## What is/are Isotropic Elastic?

Isotropic Elastic - In this paper, a calculation method of equivalent belt material parameters for the simplified FE tire model is proposed based on the three-dimensional (3-D) anisotropic elasticity of the cord reinforced composites.^{[1]}A rate-independent model for isotropic elastic–orthotropic plastic material behaviour including the plastic spin is presented in this paper.

^{[2]}Conclusions: The cornea is confirmed to be a strongly anisotropic elastic material that cannot be characterized with a single elastic modulus.

^{[3]}These inclinations were readily explained by the isotropic elastic theory of an individual TD.

^{[4]}To verify the reliability of the suggested approach, the anisotropic elastic properties of 51 clayey soil specimens from 21 different soil types relating to 15 various sites in 4 countries were collected based on the experimental laboratory tests reported in literature.

^{[5]}In this work, the main-group (sp) element dependences of anisotropic elastic moduli, including elastic constants Cij, Young's moduli En, shear moduli Gm, n, Poisson's ratioνm, n and Zener anisotropy index Az, and their correlated electronic origins in the Ni2MnZ (Z = Al, Ga, In, Si, Ge, and Sn) alloys were studied by first-principles calculations.

^{[6]}We consider multi-scale energetics, employing Molecular Statics simulations and anisotropic elasticity formalisms, to establish a Terrace-Disconnection (TD) topology as the energy-minimal nanostructure.

^{[7]}The accurate information of the thermal stresses and temperature in isotropic elastic solids is the key for many engineering applications.

^{[8]}It is shown that light earth performance can be satisfactorily predicted, whatever the wall configuration using the Transfer Matrix Method computation with isotropic elastic and porous layers.

^{[9]}These processes then enable us to not only derive the general relationship of indentation depth D and total load P that acts on the punch but also explicitly obtain the general analytical expressions of the stress fields beneath the surface of an isotropic elastic half-space.

^{[10]}It was further shown that the raster angle–dependent strength and fracture properties of 3D-printed ABS can be predicted with an acceptable accuracy by a relatively simple FE model considering the anisotropic elasticity and failure properties of FFF specimens.

^{[11]}By the dislocation interaction model based on the anisotropic elasticity theory, the improved Peierls-Nabarro (P–N) model for nonplanar dislocation core structures is obtained from the variational principle.

^{[12]}A variation model of the gradient anisotropic elasticity theory is constructed.

^{[13]}Our simulations reveal that a stronger chiral effect results in a greater anisotropic elastic behavior in α-antimonene than in β-antimonene.

^{[14]}Fourier integral transformation is applied to convert the boundary value problem for a homogeneous, isotropic elastic material to the Fredholm integral equation of second kind.

^{[15]}In addition, we provide a few simple simulations of this model in the case of isotropic elastic materials in 2D.

^{[16]}Using first-principles calculations, we predict highly stable cubic bialkali bismuthides Cs(Na, K)2Bi with several technologically important mechanical and anisotropic elastic properties.

^{[17]}By feeding the isotropic elasticity characteristics of the phosphosilicate glass to the model, such as Young's modulus, density, and maximum compressive stress of the produced glass samples to fit the aim of their clinical use.

^{[18]}The waveguide consists of anisotropic elastic crystal layer of cubic system m3m class enclosed between crystal halfspaces of same anisotropy class.

^{[19]}Also, TPMS structures could exhibit both isotropic and anisotropic elastic properties, in which Primitive and Neovius were among the most anisotropic structures.

^{[20]}We have determined how highly accurate reverse time migrated images and FWI model parameter gradients for anisotropic elastic FWI can be efficiently computed without significant disk I/O using two wavefield propagations by means of the principle of superposition.

^{[21]}The wave propagation database was constructed using FEA considering the grain orientation distribution and the anisotropic elastic constants in the welds.

^{[22]}The purpose of the proposed work is to assess the differences in stress-strain state characteristics (especially residual mesostresses) at isothermal loads of the representative volume of polycrystals due to considering the anisotropy of elastic properties of its crystallites with HCP and tetragonal lattices (as compared to the data obtained for material with isotropic elastic properties obtained using different averaging procedures – Voigt, Reuss and Hill).

^{[23]}The stability, anisotropic elastic behavior and electronic properties of trigonal In2Si2Te6, InSiTe3, In2Ge2Te6, and InGeTe3 compounds have been studied by first-principles calculations.

