## Isotropic Elastic(各向同性弹性)研究综述

Isotropic Elastic 各向同性弹性 - 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]}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.

^{[3]}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.

^{[4]}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.

^{[5]}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.

^{[6]}A variation model of the gradient anisotropic elasticity theory is constructed.

^{[7]}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.

^{[8]}However, the anisotropic elasticity and the application-driven slenderness make these profiles prone to local buckling failure, well below their ultimate load capacity.

^{[9]}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.

^{[10]}The Lame system is a classical model for isotropic elasticity and has important applications in seismology.

^{[11]}(The concept of representative crack elements (RCE) for phase-field fracture: anisotropic elasticity and thermo-elasticity.

^{[12]}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.

^{[13]}They exhibit anisotropic elasticity and internal damping.

^{[14]}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.

^{[15]}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.

^{[16]}

本文基于帘线增强复合材料的三维（3-D）各向异性弹性，提出了一种简化的FE轮胎模型等效带束材料参数的计算方法。

^{[1]}本文提出了一种与速率无关的各向同性弹性-正交各向异性塑性材料行为模型，包括塑性自旋。

^{[2]}我们考虑多尺度能量学，采用分子静力学模拟和各向异性弹性形式，以建立梯田-断开 (TD) 拓扑作为能量最小的纳米结构。

^{[3]}结果表明，无论使用具有各向同性弹性和多孔层的传递矩阵方法计算的墙体配置如何，都可以令人满意地预测轻质地球性能。

^{[4]}进一步表明，考虑到 FFF 试样的各向异性弹性和失效特性，可以通过相对简单的有限元模型以可接受的精度预测 3D 打印 ABS 的光栅角度相关强度和断裂特性。

^{[5]}通过基于各向异性弹性理论的位错相互作用模型，由变分原理得到非平面位错核心结构的改进Peierls-Nabarro（P-N）模型。

^{[6]}建立了梯度各向异性弹性理论的变分模型。

^{[7]}通过将磷硅玻璃的各向同性弹性特性馈送到模型中，例如所生产的玻璃样品的杨氏模量、密度和最大压应力，以适应其临床使用的目的。

^{[8]}然而，各向异性弹性和应用驱动的细长性使这些轮廓容易发生局部屈曲失效，远低于其极限承载能力。

^{[9]}该研究分析了通过在各向异性弹性和分子静力学两个框架内卷起具有 [011] 和 [111] 取向的薄晶体板形成的手性金属纳米管的弹性特性。

^{[10]}Lame 系统是各向同性弹性的经典模型，在地震学中具有重要应用。

^{[11]}（相场断裂的代表性裂纹单元（RCE）的概念：各向异性弹性和热弹性。

^{[12]}各向异性弹性的讨论表明，o-AlCu3 和 h-AlCu3 都是各向异性的，各向异性的顺序是：o-AlCu3 > h-AlCu3。

^{[13]}它们表现出各向异性弹性和内部阻尼。

^{[14]}提出了一种从各向异性弹性（001）拉伸变形、微裂纹产生、非极性表面重建、HF 攻击到金属溶解的新链应力腐蚀机制，以描绘 NLO 结构退化的全貌。

^{[15]}二维碳化物，即 th-XC2（X = Si、Ge、Sn 等）不仅具有动态、机械和热稳定性，而且还表现出优异的性能，如各向异性弹性、理想强度和可调谐声子带差距。

^{[16]}

## density functional theory 密度泛函理论

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]}

我们的预测分析模型基于有效介质和各向同性弹性理论，并使用小型气体空位簇的密度泛函理论 (DFT) 计算进行参数化。

^{[1]}这种基于位错的成核机制的有利性通过位错解离的各向异性弹性模型合理化，通过密度泛函理论计算参数化，这表明了断开成核和传播的条件，在这种条件下，这种 {11 2¯ 1} 孪晶机制是预期的要有效。

^{[2]}nan

^{[3]}nan

^{[4]}

## Transversely Isotropic Elastic 横向各向同性弹性

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]}

探索了各向同性和横向各向同性弹性理论的使用，以及在材料的塑性状态下应力松弛的实施。

^{[1]}之前提出的一种方法，依赖于谐波笛卡尔多项式和有理函数的使用，在这里得到了扩展，以找到一个长平行、非相交系统的非耦合二维热磁弹性问题的半解析解，横向各向同性弹性圆柱形电导体。

