)

Chaudhuri, R. Z.

1986-01-01

First two equations of equilibrium are utilized to compute the transverse shear stress variation through thickness of a thick laminated plate after in-plane stresses have been computed using an assumed quadratic displacement triangular element based on transverse inextensibility and layerwise constant shear angle theory (LCST). Centroid of the triangle is the point of exceptional accuracy for transverse shear stresses. Numerical results indicate close agreement with elasticity theory. An interesting comparison between the present theory and that based on assumed stress hybrid finite element approach suggests that the latter does not satisfy the condition of free normal traction at the edge. Comparison with numerical results obtained by using constant shear angle theory suggests that LCST is close to the elasticity solution while the CST is closer to classical (CLT) solution. It is also demonstrated that the reduced integration gives faster convergence when the present theory is applied to a thin plate.

Acoustic radiation force acting on elastic and viscoelastic spherical shells placed in a plane standing wave field.

PubMed

Mitri, F G

2005-08-01

The theory of the acoustic radiation force acting on elastic spherical shells suspended in a plane standing wave field is developed in relation to their thickness and the content of their hollow regions. The theory is modified to include the effect of a hysteresis type of absorption of compressional and shear waves in the material. The fluid-loading effect on the acoustic radiation force function Y(st) is analyzed as well. Results of numerical calculations are presented for a number of elastic and viscoelastic materials, with the hollow region filled with water or air. These results show how the damping due to absorption, the change of the interior fluid inside the shells' hollow regions, and the exterior fluid surrounding their structures, affect the acoustic radiation force.

A density functional study on adsorption and dissociation of O 2 on Ir(1 0 0) surface

NASA Astrophysics Data System (ADS)

Erikat, I. A.; Hamad, B. A.; Khalifeh, J. M.

2011-06-01

The adsorption and the reaction barrier for the dissociation of O 2 on Ir(1 0 0) surface are studied using periodic self-consistent density functional theory (DFT) calculations. Dissociative adsorption is found to be energetically more favorable compared to molecular adsorption. Parallel approaches Prl1 and Prl2 on a hollow site with the same adsorption energy of -3.93 eV for both of them are found to have the most energetically preferred sites of adsorptions among all the studied cases. Hybridization between p-O 2 and d-metal orbitals is responsible for the dissociative adsorption. The minimum energy path is determined by using the nudge elastic band method (NEB). We found that the dissociation occurs immediately and very early in the dissociation path with a small activation barrier (0.26 eV), which means that molecular adsorption of O 2 on Ir(1 0 0) surface occurs at very low temperatures; this is consistent with previous experimental and theoretical studies on Ir surfaces.

Evaluation of massless-spring modeling of suspension-line elasticity during the parachute unfurling process

NASA Technical Reports Server (NTRS)

Poole, L. R.; Huckins, E. K., III

1972-01-01

A general theory on mathematical modeling of elastic parachute suspension lines during the unfurling process was developed. Massless-spring modeling of suspension-line elasticity was evaluated in detail. For this simple model, equations which govern the motion were developed and numerically integrated. The results were compared with flight test data. In most regions, agreement was satisfactory. However, poor agreement was obtained during periods of rapid fluctuations in line tension.

Dissociation of water and Acetic acid on PbS from first principles

NASA Astrophysics Data System (ADS)

Satta, Alessandra; Ruggerone, Paolo; de Giudici, Giovanni

2008-03-01

The adsorption of complex molecules at mineral surfaces are crucial ingredients for understanding the mechanisms that rule the interaction between minerals and the biosphere and for predicting both the stability and the reactivity of minerals. The present work focuses mainly on the early stages of different adsorption reactions occurring at both the cleavage surface and a high-index vicinal surface of galena (PbS). We have studied the dissociation mechanism of water and acetic acid on the galena surfaces by means of ab initio calculations within the framework of the density functional theory in the generalized gradient approximation and of pseudopotential approach. The calculated adsorption energies of the molecules indicate the stepped surface as the most reactive, as expected. The free energy surface during the reaction process has been explored via metadynamics[1]. The optimized configurations of both reactants and products obtained, were then used to accurately calculate the dissociation energy via the Nudge Elastic Band method[2]. [1] A. Laio and M. Parrinello, PNAS 99, 12562 (2002). [2] G. Mills and H. Jonsson, Phys. Rev. Lett. 72, 1124 (1994).

Superresolution near-field imaging with surface waves

NASA Astrophysics Data System (ADS)

Fu, Lei; Liu, Zhaolun; Schuster, Gerard

2018-02-01

We present the theory for near-field superresolution imaging with surface waves and time reverse mirrors (TRMs). Theoretical formulae and numerical results show that applying the TRM operation to surface waves in an elastic half-space can achieve superresolution imaging of subwavelength scatterers if they are located less than about 1/2 of the shear wavelength from the source line. We also show that the TRM operation for a single frequency is equivalent to natural migration, which uses the recorded data to approximate the Green's functions for migration, and only costs O(N4) algebraic operations for post-stack migration compared to O(N6) operations for natural pre-stack migration. Here, we assume the sources and receivers are on an N × N grid and there are N2 trial image points on the free surface. Our theoretical predictions of superresolution are validated with tests on synthetic data. The field-data tests suggest that hidden faults at the near surface can be detected with subwavelength imaging of surface waves by using the TRM operation if they are no deeper than about 1/2 the dominant shear wavelength.

Determination of the Mechanical Properties of Plasma-Sprayed Hydroxyapatite Coatings Using the Knoop Indentation Technique

NASA Astrophysics Data System (ADS)

Hasan, Md. Fahad; Wang, James; Berndt, Christopher

2015-06-01

The microhardness and elastic modulus of plasma-sprayed hydroxyapatite coatings were evaluated using Knoop indentation on the cross section and on the top surface. The effects of indentation angle, testing direction, measurement location and applied load on the microhardness and elastic modulus were investigated. The variability and distribution of the microhardness and elastic modulus data were statistically analysed using the Weibull modulus distribution. The results indicate that the dependence of microhardness and elastic modulus on the indentation angle exhibits a parabolic shape. Dependence of the microhardness values on the indentation angle follows Pythagoras's theorem. The microhardness, Weibull modulus of microhardness and Weibull modulus of elastic modulus reach their maximum at the central position (175 µm) on the cross section of the coatings. The Weibull modulus of microhardness revealed similar values throughout the thickness, and the Weibull modulus of elastic modulus shows higher values on the top surface compared to the cross section.

Engineering the Mechanical Properties of Polymer Networks with Precise Doping of Primary Defects.

PubMed

Chan, Doreen; Ding, Yichuan; Dauskardt, Reinhold H; Appel, Eric A

2017-12-06

Polymer networks are extensively utilized across numerous applications ranging from commodity superabsorbent polymers and coatings to high-performance microelectronics and biomaterials. For many applications, desirable properties are known; however, achieving them has been challenging. Additionally, the accurate prediction of elastic modulus has been a long-standing difficulty owing to the presence of loops. By tuning the prepolymer formulation through precise doping of monomers, specific primary network defects can be programmed into an elastomeric scaffold, without alteration of their resulting chemistry. The addition of these monomers that respond mechanically as primary defects is used both to understand their impact on the resulting mechanical properties of the materials and as a method to engineer the mechanical properties. Indeed, these materials exhibit identical bulk and surface chemistry, yet vastly different mechanical properties. Further, we have adapted the real elastic network theory (RENT) to the case of primary defects in the absence of loops, thus providing new insights into the mechanism for material strength and failure in polymer networks arising from primary network defects, and to accurately predict the elastic modulus of the polymer system. The versatility of the approach we describe and the fundamental knowledge gained from this study can lead to new advancements in the development of novel materials with precisely defined and predictable chemical, physical, and mechanical properties.

Effective Field Theory of Surface-mediated Forces in Soft Matter

NASA Astrophysics Data System (ADS)

Yolcu, Cem

We propose a field theoretic formalism for describing soft surfaces modified by the presence of inclusions. Examples include particles trapped at a fluid-fluid interface, proteins attached to (or embedded in) a biological membrane, etc. We derive the energy functional for near-flat surfaces by an effective field theory approach. The two disparate length scales, particle sizes and inter-particle separations, afford the expansion parameters for controlling the accuracy of the effective theory, which is arbitrary in principle. We consider the following two surface types: (i) one where tension determines the behavior, such as a fluid-fluid interface (referred to as a film), and (ii) one where bending-elasticity dominates (referred to as a membrane). We also restrict to rigid inclusions with a circular footprint, and discuss generalizations briefly. As a result of the localized constraints imposed on the surface by the inclusions, the free energy of the system depends on their spatial arrangement, i.e. forces arise between them. Such surface-mediated interactions are believed to play an important role in the aggregation behavior of colloidal particles at interfaces and proteins on membranes. The interaction free energy consists of two parts: (i) the ground-state of the surface determined by possible deformations imposed by the particles, and (ii) the fluctuation correction. The former is analogous to classical electrostatics with the height profile of the surface playing the role of the electrostatic potential, while the latter is analogous to the Casimir effect and originates from the mere presence of constraints. We compute both interactions in truncated expansions. The efficiency of the formalism allows us to predict, with remarkable ease, quite a few orders of subleading corrections to existing results which are only valid when the inclusions are infinitely far apart. We also found that the few previous studies on finite distance corrections were incomplete. In addition to pairwise additive interactions, we compute the leading behavior of several many-body interactions, as well as subleading corrections where the leading contribution was previously calculated.

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

Analytical and numerical analyses for a penny-shaped crack embedded in an infinite transversely isotropic multi-ferroic composite medium: semi-permeable electro-magnetic boundary condition

NASA Astrophysics Data System (ADS)

Zheng, R.-F.; Wu, T.-H.; Li, X.-Y.; Chen, W.-Q.

2018-06-01

The problem of a penny-shaped crack embedded in an infinite space of transversely isotropic multi-ferroic composite medium is investigated. The crack is assumed to be subjected to uniformly distributed mechanical, electric and magnetic loads applied symmetrically on the upper and lower crack surfaces. The semi-permeable (limited-permeable) electro-magnetic boundary condition is adopted. By virtue of the generalized method of potential theory and the general solutions, the boundary integro-differential equations governing the mode I crack problem, which are of nonlinear nature, are established and solved analytically. Exact and complete coupling magneto-electro-elastic field is obtained in terms of elementary functions. Important parameters in fracture mechanics on the crack plane, e.g., the generalized crack surface displacements, the distributions of generalized stresses at the crack tip, the generalized stress intensity factors and the energy release rate, are explicitly presented. To validate the present solutions, a numerical code by virtue of finite element method is established for 3D crack problems in the framework of magneto-electro-elasticity. To evaluate conveniently the effect of the medium inside the crack, several empirical formulae are developed, based on the numerical results.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Theoretical calculations of structural, electronic, and elastic properties of CdSe1-x Te x : A first principles study

NASA Astrophysics Data System (ADS)

M, Shakil; Muhammad, Zafar; Shabbir, Ahmed; Muhammad Raza-ur-rehman, Hashmi; M, A. Choudhary; T, Iqbal

2016-07-01

The plane wave pseudo-potential method was used to investigate the structural, electronic, and elastic properties of CdSe1-x Te x in the zinc blende phase. It is observed that the electronic properties are improved considerably by using LDA+U as compared to the LDA approach. The calculated lattice constants and bulk moduli are also comparable to the experimental results. The cohesive energies for pure CdSe and CdTe binary and their mixed alloys are calculated. The second-order elastic constants are also calculated by the Lagrangian theory of elasticity. The elastic properties show that the studied material has a ductile nature.