^{[24]}However, the anisotropic elasticity and the application-driven slenderness make these profiles prone to local buckling failure, well below their ultimate load capacity.

^{[25]}This paper aims to simulate the isotropic elastic damage theory of Liu Jun (2012) using the self-programmed UMAT subroutine in the interface of ABAQUS.

^{[26]}This paper concerns a time-domain scattering problem of elastic plane wave by a rigid obstacle, which is immersed in an open space filled with homogeneous and isotropic elastic medium in two dimensions.

^{[27]}We have developed a vector elastic deconvolution migration method for high-resolution imaging of subsurface structures in isotropic and anisotropic elastic media.

^{[28]}It is demonstrated that this method allows for the determination of the isotropic elastic constants from the measured surface acoustic phonon frequencies.

^{[29]}The study analyzes the elastic properties of chiral metallic nanotubes formed by rolling up thin crystal plates with the [011] and [111] orientations within two frameworks of anisotropic elasticity and molecular statics.

^{[30]}The anisotropic elastic energy by shape change of martensite changes depending upon variants in neighbour austenite grains, whereas it does not in immediate parent grains in which martensite grows.

^{[31]}We report a study of thermally induced depolarisation of a laser beam in single cubic syngony crystals of 23 and m3 symmetry groups with an anisotropic elastic stiffness tensor.

^{[32]}Surface acoustic waves are propagated toward the edge of an anisotropic elastic medium (a silicon crystal), which supports leaky waves with a high degree of localization at the tip of the edge.

^{[33]}Our stack model provides clear insights into the key role of the flexural modes in the TBC and how the anisotropic elastic properties of h-BN affect heat dissipation.

^{[34]}The dependence of microseismic source images on these parameters provides essential insights into anisotropic model accuracy, and it suggests that misfocused energy on extended image gathers may be used as a criterion for updating earth models through anisotropic elastic image-domain inversion.

^{[35]}Although SBP methods have been applied to elastic wave equations many times, an SBP-SAT method for general anisotropic elastic wave equations has not yet been presented in the literature.

^{[36]}Besides an anisotropic elastic response that appears in the nonlinear regime and at non-zero pressure, the compounds contract when the temperature increases.

^{[37]}The inverse problem of finding the slowness vector from a known ray direction in general anisotropic elastic media is a challenging task, needed in many wave/ray-based methods, in particular, solving two-point ray bending problems.

^{[38]}The Lame system is a classical model for isotropic elasticity and has important applications in seismology.

^{[39]}(The concept of representative crack elements (RCE) for phase-field fracture: anisotropic elasticity and thermo-elasticity.

^{[40]}The discussion of anisotropic elasticity showed that both o-AlCu3 and h-AlCu3 are anisotropic, and the order of anisotropy is: o-AlCu3 > h-AlCu3.

^{[41]}In this paper, the wave based method (WBM) is extended to solve two-dimensional anisotropic elastic wave problems.

^{[42]}MSM simulations also show that α and χ-BNTs both have anisotropic elastic properties.

^{[43]}The estimates provided by the present homogenization model are compared to full-field calculations from the literature for two-phase non linear particulate composites constituted of an isotropic elasto-viscoplastic matrix phase and isotropic elastic particles, and, for radial and non-radial loadings.

^{[44]}In accordance with the theory, reinforcement is modeled by a vanishing thickness prestressed membrane embedded in an isotropic elastic matrix material.

^{[45]}They exhibit anisotropic elasticity and internal damping.

^{[46]}Firstly, crack propagation is predicted in single crystal specimens with anisotropic fracture energy but isotropic elastic constants to investigate the impact of the anisotropy strength parameter and the crystal orientation.

^{[47]}A new chain stress corrosion mechanism from anisotropic elastic (001) tensile deformation, microcrack generation, nonpolar surface reconstruction, HF attack to metal dissolution is proposed to paint the full picture of the structural degradation of NLOs.

^{[48]}Consider an isotropic elastic medium whose Lamé parameters are piecewise smooth.

^{[49]}The 2D carbides, namely th-XC2 (X = Si, Ge, Sn, and so on), are not only dynamically, mechanically, and thermally stable, but also exhibit exceptional properties such as anisotropic elasticity, ideal strength, and tunable phononic band gap.

