## What is/are Isotropic Solid?

Isotropic Solid - Strain energy release rate (SER) in conjunction with reinforcement isotropic solid (RIS) model is employed to propose a new fracture criterion in mixed-mode I/II loading named here as SERIS.^{[1]}In this study, a closed-form solution based on Elliot’s displacement potentials for transversely isotropic solids is specifically derived for validation purposes.

^{[2]}The stress field of a spherical inclusion with uniform pure dilatational eigenstrain in a radially-inhomogeneous spherical ball made of arbitrary incompressible isotropic solids is analyzed.

^{[3]}We have demonstrated a laboratory method for estimating the crack status inside a cylindrical rock sample based on a vertically cracked transversely isotropic solid model by using measured P- and S-wave velocities and porosity derived from strain data.

^{[4]}In this paper, to describe the thermoelastic behavior in isotropic solids undergoing large temperature changes more accurately, the novel coupled models of thermoelasticity and the corresponding finite element models have been presented explicitly and validated by experimental measurement.

^{[5]}The hosts are typically anisotropic solids with 2D conduction planes but can also be materials with 1D or isotropic transport pathways.

^{[6]}The initial state determines the subsequent evolution of the dense assembly into either an anisotropic solid, an isotropic or an anisotropic fluid, respectively.

^{[7]}Propagation of elastic waves in anisotropic solids is solved through a pure stress formalism.

^{[8]}Shear moduli are i) measured directly and ii) calculated by applying elasticity theory for isotropic solid materials, using Young's moduli and Poisson's ratios from compression tests.

^{[9]}The applied approach is based on the non-hypersingular traction based boundary integral equation method for the graded bulk elastic isotropic solid extended with the non-classical boundary conditions and the localized constitutive law for the matrix-nano-crack interface within the framework of the Gurtin-Murdoch theory.

^{[10]}When isotropic solids are unequally stretched in two orthogonal directions, the true stress (force per actual cross-sectional area) in the larger strain direction is typically higher than that in the smaller one.

^{[11]}This article constructs a mathematical model based on fractional-order deformations for a one-dimensional, thermoelastic, homogenous, and isotropic solid sphere.

^{[12]}Such optically anisotropic solid materials are important for the application to next-generation microlight-emitting and visualizing devices as well as for fundamental optics studies of chiral light-matter interaction.

^{[13]}The strain and stress fields of a rectangular dislocation loop in an isotropic solid that is a semi-infinite medium (half medium) are developed here for a Volterra-type dislocation.

^{[14]}For isotropic solid materials, the elastic properties can be characterized from the measurement of the Rayleigh surface wave velocity.

^{[15]}To investigate the quasi-shear wave behavior and the underlying microscopic mechanism of an anisotropic solid under dynamic deformation beyond its Hugoniot elastic limit, LiF single crystals are shock-compressed along the [310] low-symmetry crystallographic orientation via normal plate-impact method.

^{[16]}Here, the bone plate is modeled as an isotropic solid layer while the soft tissues are modeled as fluid layers.

^{[17]}We obtain objectivity of strain energy for initially stressed transversely isotropic solids to derive the invariants and study resulting symmetry.

^{[18]}Transformation of laser-induced broadband pulses of longitudinal ultrasonic waves into pulses of shear waves and back into pulses of longitudinal waves (further called as the "double" transformation) in an isotropic solid plate immersed in a liquid is theoretically studied.

^{[19]}Using a new material model called reinforcement isotropic solid (RIS) concept, it is possible to extend the isotropic mixed mode fracture criteria into composite materials.

^{[20]}The stress concentration factor (SCF) along the boundary of a hole and a rigid inclusion in an infinite isotropic solid under the anti-plane shear is revisited by using degenerate kernels in the boundary integral equation (BIE) although this result was obtained by invoking the extended circle theorem of Milne-Thomson as well as the complex variable approach.

^{[21]}However, their classification has been mostly established for homogeneous isotropic solids following the seminal works of Ericksen.

^{[22]}In the case of isotropic solids we establish the continuous dependence of solutions upon initial data and body supplies.

^{[23]}This study is the first to use the diagonalization method for the new modelling of a homogeneous, thermoelastic, and isotropic solid sphere that has been subjected to mechanical damage.

^{[24]}To this end, a general expression of the displacement vector in spherical transversely isotropic solid in terms of the vector spherical harmonics has been derived.

^{[25]}The connection of data of the applied linear coordinate transformation and the thermal material properties of anisotropic solid body is analysed.