Effect of Gaussian curvature modulus on the shape of deformed hollow spherical objects.

PubMed

Quilliet, C; Farutin, A; Marmottant, P

2016-06-01

A popular description of soft membranes uses the surface curvature energy introduced by Helfrich, which includes a spontaneous curvature parameter. In this paper we show how the Helfrich formula can also be of interest for a wider class of spherical elastic surfaces, namely with shear elasticity, and likely to model other deformable hollow objects. The key point is that when a stress-free state with spherical symmetry exists before subsequent deformation, its straightforwardly determined curvature ("geometrical spontaneous curvature") differs most of the time from the Helfrich spontaneous curvature parameter that should be considered in order to have the model being correctly used. Using the geometrical curvature in a set of independent parameters unveils the role of the Gaussian curvature modulus, which appears to play on the shape of an elastic surface even though this latter is closed, contrary to what happens for surfaces without spontaneous curvature. In appendices, clues are given to apply this alternative and convenient formulation of the elastic surface model to the particular case of thin spherical shells of isotropic material (TSSIMs).

Nonstationary Deformation of an Elastic Layer with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-11-01

The analytic solution to the plane problem for an elastic layer under a nonstationary surface load is found for mixed boundary conditions: normal stress and tangential displacement are specified on one side of the layer (fourth boundary-value problem of elasticity) and tangential stress and normal displacement are specified on the other side of the layer (second boundary-value problem of elasticity). The Laplace and Fourier integral transforms are applied. The inverse Laplace and Fourier transforms are found exactly using tabulated formulas and convolution theorems for various nonstationary loads. Explicit analytical expressions for stresses and displacements are derived. Loads applied to a constant surface area and to a surface area varying in a prescribed manner are considered. Computations demonstrate the dependence of the normal stress on time and spatial coordinates. Features of wave processes are analyzed

A first principle study for the adsorption and absorption of carbon atom and the CO dissociation on Ir(100) surface

NASA Astrophysics Data System (ADS)

Erikat, I. A.; Hamad, B. A.

2013-11-01

We employ density functional theory to examine the adsorption and absorption of carbon atom as well as the dissociation of carbon monoxide on Ir(100) surface. We find that carbon atoms bind strongly with Ir(100) surface and prefer the high coordination hollow site for all coverages. In the case of 0.75 ML coverage of carbon, we obtain a bridging metal structure due to the balance between Ir-C and Ir-Ir interactions. In the subsurface region, the carbon atom prefers the octahedral site of Ir(100) surface. We find large diffusion barrier for carbon atom into Ir(100) surface (2.70 eV) due to the strong bonding between carbon atom and Ir(100) surface, whereas we find a very small segregation barrier (0.22 eV) from subsurface to the surface. The minimum energy path and energy barrier for the dissociation of CO on Ir(100) surface are obtained by using climbing image nudge elastic band. The energy barrier of CO dissociation on Ir(100) surface is found to be 3.01 eV, which is appreciably larger than the association energy (1.61 eV) of this molecule.

Electronic structure and surface properties of MgB2(0001) upon oxygen adsorption

NASA Astrophysics Data System (ADS)

Kim, Chang-Eun; Ray, Keith G.; Bahr, David F.; Lordi, Vincenzo

2018-05-01

We use density-functional theory to investigate the bulk and surface properties of MgB2. The unique bonding structure of MgB2 is investigated by Bader's atoms-in-molecules, charge density difference, and occupancy projected band structure analyses. Oxygen adsorption on the charge-depleted surfaces of MgB2 is studied by a surface potential energy mapping method, reporting a complete map including low-symmetry binding sites. The B-terminated MgB2(0001) demonstrates reconstruction of the graphenelike B layer, and the reconstructed geometry exposes a threefold site of the subsurface Mg, making it accessible from the surface. Detailed reconstruction mechanisms are studied by simulated annealing method based on ab initio molecular dynamics and nudged elastic band calculations. The surface clustering of B atoms significantly modifies the B 2 p states to occupy low energy valence states. The present paper emphasizes that a thorough understanding of the surface phase may explain an apparent inconsistency in the experimental surface characterization of MgB2. Furthermore, these results suggest that the surface passivation can be an important technical challenge when it comes to development of a superconducting device using MgB2.

A first principle study for the adsorption and absorption of carbon atom and the CO dissociation on Ir(100) surface.

PubMed

Erikat, I A; Hamad, B A

2013-11-07

We employ density functional theory to examine the adsorption and absorption of carbon atom as well as the dissociation of carbon monoxide on Ir(100) surface. We find that carbon atoms bind strongly with Ir(100) surface and prefer the high coordination hollow site for all coverages. In the case of 0.75 ML coverage of carbon, we obtain a bridging metal structure due to the balance between Ir-C and Ir-Ir interactions. In the subsurface region, the carbon atom prefers the octahedral site of Ir(100) surface. We find large diffusion barrier for carbon atom into Ir(100) surface (2.70 eV) due to the strong bonding between carbon atom and Ir(100) surface, whereas we find a very small segregation barrier (0.22 eV) from subsurface to the surface. The minimum energy path and energy barrier for the dissociation of CO on Ir(100) surface are obtained by using climbing image nudge elastic band. The energy barrier of CO dissociation on Ir(100) surface is found to be 3.01 eV, which is appreciably larger than the association energy (1.61 eV) of this molecule.

Examples of Rate-Theory Constitutive Equations Which Unify Elasticity and Plasticity

DTIC Science & Technology

1979-01-01

8217%LEYEI IAD- E Y.30Ol CONTRACT REPORT ARBRL-CR-00389 0"I o EXAMPLES OF RATE-THEORY CONSTITUTIVE p. EQUATIONS WHICH UNIFY ELASTICITY AND PLASTICITY...of Coomerce , Springfield, Virginia 22161. ° 1I The findings in this report are not to be coustrued as an official Department of the Army position...unless so designated by other authorized docunents. ’rows )J wJ e -Aumiei or xiiiif~atwui.. ’ , j~w i th~v rwport do.Jd wro Ln’matitute i ndorvemwvstI of

Crustal deformation along the San Andreas, California

NASA Technical Reports Server (NTRS)

Li, Victor C.

1992-01-01

The goal is to achieve a better understanding of the regional and local deformation and crustal straining processes in western North America, particularly the effects of the San Andreas and nearby faults on the spatial and temporal crustal deformation behavior. Construction of theoretical models based on the mechanics of coupled elastic plate, viscoelastic foundation and large scale crack mechanics provide a rational basis for the interpretation of seismic and aseismic anomalies and expedite efforts in forecasting the stability of plate boundary deformation. Special focus is placed on the three dimensional time dependent surface deformation due to localized slippage in a elastic layer coupled to a visco-elastic substrate. The numerical analysis is based on a 3-D boundary element technique. Extension to visco-elastic coupling demands the derivation of 3-D time dependent Green's function. This method was applied to analyze the viscoelastic surface displacements due to a dislocated embedded patch. Surface uplift as a function of time and position are obtained. Comparisons between surface uplift for long and short dislocated patches are made.

Multi-phase-field method for surface tension induced elasticity

NASA Astrophysics Data System (ADS)

Schiedung, Raphael; Steinbach, Ingo; Varnik, Fathollah

2018-01-01

A method, based on the multi-phase-field framework, is proposed that adequately accounts for the effects of a coupling between surface free energy and elastic deformation in solids. The method is validated via a number of analytically solvable problems. In addition to stress states at mechanical equilibrium in complex geometries, the underlying multi-phase-field framework naturally allows us to account for the influence of surface energy induced stresses on phase transformation kinetics. This issue, which is of fundamental importance on the nanoscale, is demonstrated in the limit of fast diffusion for a solid sphere, which melts due to the well-known Gibbs-Thompson effect. This melting process is slowed down when coupled to surface energy induced elastic deformation.

Strength conditions for the elastic structures with a stress error

NASA Astrophysics Data System (ADS)

Matveev, A. D.

2017-10-01

As is known, the constraints (strength conditions) for the safety factor of elastic structures and design details of a particular class, e.g. aviation structures are established, i.e. the safety factor values of such structures should be within the given range. It should be noted that the constraints are set for the safety factors corresponding to analytical (exact) solutions of elasticity problems represented for the structures. Developing the analytical solutions for most structures, especially irregular shape ones, is associated with great difficulties. Approximate approaches to solve the elasticity problems, e.g. the technical theories of deformation of homogeneous and composite plates, beams and shells, are widely used for a great number of structures. Technical theories based on the hypotheses give rise to approximate (technical) solutions with an irreducible error, with the exact value being difficult to be determined. In static calculations of the structural strength with a specified small range for the safety factors application of technical (by the Theory of Strength of Materials) solutions is difficult. However, there are some numerical methods for developing the approximate solutions of elasticity problems with arbitrarily small errors. In present paper, the adjusted reference (specified) strength conditions for the structural safety factor corresponding to approximate solution of the elasticity problem have been proposed. The stress error estimation is taken into account using the proposed strength conditions. It has been shown that, to fulfill the specified strength conditions for the safety factor of the given structure corresponding to an exact solution, the adjusted strength conditions for the structural safety factor corresponding to an approximate solution are required. The stress error estimation which is the basis for developing the adjusted strength conditions has been determined for the specified strength conditions. The adjusted strength conditions presented by allowable stresses are suggested. Adjusted strength conditions make it possible to determine the set of approximate solutions, whereby meeting the specified strength conditions. Some examples of the specified strength conditions to be satisfied using the technical (by the Theory of Strength of Materials) solutions and strength conditions have been given, as well as the examples of stress conditions to be satisfied using approximate solutions with a small error.

Manpower Theory and Policy and the Residual Occupational Elasticity of Substitution.

ERIC Educational Resources Information Center

Rostker, Bernard Daniel

By developing the short-run policy implications of a structurally disaggregated labor market, this study attempts to show that fiscal and manpower policies are complementary means to achieve full employment. Using a constant elasticity of substitution production function, the study demonstrates mathematically that the smaller the residual…

Evidence of rayleigh-hertz surface waves and shear stiffness anomaly in granular media.

PubMed

Bonneau, L; Andreotti, B; Clément, E

2008-09-12

Using the nonlinear dependence of sound propagation speed with pressure, we evidence the anomalous elastic softness of a granular packing in the vicinity of the jamming transition. Under gravity and close to a free surface, the acoustic propagation is only possible through surface modes guided by the stiffness gradient. These Rayleigh-Hertz modes are evidenced in a controlled laboratory experiment. The shape and the dispersion relation of both transverse and sagittal modes are compared to the prediction of nonlinear elasticity including finite size effects. These results allow one to access the elastic properties of the packing under vanishing confining pressure.