^{[50]}

## density functional theory

Our predictive analytical model is based on the effective-medium and isotropic elasticity theories, and is parameterized using density functional theory (DFT) calculations of small gas-vacancy clusters.^{[1]}The favorability of this dislocation-based nucleation mechanism is rationalized by an anisotropic elasticity model of dislocation dissociation, parametrized by density functional theory calculations, which suggests the conditions for disconnection nucleation and propagation, under which this { 11 2 ¯ 1 } twinning mechanism is expected to be effective.

^{[2]}Our predictive analytical model is based on the effective-medium and isotropic elasticity theories, and is parameterized using density functional theory (DFT) calculations of small gas-vacancy clusters.

^{[3]}ABSTRACT The mechanical and anisotropic elastic properties of Bi12SiO20 (BSO) were investigated using density functional theory (DFT) calculations and nanoindentation.

^{[4]}

## Transversely Isotropic Elastic

The use of isotropic and transversely isotropic elastic theories was explored, as well as the implementation of stress relaxation in the plastic regime of the material.^{[1]}A method proposed earlier, relying on the use of harmonic Cartesian polynomial and rational functions, is extended here to find a semi-analytical solution to the uncoupled, two-dimensional problem of thermo-magnetoelasticity for a system of long parallel, non-intersecting, transversely isotropic elastic cylindrical electrical conductors.

^{[2]}The transversely isotropic elastic properties of the multi-scale composites made of unidirectional T650-35 graphite fibers embedded in graphene nanoplatelets (GNPs)-enriched PMR-15 polyimide resin are evaluated.

^{[3]}In this paper, transversely isotropic elastic properties of carbon nanocones are studied using molecular dynamics simulation implemented in the large-scale atomic/molecular massively parallel simulator (LAMMPS).

^{[4]}Introduction: In this paper, a mathematical model of Love-type wave propagation in a heterogeneous transversely isotropic elastic layer subjected to initial stress and rotation of the resting on a rigid foundation.

^{[5]}We explore transversely isotropic elasticity solutions to describe the relaxation processes in III-nitride semipolar heterostructures and compare the results for hc with those calculated within the isotropic elasticity approach.

^{[6]}Molecular dynamics (MD) simulations were carried out with a three-body Tersoff potential force field to predict the transversely isotropic elastic properties of pristine and defected BNNTs.

^{[7]}

## Homogeneou Isotropic Elastic

In this paper, we analyze a torsional problem for a nanosized penny-shaped crack in an infinite homogeneous isotropic elastic medium with surface elasticity on the boundary of the crack.^{[1]}The drill string is considered in the form of a homogeneous isotropic elastic rod with constant cross-section.

^{[2]}A problem for a nanosized penny-shaped fracture in an infinite homogeneous isotropic elastic medium is considered.

^{[3]}The constitutive relations and basic governing equations of motion for homogeneous isotropic elastic semiconductor (n-type) and homogeneous transversely isotropic ( class) piezoelectric elastic media, in the absence of body forces and electric sources are made non-dimensional in order to reduce the mathematical complexity.

^{[4]}

## Transverse Isotropic Elastic

MATERIAL AND METHOD a finite element (FE) model was used to reproduce the proximal portion of the tibia and the proximal tibiofibular joint with transverse isotropic elastic bone properties.^{[1]}In this paper we introduce a smart ultrasound approach for non-invasive real-time quantification of shear wave velocity (SWV) and elastic fractional anisotropy (FA) in locally transverse isotropic elastic medium such as the myocardium.

^{[2]}

## Linear Isotropic Elastic

This study makes a case for the application of the numeric and analytic method of boundary states with perturbations (MBSP) to analytic problems focused on the stress-strain states (SSS) of geometrically non-linear isotropic elastic bodies.^{[1]}We show that the elastic properties are correlated over a finite length scale ξ_{E}, so that the central limit theorem dictates the emergence of continuum linear isotropic elasticity on increasing the specimen size.

^{[2]}

## Infinite Isotropic Elastic

We re-examine the three-dimensional linearly elastic deformations of a composite structure consisting of an infinite isotropic elastic matrix into which is embedded a macro-sized spherical compressible gas/liquid inclusion.^{[1]}The fracture problem of an infinite isotropic elastic nanoplate with a thickness-through crack is presented and solved when the plate is subjected to uniform bending moment, twisting moment, and out-of-plane tearing load, respectively.