^{[2]}nan

^{[3]}nan

^{[4]}简介：在本文中，Love 型波在非均质横向各向同性弹性层中传播的数学模型受到初始应力和基于刚性基础的旋转的影响。

^{[5]}nan

^{[6]}nan

^{[7]}

## Homogeneou Isotropic Elastic 均匀各向同性弹性

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]}

在本文中，我们分析了在无限均质各向同性弹性介质中纳米级便士形裂纹的扭转问题，裂纹边界具有表面弹性。

^{[1]}钻柱被认为是具有恒定横截面的均质各向同性弹性杆的形式。

^{[2]}nan

^{[3]}nan

^{[4]}

## Transverse Isotropic Elastic 横向各向同性弹性

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]}

材料与方法 有限元 (FE) 模型用于再现具有横向各向同性弹性骨特性的胫骨近端部分和近端胫腓关节。

^{[1]}在本文中，我们介绍了一种智能超声方法，用于无创实时量化局部横向各向同性弹性介质（如心肌）中的剪切波速度 (SWV) 和弹性分数各向异性 (FA)。

^{[2]}

## Linear Isotropic Elastic 线性各向同性弹性

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]}

本研究为将扰动边界状态的数值和解析方法 (MBSP) 应用于以几何非线性各向同性弹性体的应力-应变状态 (SSS) 为重点的解析问题提供了一个案例。

^{[1]}我们表明弹性特性在有限长度尺度 ξ_{E} 上是相关的，因此中心极限定理决定了随着试样尺寸的增加而出现连续线性各向同性弹性。

^{[2]}

## Infinite Isotropic Elastic 无限各向同性弹性

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]}

我们重新检查了由无限各向同性弹性基质组成的复合结构的三维线性弹性变形，其中嵌入了宏观尺寸的球形可压缩气体/液体包裹体。

^{[1]}提出并解决了具有厚度贯穿裂纹的无限各向同性弹性纳米板在板分别受到均匀弯矩、扭转力矩和面外撕裂载荷时的断裂问题。

^{[2]}

## Nearly Isotropic Elastic 近各向同性弹性

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]}

打印的样本显示出在垂直和平行于打印层的方向上具有几乎各向同性的弹性模量，并且与从油墨铸造的样本相比，模量降低和断裂伸长率增加。

^{[1]}这些实验表明，每平方厘米横截面的 1000 亿个平行纳米孔的自组织形成导致垂直于孔轴的几乎各向同性的弹性和 80% 的有效刚度降低，总共导致与观察到的立方各向异性的显着偏差。体硅。

^{[2]}

## Two Isotropic Elastic 两个各向同性弹性

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]}

经典的 Johnson-Kendall-Roberts (JKR) 接触理论是针对两个各向同性弹性球体之间的无摩擦粘附接触而开发的。

^{[1]}我们考虑线性弹性设置中的最优设计问题，并将自己限制在填充两个各向同性弹性相的域中。

^{[2]}

## Different Isotropic Elastic 不同的各向同性弹性

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]}

实现了不同各向同性弹塑性散装固体中锥形压痕的系统有限元分析（FEA）。

^{[1]}实现了不同各向同性弹塑性散装固体中锥形压痕的系统有限元分析（FEA）。

^{[2]}

## Dimensional Isotropic Elastic 尺寸各向同性弹性

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]}

在最近的一篇配套论文中，开发了一种三维各向同性弹性微机械框架，以预测用高韧性、低粘度纳米分子树脂双环戊二烯 (DCPD) 增强的创新沥青修补材料在劈裂拉伸试验下的力学行为(ASTM D6931)。

^{[1]}在这项工作中，完全卷积网络 (FCN) 被训练来预测具有均匀孔隙率的二维各向同性弹性材料中的应力和应力集中因子分布。

^{[2]}

## isotropic elastic property 各向同性弹性

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]}

为了验证所建议方法的可靠性，根据文献报道的实验室实验测试，收集了来自 4 个国家 15 个不同地点的 21 个不同土壤类型的 51 个粘土样品的各向异性弹性特性。