^{[26]}Therefore, a mathematical model of thermoelastic, homogenous, and isotropic solid sphere with a rotation based on the mechanical damage definition has been constructed.

^{[27]}This criterion is developed combining the maximum shear stress (MSS) theory with reinforcement isotropic solid concept (RIS) as a superior material model.

^{[28]}They play a central role in nonlinear elasticity and their classification has been mostly accomplished for isotropic solids following Ericksen’s seminal work.

^{[29]}Unlike isotropic solids, in designed structures, peculiar couplings between shear and normal deformations can be achieved and exploited for practical applications.

^{[30]}We investigate the numerical reconstruction of the missing thermal boundary data on a part of the boundary for the steady-state heat conduction equation in anisotropic solids from the knowledge of exact or noisy Cauchy data on the remaining and accessible boundary.

^{[31]}The star-shaped lattice shows a very unique anisotropic solid when the slope of the dispersion curve is negative.

^{[32]}Carboxylic acid groups were introduced into polystyrene, and the effect both on melt rheology and on mechanical properties of stretched and quenched anisotropic solids below the glass-transition temperature (Tg) was investigated.

^{[33]}Among the numerical approaches to fracture mechanics analysis of cracked anisotropic solids, the boundary element method is notable for high accuracy and performance due to its semi-analytical nature and the use of only boundary mesh.

^{[34]}This article presents a general theory on dislocation loops in multilayered anisotropic solids with magneto-electro-elastic couplings.

^{[35]}The effectiveness of the micropolar model to represent the behavior of materials made of particles of prominent size has been widely proved in the literature, in this paper we focus on the capability of this model to grossly capture the behavior of anisotropic solids under concentrated pressures.

^{[36]}The parallel volume integral equation method (PVIEM) is applied for the analysis of two-dimensional elastic wave scattering problems in an unbounded isotropic solid containing various types of mult.

^{[37]}Further studies on directivities and scattered fields are expected to improve the quantification of scattered images in isotropic solid materials by the phased array technique.

^{[38]}The paper describes a method for determining a stress-strain state of transversally isotropic solids of revolution, which are simultaneously influenced by external pressure and a body force within a steady-state temperature field.

^{[39]}Our work enables precise radiative lifetime calculations in III-nitrides and other anisotropic solid-state emitters.

^{[40]}In the study described here, we evaluated two improvements in the numerical model applied in previous works for the design of 3-D-printed lenses: (i) allowing the propagation of shear waves in the skull by means of its simulation as an isotropic solid and (ii) introduction of absorption into the set of equations that describes the dynamics of the wave in both fluid and solid media.

^{[41]}[2] discussed the gravity field impact on S-wavesin a non-homogeneous, incompressible and initially stressed anisotropic solidmedium.

^{[42]}From the elastic mechanics theory for anisotropic solids, the degradation model of tensile strength exposed to elevated temperature was confirmed.

^{[43]}The main purpose of this study is to present a complete general solution for the Lord–Shulman non-classical equations of thermoelasticity for three-dimensional transversely isotropic solids.

^{[44]}We apply this analysis to experiments of an initially isotropic solid becoming transverse isotropic under triaxial or uniaxial stress loading.

^{[45]}In turn, the porous layer covers a homogeneous isotropic solid half-space.

^{[46]}Wave energy in anisotropic solids generally propagate along curved lines and forms non-circular wave fronts.

^{[47]}Numerical analyses show that a microelastic energy function dependent on a shear deformation measure in which rotational degrees of freedom of the particles are not included, leads to a model not capable to describe properly the elastic behavior of isotropic solids subjected to non-homogeneous deformation fields.

^{[48]}Using lubrication theory for low-Reynolds-number flows and the theory for linearly elastic isotropic solids, we obtain perturbative solutions for the flow and deformation.

^{[49]}It can also be used to deal with nonlinear acoustic wave in anisotropic solids without modification.

^{[50]}

## Transversely Isotropic Solid

In this study, a closed-form solution based on Elliot’s displacement potentials for transversely isotropic solids is specifically derived for validation purposes.^{[1]}We have demonstrated a laboratory method for estimating the crack status inside a cylindrical rock sample based on a vertically cracked transversely isotropic solid model by using measured P- and S-wave velocities and porosity derived from strain data.

^{[2]}We obtain objectivity of strain energy for initially stressed transversely isotropic solids to derive the invariants and study resulting symmetry.