^{[2]}

## Nearly Isotropic Elastic

Printed specimens are shown to have a nearly isotropic elastic modulus in directions perpendicular and parallel to the printed layers, and a decreased modulus and increased elongation at break compared to specimens cast from the ink.^{[1]}These experiments reveal that the self-organised formation of 100 billions of parallel nanopores per square centimetre cross section results in a nearly isotropic elasticity perpendicular to the pore axes and an 80% effective stiffness reduction, altogether leading to significant deviations from the cubic anisotropy observed in bulk silicon.

^{[2]}

## Two Isotropic Elastic

The classic Johnson–Kendall–Roberts (JKR) contact theory was developed for frictionless adhesive contact between two isotropic elastic spheres.^{[1]}We consider optimal design problems in the setting of linearized elasticity, and restrict ourselves to domains filled with two isotropic elastic phases.

^{[2]}

## Different Isotropic Elastic

A systematic finite element analysis (FEA) of conical indentation in different isotropic elastic-plastic bulk solids was realized.^{[1]}A systematic finite element analysis (FEA) of conical indentation in different isotropic elastic-plastic bulk solids was realized.

^{[2]}

## Dimensional Isotropic Elastic

In a recent companion paper, a three-dimensional isotropic elastic micromechanical framework was developed to predict the mechanical behaviors of the innovative asphalt patching materials reinforced with a high-toughness, low-viscosity nanomolecular resin, dicyclopentadiene (DCPD), under the splitting tension test (ASTM D6931).^{[1]}In this work, fully convolutional networks (FCNs) were trained to predict stress and stress concentration factor distributions in two-dimensional isotropic elastic materials with uniform porosity.

^{[2]}

## isotropic elastic property

To verify the reliability of the suggested approach, the anisotropic elastic properties of 51 clayey soil specimens from 21 different soil types relating to 15 various sites in 4 countries were collected based on the experimental laboratory tests reported in literature.^{[1]}Using first-principles calculations, we predict highly stable cubic bialkali bismuthides Cs(Na, K)2Bi with several technologically important mechanical and anisotropic elastic properties.

^{[2]}Also, TPMS structures could exhibit both isotropic and anisotropic elastic properties, in which Primitive and Neovius were among the most anisotropic structures.

^{[3]}The purpose of the proposed work is to assess the differences in stress-strain state characteristics (especially residual mesostresses) at isothermal loads of the representative volume of polycrystals due to considering the anisotropy of elastic properties of its crystallites with HCP and tetragonal lattices (as compared to the data obtained for material with isotropic elastic properties obtained using different averaging procedures – Voigt, Reuss and Hill).

^{[4]}Our stack model provides clear insights into the key role of the flexural modes in the TBC and how the anisotropic elastic properties of h-BN affect heat dissipation.

^{[5]}MSM simulations also show that α and χ-BNTs both have anisotropic elastic properties.

^{[6]}In this work, micro-Brillouin light scattering is employed to investigate the anisotropic elastic properties of single-crystal free-standing 2H-MoSe2 as a function of thickness, down to three molecular layers.

^{[7]}AVO inversion using pseudoisotropic elastic properties is a practical solution to this problem.

^{[8]}The transversely isotropic elastic properties of the multi-scale composites made of unidirectional T650-35 graphite fibers embedded in graphene nanoplatelets (GNPs)-enriched PMR-15 polyimide resin are evaluated.

^{[9]}The anchoring of LC molecules at the particle surface combines with the anisotropic elastic properties of the LC matrix to produce distortions in the local molecular orientation eld (director) around particles.

^{[10]}ABSTRACT The mechanical and anisotropic elastic properties of Bi12SiO20 (BSO) were investigated using density functional theory (DFT) calculations and nanoindentation.

^{[11]}In this paper, transversely isotropic elastic properties of carbon nanocones are studied using molecular dynamics simulation implemented in the large-scale atomic/molecular massively parallel simulator (LAMMPS).

^{[12]}The solution is given in the Wolfram Mathematica interactive program code, allowing the derivation of the expression of the piezoresponse both in cases of the anisotropic and isotropic elastic properties.

^{[13]}The ice cores were subsequently analyzed for temperature, salinity, texture, anisotropic elastic properties and compressive strength.

^{[14]}Obtained results demonstrate that SnSO monolayer possesses fully isotropic elastic properties and is more flexible than other two-dimensional materials.

^{[15]}To evaluate the impact of back coupling and of different closure methods in view of the manufactured solid composite the resulting anisotropic elastic properties are investigated based on the Mori–Tanaka method combined with an orientation average scheme.