Application of the aerodynamic energy concept to flutter suppression and gust alleviation by use of active controls

NASA Technical Reports Server (NTRS)

Nissim, E.; Caspi, A.; Lottati, I.

1976-01-01

The effects of active controls on flutter suppression and gust alleviation of the Arava twin turboprop STOL transport and the Westwind twinjet business transport are investigated. The active control surfaces are introduced in pairs which include, in any chosen wing strip, a 20-percent chord leading-edge control and a 20-percent chord trailing-edge control. Each control surface is driven by a combined linear-rotational sensor system located on the activated strip. The control law is based on the concept of aerodynamic energy and utilizes previously optimized control law parameters based on two-dimensional aerodynamic theory. The best locations of the activated system along the span of the wing are determined for bending-moment alleviation, reduction in fuselage accelerations, and flutter suppression. The effectiveness of the activated system over a wide range of maximum control deflections is also determined. Two control laws are investigated. The first control law utilizes both rigid-body and elastic contributions of the motion. The second control law employs primarily the elastic contribution of the wing and leads to large increases in the activated control effectiveness as compared with the basic control law. The results indicate that flutter speed can be significantly increased (over 70 percent increase) and that the bending moment due to gust loading can be almost totally eliminated by a control system of about 10 to 20 percent span with reasonable control-surface rotations.

Wrinkling Phenomena to Explain Vertical Fold Defects in DC-Cast Al-Mg4.5

NASA Astrophysics Data System (ADS)

Davis, J. Lee; Mendez, Patricio F.

Some aluminum ingots cast by the direct chill method are subject to surface defects on the molten ingot head during casting while others are not. These defects -commonly called "vertical folds" -are frozen into the casting and must be removed prior to rolling. Vertical folds are found on top of the molten ingot surface where areas of thin oxide are (a) bounded by physical constraints and (b) stretched. Physical constraints include (1) substantially thicker oxide or (2) a refractory skim ring adjacent to the thin oxide. The mechanism of wrinkling is suggested for the formation of vertical folds. Wrinkling behavior is described by physical expressions for an elastic sheet in tension whose behavior depends upon thickness h, length L, Young's modulus E, and Poisson's ratio v. The depth and frequency of folds in the thin, elastic sheet parallel to the tensile axis between the two "constraints" can be calculated from these parameters. The observed frequency (and amplitude) of vertical folds in DC-cast aluminum has been found to obey similar wrinkling laws. The frequency-dependence (λ) is examined and found to be related to classic wrinkling parameters but with significant scaling deviations. These deviations may be related to the pseudo-plasticity (self-healing behavior) of the oxide film on the molten surface. A wrinkling model coupled with pseudo-plasticity predicts subtle behaviors in DC casting of Al-Mg4.5 that are not explained by other theories.

Diffraction of electrons at intermediate energies

NASA Astrophysics Data System (ADS)

Ascolani, H.; Barrachina, R. O.; Guraya, M. M.; Zampieri, G.

1992-08-01

We present a theory of the elastic scattering of electrons from crystalline surfaces that contains both low-energy-electron-diffraction (LEED) effects at low energies and x-ray-photoelectron- and Auger-electron-diffraction (XPD/AED) effects at intermediate energies. The theory is based on a cluster-type approach to the scattering problem and includes temperature effects. The transition from one regime to the other may be explained as follows: At low energies all the scattered waves add coherently, and the intensity is dominated by LEED effects. At intermediate energies the thermal vibration of the atoms destroys the long-range coherency responsible for the LEED peaks, but affects little the interference of those waves that share parts of their paths inside the solid. Thus, the interference of these waves comes to dominate the intensity, giving rise to structures similar to those observed in XPD/AED experiments. We perform a calculation of the elastic reflection of electrons from Cu(001) that is in good agreement with the experiment in the range 200-1500 eV. At low energies the intensity is dominated by LEED peaks; at 400 eV LEED peaks and XPD/AED structures coexist; and above this energy the intensity is dominated by the latter. We analyze the contributions to the intensity at intermediate energies of the interferences in the incoming and outgoing parts of the electron path.

Receptivity of the Boundary Layer to Vibrations of the Wing Surface

NASA Astrophysics Data System (ADS)

Bernots, Tomass; Ruban, Anatoly; Pryce, David; Laminar Flow Control UK Group Team

2014-11-01

In this work we study generation of Tollmien-Schlichting (T-S) waves in the boundary layer due to elastic vibrations of the wing surface. The flow is investigated based on the asymptotic analysis of the Navier-Stokes equations at large values of the Reynolds number. It is assumed that in the spectrum of the wing vibrations there is a harmonic which comes in resonance with the T-S wave on the lower branch of the stability curve. It was found that the vibrations of the wing surface produce pressure perturbations in the flow outside the boundary layer which can be calculated with the help of the piston theory. As the pressure perturbations penetrate into the boundary layer, a Stokes layer forms on the wing surface which appears to be influenced significantly by the compressibility of the flow, and is incapable of producing the T-S waves. The situation changes when the Stokes layer encounters an roughness; near which the flow is described using the triple-deck theory. The solution of the triple-deck problem can be found in an analytic form. Our main concern is with the flow behaviour downstream of the roughness and, in particular, with the amplitude of the generated Tollmien-Schlichting waves. This research was performed in the Laminar Flow Control Centre (LFC-UK) at Imperial College London. The centre is supported by EPSRC, Airbus UK and EADS Innovation Works.

The hydrodynamics of bubble rise and impact with solid surfaces.

PubMed

Manica, Rogerio; Klaseboer, Evert; Chan, Derek Y C

2016-09-01

A bubble smaller than 1mm in radius rises along a straight path in water and attains a constant speed due to the balance between buoyancy and drag force. Depending on the purity of the system, within the two extreme limits of tangentially immobile or mobile boundary conditions at the air-water interface considerably different terminal speeds are possible. When such a bubble impacts on a horizontal solid surface and bounces, interesting physics can be observed. We study this physical phenomenon in terms of forces, which can be of colloidal, inertial, elastic, surface tension and viscous origins. Recent advances in high-speed photography allow for the observation of phenomena on the millisecond scale. Simultaneous use of such cameras to visualize both rise/deformation and the dynamics of the thin film drainage through interferometry are now possible. These experiments confirm that the drainage process obeys lubrication theory for the spectrum of micrometre to millimetre-sized bubbles that are covered in this review. We aim to bridge the colloidal perspective at low Reynolds numbers where surface forces are important to high Reynolds number fluid dynamics where the effect of the surrounding flow becomes important. A model that combines a force balance with lubrication theory allows for the quantitative comparison with experimental data under different conditions without any fitting parameter. Copyright © 2016 Elsevier B.V. All rights reserved.

Carbonation of wollastonite(001) competing hydration: microscopic insights from ion spectroscopy and density functional theory.

PubMed

Longo, Roberto C; Cho, Kyeongjae; Brüner, Philipp; Welle, Alexander; Gerdes, Andreas; Thissen, Peter

2015-03-04

In this paper, we report about the influence of the chemical potential of water on the carbonation reaction of wollastonite (CaSiO3) as a model surface of cement and concrete. Total energy calculations based on density functional theory combined with kinetic barrier predictions based on nudge elastic band method show that the exposure of the water-free wollastonite surface to CO2 results in a barrier-less carbonation. CO2 reacts with the surface oxygen and forms carbonate (CO3(2-)) complexes together with a major reconstruction of the surface. The reaction comes to a standstill after one carbonate monolayer has been formed. In case one water monolayer is covering the wollastonite surface, the carbonation is no more barrier-less, yet ending in a localized monolayer. Covered with multilayers of water, the thermodynamic ground state of the wollastonite completely changes due to a metal-proton exchange reaction (also called early stage hydration) and Ca(2+) ions are partially removed from solid phase into the H2O/wollastonite interface. Mobile Ca(2+) reacts again with CO2 and forms carbonate complexes, ending in a delocalized layer. By means of high-resolution time-of-flight secondary-ion mass spectrometry images, we confirm that hydration can lead to a partially delocalization of Ca(2+) ions on wollastonite surfaces. Finally, we evaluate the impact of our model surface results by the meaning of low-energy ion-scattering spectroscopy combined with careful discussion about the competing reactions of carbonation vs hydration.

Core muscle activity in a series of balance exercises with different stability conditions.

PubMed

Calatayud, Joaquin; Borreani, Sebastien; Martin, Julio; Martin, Fernando; Flandez, Jorge; Colado, Juan C

2015-07-01

Literature that provides progression models based on core muscle activity and postural manipulations is scarce. The purpose of this study was to investigate the core muscle activity in a series of balance exercises with different stability levels and additional elastic resistance. A descriptive study of electromyography (EMG) was performed with forty-four healthy subjects that completed 12 exercises in a random order. Exercises were performed unipedally or bipedally with or without elastic tubing as resistance on various unstable (uncontrolled multiaxial and uniaxial movement) and stable surfaces. Surface EMG on the lumbar multífidus spinae (LM), thoracic multífidus spinae (TM), lumbar erector spinae (LE), thoracic erector spinae (TE) and gluteus maximus (GM), on the dominant side of the body were collected to quantify the amount of muscle activity and were expressed as a % of the maximum voluntary isometric contraction (MVIC). Significant differences (p<.001) were found between exercises. The three unipedal standing exercises with additional elastic resistance generated the greatest EMG values, ranging from 19% MVIC to 30% MVIC. Postural manipulations with additional elastic resistance and/or unstable devices increase core muscle activity. An adequate exercise progression based on global core EMG could start with seated positions, progressing to bipedal standing stance (i.e., from either multiaxial or stable surface to uniaxial surface). Following this, unipedal standing positions may be performed (i.e., from either multiaxial or stable surface to uniaxial surface) and finally, elastic resistance must be added in order to increase EMG levels (i.e., from stable surface progressing to any of the used unstable surfaces). Copyright © 2015 Elsevier B.V. All rights reserved.

The dependency of adhesion and friction on electrostatic attraction

NASA Astrophysics Data System (ADS)

Persson, B. N. J.

2018-04-01

I develop a general mean-field theory for the influence of electrostatic attraction between two solids on the contact mechanics. I assume elastic solids with random surface roughness. I consider two cases, namely, with and without an electrically insulating layer between the conducting solids. The former case is important for, e.g., the finger-touch screen interaction. I study how the electrostatic attraction influences the adhesion and friction. For the case of an insulating layer, I find that when the applied nominal contact pressure is relatively small, as the applied voltage increases, there is a sharp increase in the contact area, and hence in the friction, at a critical voltage.