^{[3]}To this end, a general expression of the displacement vector in spherical transversely isotropic solid in terms of the vector spherical harmonics has been derived.

^{[4]}The main purpose of this study is to present a complete general solution for the Lord–Shulman non-classical equations of thermoelasticity for three-dimensional transversely isotropic solids.

^{[5]}The present investigation is concerned with the reflection and transmission phenomena of plane waves between a rotating thermoelastic transversely isotropic solid half space and a fiber-reinforced thermoelastic rotating solid half space under the effect of a magnetic field.

^{[6]}This article deals with the study of three-dimensional vibrations in stress free as well as rigidly fixed, thermally insulated (or isothermal), homogeneous transversely isotropic solid cylinder under the purview of three-phase lag model of generalized thermoelasticity.

^{[7]}The overall composite materials can be treated statistically as a transversely isotropic solid for the case of aligned ellipsoidal inclusions, or as an isotropic solid for the case of randomly oriented inclusions.

^{[8]}

## Reinforcement Isotropic Solid

Strain energy release rate (SER) in conjunction with reinforcement isotropic solid (RIS) model is employed to propose a new fracture criterion in mixed-mode I/II loading named here as SERIS.^{[1]}Using a new material model called reinforcement isotropic solid (RIS) concept, it is possible to extend the isotropic mixed mode fracture criteria into composite materials.

^{[2]}This criterion is developed combining the maximum shear stress (MSS) theory with reinforcement isotropic solid concept (RIS) as a superior material model.

^{[3]}

## Homogeneou Isotropic Solid

However, their classification has been mostly established for homogeneous isotropic solids following the seminal works of Ericksen.^{[1]}In turn, the porous layer covers a homogeneous isotropic solid half-space.

^{[2]}

## Elastic Isotropic Solid

The applied approach is based on the non-hypersingular traction based boundary integral equation method for the graded bulk elastic isotropic solid extended with the non-classical boundary conditions and the localized constitutive law for the matrix-nano-crack interface within the framework of the Gurtin-Murdoch theory.^{[1]}Using lubrication theory for low-Reynolds-number flows and the theory for linearly elastic isotropic solids, we obtain perturbative solutions for the flow and deformation.

^{[2]}

## isotropic solid material

Shear moduli are i) measured directly and ii) calculated by applying elasticity theory for isotropic solid materials, using Young's moduli and Poisson's ratios from compression tests.^{[1]}Such optically anisotropic solid materials are important for the application to next-generation microlight-emitting and visualizing devices as well as for fundamental optics studies of chiral light-matter interaction.

^{[2]}For isotropic solid materials, the elastic properties can be characterized from the measurement of the Rayleigh surface wave velocity.

^{[3]}Further studies on directivities and scattered fields are expected to improve the quantification of scattered images in isotropic solid materials by the phased array technique.

^{[4]}

## isotropic solid sphere

This article constructs a mathematical model based on fractional-order deformations for a one-dimensional, thermoelastic, homogenous, and isotropic solid sphere.^{[1]}This study is the first to use the diagonalization method for the new modelling of a homogeneous, thermoelastic, and isotropic solid sphere that has been subjected to mechanical damage.

^{[2]}Therefore, a mathematical model of thermoelastic, homogenous, and isotropic solid sphere with a rotation based on the mechanical damage definition has been constructed.

^{[3]}This study aims to study the radial wave dispersion of anisotropic solid sphere.

^{[4]}

## isotropic solid half

In turn, the porous layer covers a homogeneous isotropic solid half-space.^{[1]}The present investigation is concerned with the reflection and transmission phenomena of plane waves between a rotating thermoelastic transversely isotropic solid half space and a fiber-reinforced thermoelastic rotating solid half space under the effect of a magnetic field.

^{[2]}

## isotropic solid body

The connection of data of the applied linear coordinate transformation and the thermal material properties of anisotropic solid body is analysed.^{[1]}Principle and method for designing electroacoustic transducers operating in the mode of elastic wave excitation in isotropic solid bodies are discussed.

^{[2]}

## isotropic solid model

We have demonstrated a laboratory method for estimating the crack status inside a cylindrical rock sample based on a vertically cracked transversely isotropic solid model by using measured P- and S-wave velocities and porosity derived from strain data.^{[1]}The reinforced isotropic solid model based on collinear crack propagation along fibers is proposed as an advantageous model to study the fracture behavior of composites.

^{[2]}