^{[16]}The effective anisotropic elastic properties of each subdomain are computed using periodic boundary conditions, and are subsequently mapped back to a reduced mesh of the original micrograph.

^{[17]}Correlations for the shale anisotropic elastic properties were also developed based on ratio of horizontal and vertical elastic properties.

^{[18]}The static anisotropic elastic properties of shales can be measured by performing uniaxial compression on core specimens with bedding planes of different inclination angles (or anisotropy angles).

^{[19]}Distinctive crack-tip stress contours and energy release rates were obtained through the finite element modeling using anisotropic elastic properties of the unidirectional composite.

^{[20]}Molecular dynamics (MD) simulations were carried out with a three-body Tersoff potential force field to predict the transversely isotropic elastic properties of pristine and defected BNNTs.

^{[21]}Anisotropic elastic properties of rice stem were calculated via multiscale simulation.

^{[22]}

## isotropic elastic material

Conclusions: The cornea is confirmed to be a strongly anisotropic elastic material that cannot be characterized with a single elastic modulus.^{[1]}Fourier integral transformation is applied to convert the boundary value problem for a homogeneous, isotropic elastic material to the Fredholm integral equation of second kind.

^{[2]}In addition, we provide a few simple simulations of this model in the case of isotropic elastic materials in 2D.

^{[3]}But Griffith hedged his bets, stating that ‘The theoretical deduction—that rupture of an isotropic elastic material always occurs at a certain maximum tension—is doubtless correct’.

^{[4]}The virus SARS-CoV-2 is modeled as a rigid spherical particle and cell membrane as an anisotropic elastic material, while its fluidic nature due to lipid exchange with infinite reservoir is preserved using suitable conditions.

^{[5]}We make use of the Stroh sextic formalism to obtain explicit expressions for the net interaction force between two skewed line dislocations separated by a distance $h$ in an anisotropic elastic material with a traction-free or rigid parabolic boundary.

^{[6]}An energy approach to examining this instability when the extension and twist are prescribed was described by Gent and Hua (2004) and illustrated there for a neo-Hookean isotropic elastic material.

^{[7]}This, in turn, provides an avenue to improve microscale experiments and their analysis in porous, anisotropic elastic materials.

^{[8]}Using the Stroh sextic formalism, we derive the elastic field describing stresses and displacements for a blunt crack in a generally anisotropic elastic material subjected to two-dimensional deformations.

^{[9]}In this work, fully convolutional networks (FCNs) were trained to predict stress and stress concentration factor distributions in two-dimensional isotropic elastic materials with uniform porosity.

^{[10]}In FE simulation, the dermis and subcutaneous tissue were modeled as anisotropic hyperelastic material and isotropic elastic material, respectively.

^{[11]}In this paper, we consider antiplane deformation for an isotropic elastic material consisting of an infinite system of parallel identical circular cylindrical fibers covered with a uniform cylindrical film uniformly covering the surface of each fiber and a bonding medium weakened by a doubly periodic system of rectilinear cracks.

^{[12]}Non-linear anisotropic elastic material model for fibers and elastic-plastic isotropic model with isotropic hardening for matrix are considered for finite element analyses.

^{[13]}Rotator cuff tears are a significant clinical problem previously investigated by unvalidated computational models that either use simplified geometry or isotropic elastic material properties to represent the tendon.

^{[14]}Closed-form expressions are derived for the applied load, indentation depth, distributions of contact traction and surface displacement, which are able to link existing solutions for non-adhesive and adhesive contact problems for transversely isotropic and isotropic elastic materials, and to include the corresponding Hertz-n and JKR-n solutions as special cases.

^{[15]}A nonlinear model of an isotropic elastic material is proposed, which is a generalization of the Murnagan model, in which the expansion of the specific potential energy of the strains in a series in powers of the Genki logarithmic strain tensor is used.

^{[16]}In addition to the isotropic elastic material, the concept is discussed for anisotropic elasticity in the plane.

^{[17]}

## isotropic elastic medium

This paper concerns a time-domain scattering problem of elastic plane wave by a rigid obstacle, which is immersed in an open space filled with homogeneous and isotropic elastic medium in two dimensions.^{[1]}We have developed a vector elastic deconvolution migration method for high-resolution imaging of subsurface structures in isotropic and anisotropic elastic media.