Hydrodynamic Impact of a System with a Single Elastic Mode II : Comparison of Experimental Force and Response with Theory

NASA Technical Reports Server (NTRS)

Miller, Robert W; Merten, Kenneth F

1952-01-01

Hydrodynamic impact tests were made on an elastic model approximating a two-mass spring system to determine experimentally the effects of structural flexibility on the hydrodynamic loads encountered during seaplane landing impacts and to correlate the results with theory. A flexible seaplane was represented by a two-mass spring system consisting of a rigid prismatic float connected to a rigid upper mass by an elastic structure. The model had a ratio of sprung mass to hull mass of 0.6 and a natural frequency of 3.0 cycles per second. The tests were conducted in smooth water at fixed trims and included both high and low flight-path angles and a range of velocity. Theoretical and experimental comparisons indicated that the theoretical results agreed well with the experimental results.

Determining elastic moduli of materials in pavement systems by surface deflection data : a feasibility study.

DOT National Transportation Integrated Search

1975-01-01

The determination of the elastic, or Young's, modulus, E, of the materials in each layer in an n-layered pavement system given the number, order, thicknesses, and Poisson's ratios of the layers, and the surface load and deflection data, is not possib...

Droplets move over viscoelastic substrates by surfing a ridge

PubMed Central

Karpitschka, S.; Das, S.; van Gorcum, M.; Perrin, H.; Andreotti, B.; Snoeijer, J. H.

2015-01-01

Liquid drops on soft solids generate strong deformations below the contact line, resulting from a balance of capillary and elastic forces. The movement of these drops may cause strong, potentially singular dissipation in the soft solid. Here we show that a drop on a soft substrate moves by surfing a ridge: the initially flat solid surface is deformed into a sharp ridge whose orientation angle depends on the contact line velocity. We measure this angle for water on a silicone gel and develop a theory based on the substrate rheology. We quantitatively recover the dynamic contact angle and provide a mechanism for stick–slip motion when a drop is forced strongly: the contact line depins and slides down the wetting ridge, forming a new one after a transient. We anticipate that our theory will have implications in problems such as self-organization of cell tissues or the design of capillarity-based microrheometers. PMID:26238436

Electrostatic theory of the assembly of PAMAM dendrimers and DNA.

PubMed

Perico, Angelo

2016-05-01

The electrostatic interactions mediated by counterions between a cationic PAMAM dendrimer, modelized as a sphere of radius and cationic surface charge highly increasing with generation, and a DNA, modelized as an anionic elastic line, are analytically calculated in the framework of condensation theory. Under these interactions the DNA is wrapped around the sphere. For excess phosphates relative to dendrimer primary amines, the free energy of the DNA-dendrimer complex displays an absolute minimum when the complex is weakly negatively overcharged. This overcharging opposes gene delivery. For a highly positive dendrimer and a DNA fixed by experimental conditions to a number of phosphates less than the number of dendrimer primary amines, excess amine charges, the dendrimer may at the same time bind stably DNA and interact with negative cell membranes to activate cell transfection in fair agreement with molecular simulations and experiments. © 2016 Wiley Periodicals, Inc.

Development of basic theories and techniques for determining stresses in rotating turbine or compressor blades

NASA Technical Reports Server (NTRS)

Chien, C. H.; Swinson, W. F.; Turner, J. L.; Moslehy, F. A.; Ranson, W. F.

1980-01-01

A method for measuring in-plane displacement of a rotating structure by using two laser speckle photographs is described. From the displacement measurements one can calculate strains and stresses due to a centrifugal load. This technique involves making separate speckle photographs of a test model. One photograph is made with the model loaded (model is rotating); the second photograph is made with no load on the model (model is stationary). A sandwich is constructed from the two speckle photographs and data are recovered in a manner similar to that used with conventional speckle photography. The basic theory, experimental procedures of this method, and data analysis of a simple rotating specimen are described. In addition the measurement of in-plane surface displacement components of a deformed solid, and the application of the coupled laser speckle interferometry and boundary-integral solution technique to two dimensional elasticity problems are addressed.

Finite difference elastic wave modeling with an irregular free surface using ADER scheme

NASA Astrophysics Data System (ADS)

Almuhaidib, Abdulaziz M.; Nafi Toksöz, M.

2015-06-01

In numerical modeling of seismic wave propagation in the earth, we encounter two important issues: the free surface and the topography of the surface (i.e. irregularities). In this study, we develop a 2D finite difference solver for the elastic wave equation that combines a 4th- order ADER scheme (Arbitrary high-order accuracy using DERivatives), which is widely used in aeroacoustics, with the characteristic variable method at the free surface boundary. The idea is to treat the free surface boundary explicitly by using ghost values of the solution for points beyond the free surface to impose the physical boundary condition. The method is based on the velocity-stress formulation. The ultimate goal is to develop a numerical solver for the elastic wave equation that is stable, accurate and computationally efficient. The solver treats smooth arbitrary-shaped boundaries as simple plane boundaries. The computational cost added by treating the topography is negligible compared to flat free surface because only a small number of grid points near the boundary need to be computed. In the presence of topography, using 10 grid points per shortest shear-wavelength, the solver yields accurate results. Benchmark numerical tests using several complex models that are solved by our method and other independent accurate methods show an excellent agreement, confirming the validity of the method for modeling elastic waves with an irregular free surface.

Rainbows in rotationally inelastic scattering: a comparative study of different model potential surfaces and dynamical approximations

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

Schinke, R.; Korsch, H.J.; Poppe, D.

1982-12-15

Rainbow structures in rotationally elastic and inelastic differential cross sections in atom--diatom collisions are investigated by comparison of three model potential energy surfaces labeled I, II, and III which are represented by V(R,..gamma..) = V/sub 0/(R)+V/sub 2/(R)P/sub 2/(cos ..gamma..). The cross sections are calculated within the quantal infinite-order-sudden (IOS) approximation. The anisotropic part V/sub 2/ is the same for all potentials and purely repulsive. The isotropic part V/sub 0/ for potential I is also repulsive and the differential cross sections show the well-studied rotational rainbow structures. Structural changes occur for collisions in potential II and III which have V/sub 0/more » terms being attractive at intermediate and large atom--molecule separations and having well depths of 10% and 25% of the collision energy, respectively. For example, the elastic cross section has no classical rainbow in the case of potential I but three in the case of potential III. The rainbow structures are analyzed within the classical and semiclassical versions of the IOS approximation and interpreted in terms of catastrophe theory. The quantitative comparison of the classical with the quantal IOS cross sections manifests possible quantum effects, i.e., tunneling into nonclassical regions and interference effects due to the superposition of several contributions (up to six in the present study). They can be very prominent and thus we conclude that much caution is needed if experimental data are compared with classical calculations. The accuracy of the IOS approximation is tested by comparison of classical IOS cross sections with cross sections obtained from exact classical trajectory calculations. The agreement is generally good with the exemption of the rainbow region and small angle, rotationally elastic scattering.« less

Finite gradient elasticity and plasticity: a constitutive thermodynamical framework

NASA Astrophysics Data System (ADS)

Bertram, Albrecht

2016-05-01

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

Measurements of radiated elastic wave energy from dynamic tensile cracks

NASA Technical Reports Server (NTRS)

Boler, Frances M.

1990-01-01

The role of fracture-velocity, microstructure, and fracture-energy barriers in elastic wave radiation during a dynamic fracture was investigated in experiments in which dynamic tensile cracks of two fracture cofigurations of double cantilever beam geometry were propagating in glass samples. The first, referred to as primary fracture, consisted of fractures of intact glass specimens; the second configuration, referred to as secondary fracture, consisted of a refracture of primary fracture specimens which were rebonded with an intermittent pattern of adhesive to produce variations in fracture surface energy along the crack path. For primary fracture cases, measurable elastic waves were generated in 31 percent of the 16 fracture events observed; the condition for radiation of measurable waves appears to be a local abrupt change in the fracture path direction, such as occurs when the fracture intersects a surface flaw. For secondary fractures, 100 percent of events showed measurable elastic waves; in these fractures, the ratio of radiated elastic wave energy in the measured component to fracture surface energy was 10 times greater than for primary fracture.

Atomistic study of the graphene nanobubbles

NASA Astrophysics Data System (ADS)

Iakovlev, Evgeny; Zhilyaev, Petr; Akhatov, Iskander

2017-11-01

A two-dimensional (2D) heterostructures can be created using 2D crystals stacking method. Substance can be trapped between the layers which leads to formation of the surface nanobubbles. We study nanobubbles trapped between graphene layers with argon atoms inside using molecular dynamics approach. For bubbles with radius in range 7-34 nm the solid close-packed state of argon is found, although according to bulk argon phase diagram the fluid phase must be observed. The universal shape scaling (constant ratio of height to radius), which is found experimentally and proved by the theory of elasticity of membranes, is also observed in our atomistic simulations. An unusual pancake shape (extremely small height to radius ratio) is found for smallest nanobubble with radius 7 nm. The nanobubbles with similar shape were experimentally observed at the interface between water and hydrophobic surface.

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.

Theory of twisted nonuniformly heated bars

NASA Technical Reports Server (NTRS)

Shorr, B. F.

1980-01-01

Nonlineary distributed stresses in twisted nonuniformly heated bars of arbitrary cross section are calculated taking into account various elasticity parameters. The approximate theory is shown to be sufficiently general and accurate by comparison with experimental data.

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.

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

PubMed

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

2017-03-01

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

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.

Form finding in elastic gridshells.

PubMed

Baek, Changyeob; Sageman-Furnas, Andrew O; Jawed, Mohammad K; Reis, Pedro M

2018-01-02

Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We study elastic gridshells with a focus on the rational design of the final shapes. Our precision desktop experiments exhibit complex geometries, even from seemingly simple initial configurations and actuation processes. The numerical simulations capture this nonintuitive behavior with excellent quantitative agreement, allowing for an exploration of parameter space that reveals multistable states. We then turn to the theory of smooth Chebyshev nets to address the inverse design of hemispherical elastic gridshells. The results suggest that rod inextensibility, not elastic response, dictates the zeroth-order shape of an actuated elastic gridshell. As it turns out, this is the shape of a common household strainer. Therefore, the geometry of Chebyshev nets can be further used to understand elastic gridshells. In particular, we introduce a way to quantify the intrinsic shape of the empty, but enclosed regions, which we then use to rationalize the nonlocal deformation of elastic gridshells to point loading. This justifies the observed difficulty in form finding. Nevertheless, we close with an exploration of concatenating multiple elastic gridshell building blocks.

Form finding in elastic gridshells

NASA Astrophysics Data System (ADS)

Baek, Changyeob; Sageman-Furnas, Andrew O.; Jawed, Mohammad K.; Reis, Pedro M.

2018-01-01

Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We study elastic gridshells with a focus on the rational design of the final shapes. Our precision desktop experiments exhibit complex geometries, even from seemingly simple initial configurations and actuation processes. The numerical simulations capture this nonintuitive behavior with excellent quantitative agreement, allowing for an exploration of parameter space that reveals multistable states. We then turn to the theory of smooth Chebyshev nets to address the inverse design of hemispherical elastic gridshells. The results suggest that rod inextensibility, not elastic response, dictates the zeroth-order shape of an actuated elastic gridshell. As it turns out, this is the shape of a common household strainer. Therefore, the geometry of Chebyshev nets can be further used to understand elastic gridshells. In particular, we introduce a way to quantify the intrinsic shape of the empty, but enclosed regions, which we then use to rationalize the nonlocal deformation of elastic gridshells to point loading. This justifies the observed difficulty in form finding. Nevertheless, we close with an exploration of concatenating multiple elastic gridshell building blocks.