^{[1]}使用第一性原理计算，我们预测高度稳定的立方双碱铋 Cs(Na, K)2Bi 具有几个技术上重要的机械和各向异性弹性特性。

^{[2]}此外，TPMS 结构可以表现出各向同性和各向异性的弹性特性，其中 Primitive 和 Neovius 是最各向异性的结构之一。

^{[3]}所提议工作的目的是评估多晶代表体积等温载荷下应力-应变状态特性（尤其是残余中应力）的差异，这是由于考虑了其微晶与 HCP 和四方晶格的弹性特性的各向异性（比较使用不同的平均程序（Voigt、Reuss 和 Hill）获得的具有各向同性弹性特性的材料获得的数据。

^{[4]}我们的堆栈模型清楚地了解了弯曲模式在 TBC 中的关键作用以及 h-BN 的各向异性弹性特性如何影响散热。

^{[5]}MSM 模拟还表明 α 和 χ-BNT 都具有各向异性的弹性特性。

^{[6]}nan

^{[7]}nan

^{[8]}nan

^{[9]}nan

^{[10]}nan

^{[11]}nan

^{[12]}nan

^{[13]}nan

^{[14]}nan

^{[15]}nan

^{[16]}nan

^{[17]}nan

^{[18]}nan

^{[19]}nan

^{[20]}nan

^{[21]}nan

^{[22]}

## isotropic elastic material 各向同性弹性材料

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]}

结论：角膜被证实是一种强各向异性的弹性材料，不能用单一的弹性模量来表征。

^{[1]}傅里叶积分变换用于将均匀、各向同性弹性材料的边值问题转换为第二类 Fredholm 积分方程。

^{[2]}此外，我们在二维各向同性弹性材料的情况下对该模型进行了一些简单的模拟。

^{[3]}nan

^{[4]}nan

^{[5]}nan

^{[6]}nan

^{[7]}nan

^{[8]}nan

^{[9]}在这项工作中，完全卷积网络 (FCN) 被训练来预测具有均匀孔隙率的二维各向同性弹性材料中的应力和应力集中因子分布。

^{[10]}nan

^{[11]}nan

^{[12]}nan

^{[13]}nan

^{[14]}nan

^{[15]}nan

^{[16]}nan

^{[17]}

## isotropic elastic medium 各向同性弹性介质

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]}

本文研究了一个刚性障碍物对弹性平面波的时域散射问题，该障碍物浸入一个充满二维均质各向同性弹性介质的开放空间中。

^{[1]}我们开发了一种矢量弹性反卷积偏移方法，用于对各向同性和各向异性弹性介质中的地下结构进行高分辨率成像。

^{[2]}在本文中，我们分析了在无限均质各向同性弹性介质中纳米级便士形裂纹的扭转问题，裂纹边界具有表面弹性。

^{[3]}表面声波向各向异性弹性介质（硅晶体）的边缘传播，该介质支持边缘尖端高度局部化的泄漏波。

^{[4]}在一般各向异性弹性介质中从已知射线方向找到慢度矢量的逆问题是一项具有挑战性的任务，在许多基于波/射线的方法中都需要，特别是解决两点射线弯曲问题。

^{[5]}nan

^{[6]}考虑一个各向同性的弹性介质，其 Lamé 参数是分段光滑的。

^{[7]}nan

^{[8]}nan

^{[9]}在本文中，我们介绍了一种智能超声方法，用于无创实时量化局部横向各向同性弹性介质（如心肌）中的剪切波速度 (SWV) 和弹性分数各向异性 (FA)。

^{[10]}nan

^{[11]}nan

^{[12]}nan

^{[13]}

## isotropic elastic constant 各向同性弹性常数

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]}

考虑到焊缝中的晶粒取向分布和各向异性弹性常数，使用 FEA 构建波传播数据库。

^{[1]}证明该方法允许从测量的表面声学声子频率确定各向同性弹性常数。

^{[2]}首先，预测具有各向异性断裂能但各向同性弹性常数的单晶试样的裂纹扩展，以研究各向异性强度参数和晶体取向的影响。

^{[3]}nan

^{[4]}nan

^{[5]}nan

^{[6]}nan

^{[7]}nan

^{[8]}nan

^{[9]}nan

^{[10]}

## isotropic elastic behavior 各向同性弹性行为

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]}

我们的模拟表明，与 β-锑烯相比，更强的手性效应导致 α-锑烯的各向异性弹性行为更大。

^{[1]}通过第一性原理计算研究了三角In2Si2Te6、InSiTe3、In2Ge2Te6和InGeTe3化合物的稳定性、各向异性弹性行为和电子特性。

^{[2]}nan

^{[3]}nan

^{[4]}nan

^{[5]}nan

^{[6]}nan

^{[7]}nan

^{[8]}nan

^{[9]}

## isotropic elastic solid 各向同性弹性固体

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]}