^{[2]}In this paper, we analyze a torsional problem for a nanosized penny-shaped crack in an infinite homogeneous isotropic elastic medium with surface elasticity on the boundary of the crack.

^{[3]}Surface acoustic waves are propagated toward the edge of an anisotropic elastic medium (a silicon crystal), which supports leaky waves with a high degree of localization at the tip of the edge.

^{[4]}The inverse problem of finding the slowness vector from a known ray direction in general anisotropic elastic media is a challenging task, needed in many wave/ray-based methods, in particular, solving two-point ray bending problems.

^{[5]}Some mathematical model of the heteromodular isotropic elastic medium is given by a stress-strain relation with variable elastic moduli that are nonanalytic functions of deformation invariants.

^{[6]}Consider an isotropic elastic medium whose Lamé parameters are piecewise smooth.

^{[7]}We derive closed-form solutions for reverberant elastography in anisotropic elastic media by adapting the framework used in electromagnetic theory to treat transverse isotropic materials.

^{[8]}In this paper, we established the generalized thermoelasticity phenomenon in an isotropic elastic medium considering the electromagnetic field, rotation and two-temperature.

^{[9]}In this paper we introduce a smart ultrasound approach for non-invasive real-time quantification of shear wave velocity (SWV) and elastic fractional anisotropy (FA) in locally transverse isotropic elastic medium such as the myocardium.

^{[10]}Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions.

^{[11]}A problem for a nanosized penny-shaped fracture in an infinite homogeneous isotropic elastic medium is considered.

^{[12]}The propagation of harmonic plane waves is considered in a general anisotropic elastic medium, in the presence of prestress.

^{[13]}

## isotropic elastic constant

The wave propagation database was constructed using FEA considering the grain orientation distribution and the anisotropic elastic constants in the welds.^{[1]}It is demonstrated that this method allows for the determination of the isotropic elastic constants from the measured surface acoustic phonon frequencies.

^{[2]}Firstly, crack propagation is predicted in single crystal specimens with anisotropic fracture energy but isotropic elastic constants to investigate the impact of the anisotropy strength parameter and the crystal orientation.

^{[3]}To this end, we use an elastic–plastic continuum constitutive model of single crystal HMX in which the anisotropic elastic constants and direction-dependent yield stress are rendered pressure-sensitive.

^{[4]}Using the proposed closed-form expressions of the anisotropic elastic constants, the elastic moduli, Poisson’s ratios, Cauchy and Cosserat shear moduli and bending moduli can be expressed as functions of the microscopic parameters pertaining to the particle shape, size and contact properties.

^{[5]}By estimating the phase velocity from EBSD data, our measurements suggest that the measured ultrasonic phase velocity is sensitive to changes in anisotropic elastic constants, while the measured uniaxial tensile moduli are not as sensitive to the same changes.

^{[6]}The bilayers thickness in each multilayered system, as well as the isotropic elastic constants (Young´s modulus and Poisson´s ratio) of each thin film, were fixed to be constant in all the cases.

^{[7]}Bayesian inference with sequential Monte Carlo is used to quantify the orientation distribution function coefficients and to calculate the fully anisotropic elastic constants of additively manufactured specimens from only the experimentally-measured resonant frequencies.

^{[8]}The material behavior in the elastic regime is described by temperature-dependent anisotropic elastic constants.

^{[9]}This paper introduces a methodology to study the anisotropic elastic constants of technical phenylene polysulfide thermoplastic (PPS), printed using fused deposition modeling (FDM) in order to provide designers with a guide to achieve the required mechanical properties in a printed part.

^{[10]}

## isotropic elastic behavior

Our simulations reveal that a stronger chiral effect results in a greater anisotropic elastic behavior in α-antimonene than in β-antimonene.^{[1]}The stability, anisotropic elastic behavior and electronic properties of trigonal In2Si2Te6, InSiTe3, In2Ge2Te6, and InGeTe3 compounds have been studied by first-principles calculations.

^{[2]}Both these compounds are ductile in nature and have anisotropic elastic behavior and high stiffness.

^{[3]}The research presented addresses this problem by studying for the first time the anisotropic elastic behavior of human costal cartilage.

^{[4]}However, for low-density networks, cooperative buckling of the fiber segments can take place at small strains, leading to nonlinear, anisotropic elastic behaviors.