A comparison of the uniaxial deformation of copper and nickel (1 1 19) surfaces: a molecular dynamics study

PubMed Central

Pukšič, Nuša; Jenko, Monika; Godec, Matjaž; McGuiness, Paul J.

2017-01-01

While a lot is known about the deformation of metallic surfaces from experiments, elasticity theory and simulations, this investigation represents the first molecular-dynamics-based simulation of uniaxial deformation for the vicinal surfaces in a comparison of copper and nickel. These vicinal surfaces are composed of terraces divided by equidistant, mono-atomic steps. The periodicity of vicinals makes them good candidates for the study of the surface steps’ influences on surface dynamics. The simulations of tensile and compressive uniaxial deformations were performed for the (1 1 19) vicinal surfaces. Since the steps on the surfaces serve as stress concentrators, the first defects were expected to nucleate here. In the case of copper, this was found to be the case. In the case of nickel, however, dislocations nucleated beneath the near-surface layer affected by the displacement field generated by the steps. Slip was hindered at the surface step by the vortex in the displacement field. The differences in the deformation mechanisms for the Ni(1 1 19) and Cu(1 1 19) surfaces can be linked to the differences in their displacement fields. This could lead to novel bottom-up approaches to the nanostructuring of surfaces using strain. PMID:28169377

Surface-wave amplitude analysis for array data with non-linear waveform fitting: Toward high-resolution attenuation models of the upper mantle

NASA Astrophysics Data System (ADS)

Hamada, K.; Yoshizawa, K.

2013-12-01

Anelastic attenuation of seismic waves provides us with valuable information on temperature and water content in the Earth's mantle. While seismic velocity models have been investigated by many researchers, anelastic attenuation (or Q) models have yet to be investigated in detail mainly due to the intrinsic difficulties and uncertainties in the amplitude analysis of observed seismic waveforms. To increase the horizontal resolution of surface wave attenuation models on a regional scale, we have developed a new method of fully non-linear waveform fitting to measure inter-station phase velocities and amplitude ratios simultaneously, using the Neighborhood Algorithm (NA) as a global optimizer. Model parameter space (perturbations of phase speed and amplitude ratio) is explored to fit two observed waveforms on a common great-circle path by perturbing both phase and amplitude of the fundamental-mode surface waves. This method has been applied to observed waveform data of the USArray from 2007 to 2008, and a large-number of inter-station amplitude and phase speed data are corrected in a period range from 20 to 200 seconds. We have constructed preliminary phase speed and attenuation models using the observed phase and amplitude data, with careful considerations of the effects of elastic focusing and station correction factors for amplitude data. The phase velocity models indicate good correlation with the conventional tomographic results in North America on a large-scale; e.g., significant slow velocity anomaly in volcanic regions in the western United States. The preliminary results of surface-wave attenuation achieved a better variance reduction when the amplitude data are inverted for attenuation models in conjunction with corrections for receiver factors. We have also taken into account the amplitude correction for elastic focusing based on a geometrical ray theory, but its effects on the final model is somewhat limited and our attenuation model show anti-correlation with the phase velocity models; i.e., lower attenuation is found in slower velocity areas that cannot readily be explained by the temperature effects alone. Some former global scale studies (e.g., Dalton et al., JGR, 2006) indicated that the ray-theoretical focusing corrections on amplitude data tend to eliminate such anti-correlation of phase speed and attenuation, but this seems not to work sufficiently well for our regional scale model, which is affected by stronger velocity gradient relative to global-scale models. Thus, the estimated elastic focusing effects based on ray theory may be underestimated in our regional-scale studies. More rigorous ways to estimate the focusing corrections as well as data selection criteria for amplitude measurements are required to achieve a high-resolution attenuation models on regional scales in the future.

The design, analysis and experimental evaluation of an elastic model wing

NASA Technical Reports Server (NTRS)

Cavin, R. K., III; Thisayakorn, C.

1974-01-01

An elastic orbiter model was developed to evaluate the effectiveness of aeroelasticity computer programs. The elasticity properties were introduced by constructing beam-like straight wings for the wind tunnel model. A standard influence coefficient mathematical model was used to estimate aeroelastic effects analytically. In general good agreement was obtained between the empirical and analytical estimates of the deformed shape. However, in the static aeroelasticity case, it was found that the physical wing exhibited less bending and more twist than was predicted by theory.

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.

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).

Anisotropy and temperature dependence of structural, thermodynamic, and elastic properties of crystalline cellulose Iβ: a first-principles investigation

Treesearch

ShunLi Shang; Louis G. Hector Jr.; Paul Saxe; Zi-Kui Liu; Robert J. Moon; Pablo D. Zavattieri

2014-01-01

Anisotropy and temperature dependence of structural, thermodynamic and elastic properties of crystalline cellulose Iβ were computed with first-principles density functional theory (DFT) and a semi-empirical correction for van der Waals interactions. Specifically, we report the computed temperature variation (up to 500...

Teaching Price, Income, and Cross Elasticity of Demand: Another Approach.

ERIC Educational Resources Information Center

Zahka, William J.

One of the most important, yet difficult concepts to teach in an undergraduate course in intermediate microeconomics is the all-embracing concept of elasticity of demand. This paper details a four part teaching approach developed to make this most important aspect of microeconomic theory more understandable. Part 1 develops the approach for…

An Laudau-Lifschitz theory based algorithm on calculating post-buckling configuration of a rod buckling in elastic media

NASA Astrophysics Data System (ADS)

Huang, Shicheng; Tan, Likun; Hu, Nan; Grover, Hannah; Chu, Kevin; Chen, Zi

This reserach introduces a new numerical approach of calculating the post-buckling configuration of a thin rod embedded in elastic media. The theoretical base is the governing ODEs describing the balance of forces and moments, the length conservation, and the physics of bending and twisting by Laudau and Lifschitz. The numerical methods applied in the calculation are continuation method and Newton's method of iteration in combination with spectrum method. To the authors' knowledge, it is the first trial of directly applying the L-L theory to numerically studying the phenomenon of rod buckling in elastic medium. This method accounts for nonlinearity of geometry, thus is capable of calculating large deformation. The stability of this method is another advantage achieved by expressing the governing equations in a set of first-order derivative form. The wave length, amplitude, and decay effect all agree with the experiment without any further assumptions. This program can be applied to different occasions with varying stiffness of the elastic medai and rigidity of the rod.

Velocity and attenuation of shear waves in the phantom of a muscle-soft tissue matrix with embedded stretched fibers

NASA Astrophysics Data System (ADS)

Rudenko, O. V.; Tsyuryupa, S. N.; Sarvazyan, A. P.

2016-09-01

We develop a theory of the elasticity moduli and dissipative properties of a composite material: a phantom simulating muscle tissue anisotropy. The model used in the experiments was made of a waterlike polymer with embedded elastic filaments imitating muscle fiber. In contrast to the earlier developed phenomenological theory of the anisotropic properties of muscle tissue, here we obtain the relationship of the moduli with characteristic sizes and moduli making up the composite. We introduce the effective elasticity moduli and viscosity tensor components, which depend on stretching of the fibers. We measure the propagation velocity of shear waves and the shear viscosity of the model for regulated tension. Waves were excited by pulsed radiation pressure generated by modulated focused ultrasound. We show that with increased stretching of fibers imitating muscle contraction, an increase in both elasticity and viscosity takes place, and this effect depends on the wave propagation direction. The results of theoretical and experimental studies support our hypothesis on the protective function of stretched skeletal muscle, which protects bones and joints from trauma.

Viscoplasticity based on overstress with a differential growth law for the equilibrium stress

NASA Technical Reports Server (NTRS)

Krempl, E.; Mcmahon, J. J.; Yao, D.

1985-01-01

Two coupled, nonlinear differential equations are proposed for the modeling of the elastic and rate (time) dependent inelastic behavior of structural metals in the absence of recovery and aging. The structure of the model is close to the unified theories but contains essential differences. It is shown that the model reproduces almost elastic regions upon initial loading and in the unloading regions of the hysteresis loop. Under loading, unloading and reloading in strain control the model simulated the experimentally observed sharp transition from nearly elastic to inelastic behavior. When a formulation akin to existing unified theories is adopted the almost elastic regions reduce the points and the transition upon reloading is very gradual. For different formulations the behavior under sudden in(de)creases of the strain rate by two orders of magnitude is simulated by numerical experiments and differences are noted. The model represents cyclically neutral behavior and contains three constants and two positive, decreasing functions. The determination of constants and functions from monotonic loading with strain rate changes and relaxation periods is described.

Elastic medium equivalent to Fresnel's double-refraction crystal.

PubMed

Carcione, José M; Helbig, Klaus

2008-10-01

In 1821, Fresnel obtained the wave surface of an optically biaxial crystal, assuming that light waves are vibrations of the ether in which longitudinal vibrations (P waves) do not propagate. An anisotropic elastic medium mathematically analogous to Fresnel's crystal exists. The medium has four elastic constants: a P-wave modulus, associated with a spherical P wave surface, and three elastic constants, c(44), c(55), and c(66), associated with the shear waves, which are mathematically equivalent to the three dielectric permittivity constants epsilon(11), epsilon(22), and epsilon(33) as follows: mu(0)epsilon(11)<==>rho/c(44), mu(0)epsilon(22)<==>rho/c(55), mu(0)epsilon(33)<==>rho/c(66), where mu(0) is the magnetic permeability of vacuum and rho is the mass density. These relations also represent the equivalence between the elastic and electromagnetic wave velocities along the principal axes of the medium. A complete mathematical equivalence can be obtained by setting the P-wave modulus equal to zero, but this yields an unstable elastic medium (the hypothetical ether). To obtain stability the P-wave velocity has to be assumed infinite (incompressibility). Another equivalent Fresnel's wave surface corresponds to a medium with anomalous polarization. This medium is physically unstable even for a nonzero P-wave modulus.

Free vibration analysis of embedded magneto-electro-thermo-elastic cylindrical nanoshell based on the modified couple stress theory

NASA Astrophysics Data System (ADS)

Ghadiri, Majid; Safarpour, Hamed

2016-09-01

In this paper, size-dependent effect of an embedded magneto-electro-elastic (MEE) nanoshell subjected to thermo-electro-magnetic loadings on free vibration behavior is investigated. Also, the surrounding elastic medium has been considered as the model of Winkler characterized by the spring. The size-dependent MEE nanoshell is investigated on the basis of the modified couple stress theory. Taking attention to the first-order shear deformation theory (FSDT), the modeled nanoshell and its equations of motion are derived using principle of minimum potential energy. The accuracy of the presented model is validated with some cases in the literature. Finally, using the Navier-type method, an analytical solution of governing equations for vibration behavior of simply supported MEE cylindrical nanoshell under combined loadings is presented and the effects of material length scale parameter, temperature changes, external electric potential, external magnetic potential, circumferential wave numbers, constant of spring, shear correction factor and length-to-radius ratio of the nanoshell on natural frequency are identified. Since there has been no research about size-dependent analysis MEE cylindrical nanoshell under combined loadings based on FSDT, numerical results are presented to be served as benchmarks for future analysis of MEE nanoshells using the modified couple stress theory.