各向同性弹性固体中热应力和温度的准确信息是许多工程应用的关键。

^{[1]}虽然体域被视为线性各向同性弹性固体，但半空间平面边界和基体/非均匀界面均由 Steigmann-Ogden 理论建模。

^{[2]}nan

^{[3]}nan

^{[4]}nan

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^{[8]}

## isotropic elastic half 各向同性弹性半

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]}

然后，这些过程使我们不仅能够推导出压痕深度 D 和作用在冲头上的总载荷 P 的一般关系，而且还能明确获得各向同性弹性半空间表面下应力场的一般解析表达式。

^{[1]}本研究涉及各向同性弹性半空间 (ES) 和生物热弹性扩散半空间 (BDS) 中的反射和透射现象，用于研究平面谐波。

^{[2]}nan

^{[3]}nan

^{[4]}nan

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^{[7]}

## isotropic elastic wave 各向同性弹性波

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]}

虽然 SBP 方法已多次应用于弹性波方程，但文献中尚未提出用于一般各向异性弹性波方程的 SBP-SAT 方法。

^{[1]}本文将基于波的方法（WBM）扩展到解决二维各向异性弹性波问题。

^{[2]}nan

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^{[7]}

## isotropic elastic moduli 各向同性弹性模量

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]}

在这项工作中，各向异性弹性模量的主族 (sp) 元素依赖性，包括弹性常数 Cij、杨氏模量 En、剪切模量 Gm、n、泊松比νm、n 和齐纳各向异性指数 Az，以及它们在通过第一性原理计算研究了 Ni2MnZ（Z = Al、Ga、In、Si、Ge 和 Sn）合金。

^{[1]}研究 Ce 掺杂对过共晶 Fe-Cr-C 堆焊合金中 M7C3 (Fe3Cr4C3) 碳化物各向异性和力学性能的影响，研究 Ce 掺杂的 M7C3 (Fe3Cr3CeC3) 的稳定性、各向异性弹性模量、本征硬度、拉伸性能和电子结构碳化物采用第一原理法计算。

^{[2]}nan

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^{[5]}

## isotropic elastic model 各向同性弹性模型

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]}

头皮、缝线和大脑使用超弹性材料模型表示，而颅骨使用各向同性弹性模型。

^{[1]}我们开发了一种新的微震（扩展）PS 能量成像条件，与现有成像条件相比，该条件明确结合了刚度张量，并且对各向同性弹性模型扰动表现出更高的敏感性。

^{[2]}nan

^{[3]}

## isotropic elastic body 各向同性弹性体

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]}

本研究为将扰动边界状态的数值和解析方法 (MBSP) 应用于以几何非线性各向同性弹性体的应力-应变状态 (SSS) 为重点的解析问题提供了一个案例。

^{[1]}提出了不使用半经典量化的各向同性弹性体中表面波的量子描述。

^{[2]}nan

^{[3]}

## isotropic elastic response 各向同性弹性响应

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]}

除了出现在非线性状态和非零压力下的各向异性弹性响应外，当温度升高时，化合物会收缩。

^{[1]}影响GCS各向异性弹性响应的主要因素是结构各向异性、孔隙率和加载方向。

^{[2]}nan

^{[3]}

## isotropic elastic theory 各向同性弹性理论

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]}

这些倾向很容易通过单个 TD 的各向同性弹性理论来解释。

^{[1]}探索了各向同性和横向各向同性弹性理论的使用，以及在材料的塑性状态下应力松弛的实施。

^{[2]}

## isotropic elastic matrix 各向同性弹性矩阵

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]}

我们重新检查了由无限各向同性弹性基质组成的复合结构的三维线性弹性变形，其中嵌入了宏观尺寸的球形可压缩气体/液体包裹体。

^{[1]}根据该理论，钢筋通过嵌入各向同性弹性基体材料中的消失厚度预应力膜进行建模。

^{[2]}