^{[5]}Fabric recognition remains an ongoing challenge caused by complicated nonlinear and anisotropic elastic behavior of textiles.

^{[6]}3D image-based finite element (FE) and bone volume fraction (BV/TV)/fabric tensor modeling techniques are currently used to determine the apparent stiffness tensor of trabecular bone for assessing its anisotropic elastic behavior.

^{[7]}The strongly layered nature of unconventional mudstones, however, requires representation of the high contrast in properties between layers, and their anisotropic elastic behavior.

^{[8]}Previous experimental tests on WAAM-produced stainless steel plates showed in particular a strong anisotropic elastic behavior.

^{[9]}

## isotropic elastic solid

The accurate information of the thermal stresses and temperature in isotropic elastic solids is the key for many engineering applications.^{[1]}While bulk domains are treated as linearly isotropic elastic solids, both the half-space plane boundary and the matrix/inhomogeneity interface are modeled by the Steigmann–Ogden theory.

^{[2]}This study presents an analytical method for the solution of dynamic frictional contact problem between a rigid punch and an isotropic elastic solid.

^{[3]}A plane strain strip of finite thickness is analyzed within a small deformation framework and with the STZs modeled as Eshelby inclusions in an isotropic elastic solid.

^{[4]}Our current work is related to the study of vibrations induced by laser beams on the behalf of distinct theories of magneto-thermo-elastic diffusion problem in a semi-infinitely long, conducting isotropic elastic solid with cylindrical hole in a uniform magnetic field acting on the surface of the cylindrical hole of the solid in the direction of the axis of the cylindrical hole.

^{[5]}5 We present a numerical method for the simulation of earthquake cycles on a 1D fault 6 interface embedded in a 2D homogeneous, anisotropic elastic solid.

^{[6]}Present approach can be combined with Sih’s strain energy density criterion to study 3D cracks propagation in anisotropic elastic solids under fatigue loading, which is the direction of future research.

^{[7]}In this study, we follow two main objectives via analyzing a benchmark problem where an isotropic elastic solid circular cylinder of finite length is subjected to normal lateral loading.

^{[8]}

## isotropic elastic half

These processes then enable us to not only derive the general relationship of indentation depth D and total load P that acts on the punch but also explicitly obtain the general analytical expressions of the stress fields beneath the surface of an isotropic elastic half-space.^{[1]}The present investigation deals with the reflection and transmission phenomena in isotropic elastic half-space (ES) and bio-thermoelastic diffusive half-space (BDS) for the study of plane harmonic waves.

^{[2]}Nix presented a series of numerical computations in which he calculated the net interaction force between two skew dislocations separated by a distance h that are parallel to the traction-free surface of an isotropic elastic half-space.

^{[3]}02 ps pulse duration of the non-Gaussian laser beam is apt for heating a homogenous isotropic elastic half-space.

^{[4]}The article is concerned with the analysis of the problem for a concentrated line load moving at a constant speed along the surface of a pre-stressed, incompressible, isotropic elastic half-space, within the framework of the plane-strain assumption.

^{[5]}The present analysis confers the propagation characteristics of horizontally polarized shear (SH) wave through a heterogeneous transversely isotropic fluid-saturated poroelastic sandwiched layer of finite width embedded between two heterogeneous isotropic elastic half-spaces due to the impact of an impulsive line source.

^{[6]}We derive analytical solutions for deformations and gravity changes due to the volume changes of triaxial point-sources in an isotropic elastic half-space.

^{[7]}

## isotropic elastic wave

Although SBP methods have been applied to elastic wave equations many times, an SBP-SAT method for general anisotropic elastic wave equations has not yet been presented in the literature.^{[1]}In this paper, the wave based method (WBM) is extended to solve two-dimensional anisotropic elastic wave problems.

^{[2]}The application of non-classical approach of the boundary integral equation method in combination with the integral Laplace transform in time to anisotropic elastic wave modeling is considered.

^{[3]}The parameterization of the isotropic elastic wave-equation is directly in terms of elastic moduli, or compliances, which are closer to the desired reservoir properties than the conventional impedances.

^{[4]}The isotropic elastic wave equation is used to simulate ultrasonic propagation between bone and soft tissue, and the Gauss–Newton algorithm based on symmetric nonlinear equations is applied to solve the optimal solution in the inversion.

^{[5]}We evaluate our scheme using isotropic acoustic, anisotropic acoustic, and isotropic elastic wave propagators of industrial significance.