The Effect of Sedimentary Basins on Through-Passing Short-Period Surface Waves

NASA Astrophysics Data System (ADS)

Feng, L.; Ritzwoller, M. H.

2017-12-01

Surface waves propagating through sedimentary basins undergo elastic wave field complications that include multiple scattering, amplification, the formation of secondary wave fronts, and subsequent wave front healing. Unless these effects are accounted for accurately, they may introduce systematic bias to estimates of source characteristics, the inference of the anelastic structure of the Earth, and ground motion predictions for hazard assessment. Most studies of the effects of basins on surface waves have centered on waves inside the basins. In contrast, we investigate wave field effects downstream from sedimentary basins, with particular emphasis on continental basins and propagation paths, elastic structural heterogeneity, and Rayleigh waves at 10 s period. Based on wave field simulations through a recent 3D crustal and upper mantle model of East Asia, we demonstrate significant Rayleigh wave amplification downstream from sedimentary basins in eastern China such that Ms measurements obtained on the simulated wave field vary by more than a magnitude unit. We show that surface wave amplification caused by basins results predominantly from elastic focusing and that amplification effects produced through 3D basin models are reproduced using 2D membrane wave simulations through an appropriately defined phase velocity map. The principal characteristics of elastic focusing in both 2D and 3D simulations include (1) retardation of the wave front inside the basins; (2) deflection of the wave propagation direction; (3) formation of a high amplitude lineation directly downstream from the basin bracketed by two low amplitude zones; and (4) formation of a secondary wave front. Finally, by comparing the impact of elastic focusing with anelastic attenuation, we argue that on-continent sedimentary basins are expected to affect surface wave amplitudes more strongly through elastic focusing than through the anelastic attenuation.

Effect of surface modification by nitrogen ion implantation on the electrochemical and cellular behaviors of super-elastic NiTi shape memory alloy.

PubMed

Maleki-Ghaleh, H; Khalil-Allafi, J; Sadeghpour-Motlagh, M; Shakeri, M S; Masoudfar, S; Farrokhi, A; Beygi Khosrowshahi, Y; Nadernezhad, A; Siadati, M H; Javidi, M; Shakiba, M; Aghaie, E

2014-12-01

The aim of this investigation was to enhance the biological behavior of NiTi shape memory alloy while preserving its super-elastic behavior in order to facilitate its compatibility for application in human body. The surfaces of NiTi samples were bombarded by three different nitrogen doses. Small-angle X-ray diffraction was employed for evaluating the generated phases on the bombarded surfaces. The electrochemical behaviors of the bare and surface-modified NiTi samples were studied in simulated body fluid (SBF) using electrochemical impedance and potentio-dynamic polarization tests. Ni ion release during a 2-month period of service in the SBF environment was evaluated using atomic absorption spectrometry. The cellular behavior of nitrogen-modified samples was studied using fibroblast cells. Furthermore, the effect of surface modification on super-elasticity was investigated by tensile test. The results showed the improvement of both corrosion and biological behaviors of the modified NiTi samples. However, no significant change in the super-elasticity was observed. Samples modified at 1.4E18 ion cm(-2) showed the highest corrosion resistance and the lowest Ni ion release.

Enhanced sensing and conversion of ultrasonic Rayleigh waves by elastic metasurfaces.

PubMed

Colombi, Andrea; Ageeva, Victoria; Smith, Richard J; Clare, Adam; Patel, Rikesh; Clark, Matt; Colquitt, Daniel; Roux, Philippe; Guenneau, Sebastien; Craster, Richard V

2017-07-28

Recent years have heralded the introduction of metasurfaces that advantageously combine the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. An important topic within metasurfaces is the tailored rainbow trapping and selective spatial frequency separation of electromagnetic and acoustic waves using graded metasurfaces. This frequency dependent trapping and spatial frequency segregation has implications for energy concentrators and associated energy harvesting, sensing and wave filtering techniques. Different demonstrations of acoustic and electromagnetic rainbow devices have been performed, however not for deep elastic substrates that support both shear and compressional waves, together with surface Rayleigh waves; these allow not only for Rayleigh wave rainbow effects to exist but also for mode conversion from surface into shear waves. Here we demonstrate experimentally not only elastic Rayleigh wave rainbow trapping, by taking advantage of a stop-band for surface waves, but also selective mode conversion of surface Rayleigh waves to shear waves. These experiments performed at ultrasonic frequencies, in the range of 400-600 kHz, are complemented by time domain numerical simulations. The metasurfaces we design are not limited to guided ultrasonic waves and are a general phenomenon in elastic waves that can be translated across scales.

Relativistic elasticity of stationary fluid branes

NASA Astrophysics Data System (ADS)

Armas, Jay; Obers, Niels A.

2013-02-01

Fluid mechanics can be formulated on dynamical surfaces of arbitrary codimension embedded in a background space-time. This has been the main object of study of the blackfold approach in which the emphasis has primarily been on stationary fluid configurations. Motivated by this approach we show under certain conditions that a given stationary fluid configuration living on a dynamical surface of vanishing thickness and satisfying locally the first law of thermodynamics will behave like an elastic brane when the surface is subject to small deformations. These results, which are independent of the number of space-time dimensions and of the fluid arising from a gravitational dual, reveal the (electro)elastic character of (charged) black branes when considering extrinsic perturbations.

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.

Surface tension profiles in vertical soap films

NASA Astrophysics Data System (ADS)

Adami, N.; Caps, H.

2015-01-01

Surface tension profiles in vertical soap films are experimentally investigated. Measurements are performed by introducing deformable elastic objets in the films. The shape adopted by those objects once set in the film is related to the surface tension value at a given vertical position by numerically solving the adapted elasticity equations. We show that the observed dependency of the surface tension versus the vertical position is predicted by simple modeling that takes into account the mechanical equilibrium of the films coupled to previous thickness measurements.

An analytical and experimental study of crack extension in center-notched composites

NASA Technical Reports Server (NTRS)

Beuth, Jack L., Jr.; Herakovich, Carl T.

1987-01-01

The normal stress ratio theory for crack extension in anisotropic materials is studied analytically and experimentally. The theory is applied within a microscopic-level analysis of a single center notch of arbitrary orientation in a unidirectional composite material. The bulk of the analytical work of this study applies an elasticity solution for an infinite plate with a center line to obtain critical stress and crack growth direction predictions. An elasticity solution for an infinite plate with a center elliptical flaw is also used to obtain qualitative predictions of the location of crack initiation on the border of a rounded notch tip. The analytical portion of the study includes the formulation of a new crack growth theory that includes local shear stress. Normal stress ratio theory predictions are obtained for notched unidirectional tensile coupons and unidirectional Iosipescu shear specimens. These predictions are subsequently compared to experimental results.

Theory of chemical kinetics and charge transfer based on nonequilibrium thermodynamics.

PubMed

Bazant, Martin Z

2013-05-21

Advances in the fields of catalysis and electrochemical energy conversion often involve nanoparticles, which can have kinetics surprisingly different from the bulk material. Classical theories of chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations. In condensed matter, strong interactions alter chemical activities and create variations that can dramatically affect the reaction rate. The extreme case is that of a reaction coupled to a phase transformation, whose kinetics must depend not only on the order parameter but also on its gradients at phase boundaries. Reaction-driven phase transformations are common in electrochemistry, when charge transfer is accompanied by ion intercalation or deposition in a solid phase. Examples abound in Li-ion, metal-air, and lead-acid batteries, as well as metal electrodeposition-dissolution. Despite complex thermodynamics, however, the standard kinetic model is the Butler-Volmer equation, based on a dilute solution approximation. The Marcus theory of charge transfer likewise considers isolated reactants and neglects elastic stress, configurational entropy, and other nonidealities in condensed phases. The limitations of existing theories recently became apparent for the Li-ion battery material LixFePO4 (LFP). It has a strong tendency to separate into Li-rich and Li-poor solid phases, which scientists believe limits its performance. Chemists first modeled phase separation in LFP as an isotropic "shrinking core" within each particle, but experiments later revealed striped phase boundaries on the active crystal facet. This raised the question: What is the reaction rate at a surface undergoing a phase transformation? Meanwhile, dramatic rate enhancement was attained with LFP nanoparticles, and classical battery models could not predict the roles of phase separation and surface modification. In this Account, I present a general theory of chemical kinetics, developed over the past 7 years, which is capable of answering these questions. The reaction rate is a nonlinear function of the thermodynamic driving force, the free energy of reaction, expressed in terms of variational chemical potentials. The theory unifies and extends the Cahn-Hilliard and Allen-Cahn equations through a master equation for nonequilibrium chemical thermodynamics. For electrochemistry, I have also generalized both Marcus and Butler-Volmer kinetics for concentrated solutions and ionic solids. This new theory provides a quantitative description of LFP phase behavior. Concentration gradients and elastic coherency strain enhance the intercalation rate. At low currents, the charge-transfer rate is focused on exposed phase boundaries, which propagate as "intercalation waves", nucleated by surface wetting. Unexpectedly, homogeneous reactions are favored above a critical current and below a critical size, which helps to explain the rate capability of LFP nanoparticles. Contrary to other mechanisms, elevated temperatures and currents may enhance battery performance and lifetime by suppressing phase separation. The theory has also been extended to porous electrodes and could be used for battery engineering with multiphase active materials. More broadly, the theory describes nonequilibrium chemical systems at mesoscopic length and time scales, beyond the reach of molecular simulations and bulk continuum models. The reaction rate is consistently defined for inhomogeneous, nonequilibrium states, for example, with phase separation, large electric fields, or mechanical stresses. This research is also potentially applicable to fluid extraction from nanoporous solids, pattern formation in electrophoretic deposition, and electrochemical dynamics in biological cells.

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.

Surface corrections for peridynamic models in elasticity and fracture

NASA Astrophysics Data System (ADS)

Le, Q. V.; Bobaru, F.

2018-04-01

Peridynamic models are derived by assuming that a material point is located in the bulk. Near a surface or boundary, material points do not have a full non-local neighborhood. This leads to effective material properties near the surface of a peridynamic model to be slightly different from those in the bulk. A number of methods/algorithms have been proposed recently for correcting this peridynamic surface effect. In this study, we investigate the efficacy and computational cost of peridynamic surface correction methods for elasticity and fracture. We provide practical suggestions for reducing the peridynamic surface effect.

Budget Constraints Affect Male Rats’ Choices between Differently Priced Commodities

PubMed Central

Kalenscher, Tobias

2015-01-01

Demand theory can be applied to analyse how a human or animal consumer changes her selection of commodities within a certain budget in response to changes in price of those commodities. This change in consumption assessed over a range of prices is defined as demand elasticity. Previously, income-compensated and income-uncompensated price changes have been investigated using human and animal consumers, as demand theory predicts different elasticities for both conditions. However, in these studies, demand elasticity was only evaluated over the entirety of choices made from a budget. As compensating budgets changes the number of attainable commodities relative to uncompensated conditions, and thus the number of choices, it remained unclear whether budget compensation has a trivial effect on demand elasticity by simply sampling from a different total number of choices or has a direct effect on consumers’ sequential choice structure. If the budget context independently changes choices between commodities over and above price effects, this should become apparent when demand elasticity is assessed over choice sets of any reasonable size that are matched in choice opportunities between budget conditions. To gain more detailed insight in the sequential choice dynamics underlying differences in demand elasticity between budget conditions, we trained N=8 rat consumers to spend a daily budget by making a number of nosepokes to obtain two liquid commodities under different price regimes, in sessions with and without budget compensation. We confirmed that demand elasticity for both commodities differed between compensated and uncompensated budget conditions, also when the number of choices considered was matched, and showed that these elasticity differences emerge early in the sessions. These differences in demand elasticity were driven by a higher choice rate and an increased reselection bias for the preferred commodity in compensated compared to uncompensated budget conditions, suggesting a budget context effect on relative valuation. PMID:26053764

Budget Constraints Affect Male Rats' Choices between Differently Priced Commodities.

PubMed

van Wingerden, Marijn; Marx, Christine; Kalenscher, Tobias

2015-01-01

Demand theory can be applied to analyse how a human or animal consumer changes her selection of commodities within a certain budget in response to changes in price of those commodities. This change in consumption assessed over a range of prices is defined as demand elasticity. Previously, income-compensated and income-uncompensated price changes have been investigated using human and animal consumers, as demand theory predicts different elasticities for both conditions. However, in these studies, demand elasticity was only evaluated over the entirety of choices made from a budget. As compensating budgets changes the number of attainable commodities relative to uncompensated conditions, and thus the number of choices, it remained unclear whether budget compensation has a trivial effect on demand elasticity by simply sampling from a different total number of choices or has a direct effect on consumers' sequential choice structure. If the budget context independently changes choices between commodities over and above price effects, this should become apparent when demand elasticity is assessed over choice sets of any reasonable size that are matched in choice opportunities between budget conditions. To gain more detailed insight in the sequential choice dynamics underlying differences in demand elasticity between budget conditions, we trained N=8 rat consumers to spend a daily budget by making a number of nosepokes to obtain two liquid commodities under different price regimes, in sessions with and without budget compensation. We confirmed that demand elasticity for both commodities differed between compensated and uncompensated budget conditions, also when the number of choices considered was matched, and showed that these elasticity differences emerge early in the sessions. These differences in demand elasticity were driven by a higher choice rate and an increased reselection bias for the preferred commodity in compensated compared to uncompensated budget conditions, suggesting a budget context effect on relative valuation.

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

Mechanical and optical behavior of a tunable liquid lens using a variable cross section membrane: modeling results

NASA Astrophysics Data System (ADS)

Flores-Bustamante, Mario C.; Rosete-Aguilar, Martha; Calixto, Sergio

2016-03-01

A lens containing a liquid medium and having at least one elastic membrane as one of its components is known as an elastic membrane lens (EML). The elastic membrane may have a constant or variable thickness. The optical properties of the EML change by modifying the profile of its elastic membrane(s). The EML formed of elastic constant thickness membrane(s) have been studied extensively. However, EML information using elastic membrane of variable thickness is limited. In this work, we present simulation results of the mechanical and optical behavior of two EML with variable thickness membranes (convex-plane membranes). The profile of its surfaces were modified by liquid medium volume increases. The model of the convex-plane membranes, as well as the simulation of its mechanical behavior, were performed using Solidworks® software; and surface's points of the deformed elastic lens were obtained. Experimental stress-strain data, obtained from a silicone rubber simple tensile test, according to ASTM D638 norm, were used in the simulation. Algebraic expressions, (Schwarzschild formula, up to four deformation coefficients, in a cylindrical coordinate system (r, z)), of the meridional profiles of the first and second surfaces of the deformed convex-plane membranes, were obtained using the results from Solidworks® and a program in the software Mathematica®. The optical performance of the EML was obtained by simulation using the software OSLO® and the algebraic expressions obtained in Mathematica®.

Lattice dynamics and elasticity for ε-plutonium [First-principles lattice dynamics for ε-plutonium

DOE PAGES

Söderlind, Per

2017-04-25

Here, lattice dynamics and elasticity for the high-temperature ε phase (body-centered cubic; bcc) of plutonium is predicted utilizing first-principles electronic structure coupled with a self-consistent phonon method that takes phonon-phonon interaction and strong anharmonicity into account. These predictions establish the first sensible lattice-dynamics and elasticity data on ε-Pu. The atomic forces required for the phonon scheme are highly accurate and derived from the total energies obtained from relativistic and parameter-free density-functional theory. The results appear reasonable but no data exist to compare with except those from dynamical mean-field theory that suggest ε-plutonium is mechanically unstable. Fundamental knowledge and understanding ofmore » the high-temperature bcc phase, that is generally present in all actinide metals before melting, is critically important for a proper interpretation of the phase diagram as well as practical modeling of high-temperature properties.« less

The Einstein viscosity with fluid elasticity

NASA Astrophysics Data System (ADS)

Einarsson, Jonas; Yang, Mengfei; Shaqfeh, Eric S. G.

2017-11-01

We give the first correction to the suspension viscosity due to fluid elasticity for a dilute suspension of spheres in a viscoelastic medium. Our perturbation theory is valid to O (Wi2) in the Weissenberg number Wi = γ . λ , where γ is the typical magnitude of the suspension velocity gradient, and λ is the relaxation time of the viscoelastic fluid. For shear flow we find that the suspension shear-thickens due to elastic stretching in strain `hot spots' near the particle, despite the fact that the stress inside the particles decreases relative to the Newtonian case. We thus argue that it is crucial to correctly model the extensional rheology of the suspending medium to predict the shear rheology of the suspension. For uniaxial extensional flow we correct existing results at O (Wi) , and find dramatic strain-rate thickening at O (Wi2) . We validate our theory with fully resolved numerical simulations.

Einstein viscosity with fluid elasticity

NASA Astrophysics Data System (ADS)

Einarsson, Jonas; Yang, Mengfei; Shaqfeh, Eric S. G.

2018-01-01

We give the first correction to the suspension viscosity due to fluid elasticity for a dilute suspension of spheres in a viscoelastic medium. Our perturbation theory is valid to O (ϕ Wi2) in the particle volume fraction ϕ and the Weissenberg number Wi =γ ˙λ , where γ ˙ is the typical magnitude of the suspension velocity gradient, and λ is the relaxation time of the viscoelastic fluid. For shear flow we find that the suspension shear-thickens due to elastic stretching in strain "hot spots" near the particle, despite the fact that the stress inside the particles decreases relative to the Newtonian case. We thus argue that it is crucial to correctly model the extensional rheology of the suspending medium to predict the shear rheology of the suspension. For uniaxial extensional flow we correct existing results at O (ϕ Wi ) , and find dramatic strain-rate thickening at O (ϕ Wi2) . We validate our theory with fully resolved numerical simulations.

The power transfer from the neuromuscular machinery to its load as a vegetative and somatic behaviour.

PubMed

Federici, A; Nocera, L

1990-01-01

Models have been proposed in literature describing the contraction of visceral and somatic muscles as an interaction between the time-varying elastances of them and the loads they are working against. The aim of this paper is: 1) to make clear similarities between the models of visceral and somatic muscular contraction; 2) to stress the concept that the power transfer from a time-varying elastance to its load is a behaviour, i.e. an interaction between the entire neuromuscular machinery and the surrounding environment; 3) to propose a theory describing the various physiological and pathological behaviours of both visceral and somatic muscles as different ways of coupling between the time-varying muscular elastances and their loads. In this theory it is assumed that the entire neuromuscular machinery acts as a whole to set the most appropriate power transfer to achieve behavioural goals.

First-principles theory of iron up to earth-core pressures: Structural, vibrational, and elastic properties

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

Soederlind, P.; Moriarty, J.A.; Wills, J.M.

1996-06-01

{ital Ab} {ital initio} electronic-structure calculations, based on density-functional theory and a full-potential linear-muffin-tin-orbital method, have been used to predict crystal-structure phase stabilities, elastic constants, and Brillouin-zone-boundary phonons for iron under compression. Total energies for five crystal structures, bcc, fcc, bct, hcp, and dhcp, have been calculated over a wide volume range. In agreement with experiment and previous theoretical calculations, a magnetic bcc ground state is obtained at ambient pressure and a nonmagnetic hcp ground state is found at high pressure, with a predicted bcc {r_arrow} hcp phase transition at about 10 GPa. Also in agreement with very recent diamond-anvil-cellmore » experiments, a metastable dhcp phase is found at high pressure, which remains magnetic and consequently accessible at high temperature up to about 50 GPa. In addition, the bcc structure becomes mechanically unstable at pressures above 2 Mbar (200 GPa) and a metastable, but still magnetic, bct phase ({ital c}/{ital a} {approx_equal} 0.875) develops. For high-pressure nonmagnetic iron, fcc and hcp elastic constants and fcc phonon frequencies have been calculated to above 4 Mbar. These quantities rise smoothly with pressure, but an increasing tendency towards elastic anisotropy as a function of compression is observed, and this has important implications for the solid inner-core of the earth. The fcc elastic-constant and phonon data have also been used in combination with generalized pseudopotential theory to develop many-body interatomic potentials, from which high-temperature thermodynamic properties and melting can be obtained. In this paper, these potentials have been used to calculate full fcc and hcp phonon spectra and corresponding Debye temperatures as a function of compression. {copyright} {ital 1996 The American Physical Society.}« less

Elastic expansion of the lithosphere caused by groundwater withdrawal in south-central Arizona

USGS Publications Warehouse

Holzer, T.L.