^{[6]}The acoustic, elastic, poroelastic, and anisotropic elastic wave equations are unified into a first-order velocity–stress system.

^{[7]}

## isotropic elastic moduli

In this work, the main-group (sp) element dependences of anisotropic elastic moduli, including elastic constants Cij, Young's moduli En, shear moduli Gm, n, Poisson's ratioνm, n and Zener anisotropy index Az, and their correlated electronic origins in the Ni2MnZ (Z = Al, Ga, In, Si, Ge, and Sn) alloys were studied by first-principles calculations.^{[1]}To investigate effects of Ce doping on anisotropy and mechanical properties of M7C3 (Fe3Cr4C3) carbides in hypereutectic Fe–Cr–C hardfacing alloy, the stability, anisotropic elastic moduli, intrinsic hardness, tensile property and electronic structures of Ce-doped M7C3 (Fe3Cr3CeC3) carbide were calculated by first principles method.

^{[2]}It was found that (i) hot swaging process leads to change in grain morphology and increase in microstrain; (ii) thermal expansion coefficients of martensite and austenite variants were weakly affected by the texture and phase transformation constraint; (iii) significant texture effect on the elastic properties at both macro- and micro-scale was quantified by Elasto-Plastic Self-Consistent (EPSC) modelling approach, while the anisotropic elastic moduli lie within the range of single crystal state and twinned structure; (iv) texture evolution during SME is weakly related to the initial microstructure; (v) martensite reoriented so that the axis became aligned parallel to the loading direction, and retained this orientation upon unloading, revealing the underlying correlation between texture evolution and detwinning.

^{[3]}Comparison shows that using isotropic elastic moduli in determining band offsets and core band gaps gives better agreement with experiment than anisotropic elastic moduli for core bandgaps of CdSe/CdS, CdSe/ZnS, ZnSe/ZnS, and ZnSe/CdS core/shell QDs.

^{[4]}The isotropic elastic moduli, known as bulk modulus ( B ), shear modulus ( G ), young's modulus ( E ), poisson's ratio ( ν ), vickers hardness ( H v ) and linear compressibility coefficients ( α ) have been studied within framework of the Voigt–Reuss–Hill approximation for ideal polycrystalline Ti 2 AN (A = Si, Ge and Sn) MAX aggregates.

^{[5]}

## isotropic elastic model

The scalp, suture and brain were represented using hyperelastic material models, while an isotropic elastic model was used for the skull.^{[1]}We have developed a novel microseismic (extended) PS energy imaging condition that explicitly incorporates the stiffness tensor and exhibits heightened sensitivity to isotropic elastic model perturbations compared with existing imaging conditions.

^{[2]}An isotropic elastic model was used for the pile, piles cap, tunnel lining and tunnel boring machine shield (TBM).

^{[3]}

## isotropic elastic body

This study makes a case for the application of the numeric and analytic method of boundary states with perturbations (MBSP) to analytic problems focused on the stress-strain states (SSS) of geometrically non-linear isotropic elastic bodies.^{[1]}A quantum description of the surface waves in an isotropic elastic body without the use of the semiclassical quantization is proposed.

^{[2]}Based on this new model, an infinitely long homogeneous, isotropic elastic body with a cylindrical hole is analyzed for thermal behavior analysis.

^{[3]}

## isotropic elastic response

Besides an anisotropic elastic response that appears in the nonlinear regime and at non-zero pressure, the compounds contract when the temperature increases.^{[1]}The main factors affecting the anisotropic elastic response of GCS were structure anisotropy, porosity, and loading direction.

^{[2]}Furthermore, we traced magnetic field-temperature phase diagrams up to 30 T and observed a highly anisotropic elastic response within the honeycomb layer.

^{[3]}

## isotropic elastic theory

These inclinations were readily explained by the isotropic elastic theory of an individual TD.^{[1]}The use of isotropic and transversely isotropic elastic theories was explored, as well as the implementation of stress relaxation in the plastic regime of the material.

^{[2]}

## isotropic elastic matrix

We re-examine the three-dimensional linearly elastic deformations of a composite structure consisting of an infinite isotropic elastic matrix into which is embedded a macro-sized spherical compressible gas/liquid inclusion.^{[1]}In accordance with the theory, reinforcement is modeled by a vanishing thickness prestressed membrane embedded in an isotropic elastic matrix material.

^{[2]}