1979-01-01

Relative crustal uplift observed from 1948-1949 to 1967 in the Lower Santa Cruz River Basin in south-central Arizona is attributed at least in part to elastic expansion of the lithosphere induced by the removal, and subsequent loss by evapo transpiration, of 4.35 ?? 1013 kg of groundwater from alluvium. The area of unloading is approximately 8070 km2. Uplift, relative to an apparently stable area west of the unloaded area, was observed in two areas near Casa Grande and Florence where crystalline bedrock is either close to the land surface or crops out through alluvium from which groundwater was withdrawn. The magnitudes of uplift were approximately 6.3 and 7.5 cm respectively. The observations are based on first-order leveling. The observations are significant at three standard deviations for random surveying errors, and are not believed to be affected by systematic errors. However, the 7.5-cm uplift observed at Florence may be from 1 to 2 cm in excess of the actual uplift because of the possibility of subsidence of a tie point due to groundwater pumping during the leveling in 1948-1949. Uplift is attributed to groundwater withdrawal on three bases. First, the observed uplift is consistent with a theoretical evaluation of elastic expansion based on linear elasticity theory. For the observed distribution of unloading and uplift and a Poisson's ratio of 0.25, a Young's modulus for the lithosphere of approximately 0.68 Mbar is implied. This value is comparable to values of the lithosphere reported elsewhere. Second, the magnitude of uplift compares favorably with the magnitude of elastic depression caused by the formation of Lake Mead, Arizona-Nevada, 430 km northwest of the study area, when allowance is made for the different magnitudes and areal distributions of surface (un)loading. And third, in the area near Casa Grande, a reversal in the sense of bedrock displacement form subsidence of tectonic origin to uplift approximately coincided with the beginning of large groundwater overdraft. The uplift from 1948 to 1967 near Casa Grande was preceded from 1905 to 1948 by 7-8 cm of tectonic subsidence; no precise data for the area near Florence are available before 1948. ?? 1979.

Experimental Study in Taguchi Method on Surface Quality Predication of HSM

NASA Astrophysics Data System (ADS)

Ji, Yan; Li, Yueen

2018-05-01

Based on the study of ball milling mechanism and machining surface formation mechanism, the formation of high speed ball-end milling surface is a time-varying and cumulative Thermos-mechanical coupling process. The nature of this problem is that the uneven stress field and temperature field affect the machined surface Process, the performance of the processing parameters in the processing interaction in the elastic-plastic materials produced by the elastic recovery and plastic deformation. The surface quality of machining surface is characterized by multivariable nonlinear system. It is still an indispensable and effective method to study the surface quality of high speed ball milling by experiments.

Theoretical and numerical aspects of fluid-saturated elasto-plastic soils

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

Ehlers, W.

1995-12-31

The theoretical and numerical treatment of fluid-saturated porous solid materials generally falls into the category of porous media models, which are described within the framework of the classical theory of mixtures extended by the concept of volume fractions (porous media theories). In particular, this concept allows for the description of saturated, unsaturated and empty porous matrix materials, thus offering a well-founded theoretical background for a lot of engineering problems occurring, for instance, in the fields of geomechanics (soil and rock mechanics as well as glacier and rock ice mechanics), oil producing industries, sintering technologies, biomechanics, etc. In the present contribution,more » theoretical and numerical studies are outlined to describe a two-phase material composed of an incompressible elasto-plastic soil matrix saturated by an incompressible viscous pore fluid. In this context, the phenomenon of phase incompressibility is well known as a microscopic effect not implying bulk incompressibility in the macro regime. This is seen from the fact that even if the material density functions of the individual constituents are constant during deformation, the corresponding bulk densities can still change through changes in the volume fractions. Within the framework of a pure mechanical theory, constitutive equations are given for both the solid and the fluid partial stress tensors and for the interaction force acting between the two materials. Concerning the porous soil matrix, the elastic properties are described by an elasticity law of Hookean type, while the plastic range is governed by a {open_quote}single surface{close_quote} yield function exhibiting a smooth and closed shape in the principal stress space together with a non-associated flow rule. The viscosity effects of the pore fluid are included in the fluid stress tensor and in the drag force.« less

Structural stability, elastic and thermodynamic properties of Au-Cu alloys from first-principles calculations

NASA Astrophysics Data System (ADS)

Kong, Ge-Xing; Ma, Xiao-Juan; Liu, Qi-Jun; Li, Yong; Liu, Zheng-Tang

2018-03-01

Using first-principles calculations method based on density functional theory (DFT) with the Perdew-Burke-Ernzerhof (PBE) implementation of the generalized gradient approximation (GGA), we investigate the structural, elastic and thermodynamic properties of gold-copper intermetallic compounds (Au-Cu ICs). The calculated lattice parameters are in excellent agreement with experimental data. The elastic constants show that all the investigated Au-Cu alloys are mechanically stable. Elastic properties, including the shear modulus, Young's modulus, Poisson's ratio and Pugh's indicator, of the intermetallic compounds are evaluated and discussed, with special attention to the remarkable anisotropy displayed by Au-Cu ICs. Thermodynamic and transport properties including the Debye temperature, thermal conductivity and melting point are predicted from the averaged sound velocity and elastic moduli, using semi-empirical formulas.

Elastic Network Models For Biomolecular Dynamics: Theory and Application to Membrane Proteins and Viruses

NASA Astrophysics Data System (ADS)

Lezon, Timothy R.; Shrivastava, Indira H.; Yang, Zheng; Bahar, Ivet

The following sections are included: * Introduction * Theory and Assumptions * Statistical mechanical foundations * Anisotropic network models * Gaussian network model * Rigid block models * Treatment of perturbations * Langevin dynamics * Applications * Membrane proteins * Viruses * Conclusion * References

Modeling Outburst Flooding as a Turbulent Hydraulic Fracture Parallel to a Nearby Free Surface

NASA Astrophysics Data System (ADS)

Tsai, V. C.; Rice, J. R.

2009-12-01

Meltwater generated at the surface and base of glaciers and ice sheets is known to have a large impact on how ice masses behave dynamically, but much is still unknown about the physical processes responsible for how this meltwater drains out of the glacier. For example, little attention has been paid to short-timescale processes like turbulent hydraulic fracture, which is likely an important mechanism by which drainage channels initially form when water pressures are high. In recent work (Tsai and Rice [Fall AGU, 2008; JGR subm., 2009]), we have constructed a model of this turbulent hydraulic fracture process in which over-pressurized water is assumed to flow turbulently through a crack, leading to crack growth. However, one important limitation of this prior work is that it only strictly applies in the limit of short crack length 2L compared to glacier height H, whereas relevant observations of supraglacial lake drainage, jokulhlaups and sub-glacial lake-to-lake transport episodes do not fall in this regime. Here, we improve somewhat upon this model by explicitly accounting for a nearby free surface. We accomplish this by applying the approach of Erdogan et al. [Meth. Anal. Sol. Crack Prob., 1973] to numerically calculate elastic displacements consistent with crack pressure distribution for a crack near a free surface, and use these results as before to simultaneously satisfy the governing fluid, elastic and fracture equations. Our results are analogous to the zero fracture toughness results of Zhang et al. [Int. J. Numer. Anal. Meth. Geomech., 2005], but applied to the case of turbulent flow rather than laminar flow of a Newtonian viscous fluid. Our new results clarify the importance of the free surface and potentially explain discrepancies between our previous modeling results and observations of supraglacial lake drainage by Das et al. [Science, 2008]. However, the numerical challenges increase as 2L becomes comparable to or much larger than H. We hope to ultimately develop simpler analyses for that range which make use of (visco)elastic plate theory at positions along the uplifted ice sheet that are remote from the fracturing front. This approach may also be of interest for tidal interactions with the ice-shelf grounding line location.

Modeling Outburst Flooding as a Turbulent Hydraulic Fracture Parallel to a Nearby Free Surface

NASA Astrophysics Data System (ADS)

Tsai, Victor; Rice, James

2010-05-01

Meltwater generated at the surface and base of glaciers and ice sheets is known to have a large impact on how ice masses behave dynamically, but much is still unknown about the physical processes responsible for how this meltwater drains out of the glacier. For example, little attention has been paid to short-timescale processes like turbulent hydraulic fracture, which is likely an important mechanism by which drainage channels initially form when water pressures are high. In recent work (Tsai and Rice [Fall AGU, 2008; JGR subm., 2009]), we have constructed a model of this turbulent hydraulic fracture process in which over-pressurized water is assumed to flow turbulently through a crack, leading to crack growth. However, one important limitation of this prior work is that it only strictly applies in the limit of short crack length, 2L, compared to glacier height, H, whereas relevant observations of supraglacial lake drainage, jokulhlaups and sub-glacial lake-to-lake transport episodes do not fall in this regime. Here, we improve somewhat upon this model by explicitly accounting for a nearby free surface. We accomplish this by applying the approach of Erdogan et al. [Meth. Anal. Sol. Crack Prob., 1973] to numerically calculate elastic displacements consistent with crack pressure distribution for a crack near a free surface, and use these results as before to simultaneously satisfy the governing fluid, elastic and fracture equations. Our results are analogous to the zero fracture toughness results of Zhang et al. [Int. J. Numer. Anal. Meth. Geomech., 2005], but applied to the case of turbulent flow rather than laminar flow of a Newtonian viscous fluid. Our new results clarify the importance of the free surface and potentially explain discrepancies between our previous modeling results and observations of supraglacial lake drainage by Das et al. [Science, 2008]. However, the numerical challenges increase as 2L becomes comparable to or much larger than H. We hope to ultimately develop simpler analyses for that range which make use of (visco)elastic plate theory at positions along the uplifted ice sheet that are remote from the fracturing front. This approach may also be of interest for tidal interactions with the ice-shelf grounding line location.

Preferential sites for InAsP/InP quantum wire nucleation using molecular dynamics

NASA Astrophysics Data System (ADS)

Nuñez-Moraleda, Bernardo; Pizarro, Joaquin; Guerrero, Elisa; Guerrero-Lebrero, Maria P.; Yáñez, Andres; Molina, Sergio Ignacio; Galindo, Pedro Luis

2014-11-01

In this paper, stress fields at the surface of the capping layer of self-assembled InAsP quantum wires grown on an InP (001) substrate have been determined from atomistic models using molecular dynamics and Stillinger-Weber potentials. To carry out these calculations, the quantum wire compositional distribution was extracted from previous works, where the As and P distributions were determined by electron energy loss spectroscopy and high-resolution aberration-corrected Z-contrast imaging. Preferential sites for the nucleation of wires on the surface of the capping layer were studied and compared with (i) previous simulations using finite element analysis to solve anisotropic elastic theory equations and (ii) experimentally measured locations of stacked wires. Preferential nucleation sites of stacked wires were determined by the maximum stress location at the MD model surface in good agreement with experimental results and those derived from finite element analysis. This indicates that MD simulations based on empirical potentials provide a suitable and flexible tool to study strain dependent atom processes.

Thermal elastic deformations of the planet Mercury

NASA Technical Reports Server (NTRS)

Liu, H.

1971-01-01

The variation in solar heating due to the resonance rotation of Mercury produces periodic elastic deformations on the surface of the planet. The thermal stress and strain fields under Mercury's surface are calculated after certain simplifications. It is shown that deformations penetrate to a greater depth than the variation of solar heating, and that the thermal strain on the surface of the planet pulsates with an amplitude of 0.004 and a period of 176 days.

Thermal elastic deformations of the planet Mercury.

NASA Technical Reports Server (NTRS)

Liu, H.-S.

1972-01-01

The variation in solar heating due to the resonance rotation of Mercury produces periodic elastic deformations on the surface of the planet. The thermal stress and strain fields under Mercury's surface are calculated after certain simplifications. It is found that deformations penetrate to a greater depth than the variation of solar heating, and that the thermal strain on the surface of the planet pulsates with an amplitude of .004 and a period of 176 days.

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.