## Graded Solid(分级固体)研究综述

Graded Solid 分级固体 - Such a unified solving framework offers a simple solution approach to more complex elastic problems such as thermoelasticity in functionally graded solids.^{[1]}Graded solid elements with continuous property distribution at different Gauss points were implemented by a user material subroutine (UMAT) in ABAQUS Finite Element (FE) software.

^{[2]}Specifically, we (i) gain insight into the crack growth resistance of FGMs by conducting numerical experiments over a wide range of material gradation profiles and orientations, (ii) accurately reproduce the crack trajectories observed in graded photodegradable copolymers and glass-filled epoxy FGMs, (iii) benchmark our predictions with results from alternative numerical methodologies, and (iv) model complex crack paths and failure in three dimensional functionally graded solids.

^{[3]}A singular integral equation (SIE) approach and a finite element method are developed for the solution of the frictional sliding contact problem between a finite-thickness laterally graded solid and a rigid stamp of an arbitrary tip-shape considering the plane strain assumption.

^{[4]}The results demonstrate the effectiveness of the present method for the analysis of elastic wave propagation in functionally graded solids with axial symmetry and the material composition variation has an important effect on structural wave propagation behavior.

^{[5]}

这种统一的求解框架为更复杂的弹性问题提供了一种简单的解决方法，例如功能梯度固体中的热弹性问题。

^{[1]}在 ABAQUS 有限元 (FE) 软件中通过用户材料子程序 (UMAT) 实现在不同高斯点具有连续属性分布的梯度实体单元。

^{[2]}具体来说，我们 (i) 通过在广泛的材料级配分布和方向上进行数值实验，深入了解 FGM 的裂纹扩展阻力，(ii) 准确再现在分级光降解共聚物和玻璃填充环氧树脂 FGM 中观察到的裂纹轨迹， (iii) 用替代数值方法的结果对我们的预测进行基准测试，以及 (iv) 对三维功能梯度固体中的复杂裂纹路径和失效进行建模。

^{[3]}在考虑平面应变假设的情况下，开发了一种奇异积分方程（SIE）方法和一种有限元方法，用于解决有限厚度横向渐变固体与任意尖端形状的刚性印模之间的摩擦滑动接触问题。

^{[4]}结果证明了本方法对轴对称功能梯度固体中弹性波传播分析的有效性，材料成分变化对结构波传播行为有重要影响。

^{[5]}

## Functionally Graded Solid 功能分级固体

Such a unified solving framework offers a simple solution approach to more complex elastic problems such as thermoelasticity in functionally graded solids.^{[1]}Specifically, we (i) gain insight into the crack growth resistance of FGMs by conducting numerical experiments over a wide range of material gradation profiles and orientations, (ii) accurately reproduce the crack trajectories observed in graded photodegradable copolymers and glass-filled epoxy FGMs, (iii) benchmark our predictions with results from alternative numerical methodologies, and (iv) model complex crack paths and failure in three dimensional functionally graded solids.

^{[2]}The results demonstrate the effectiveness of the present method for the analysis of elastic wave propagation in functionally graded solids with axial symmetry and the material composition variation has an important effect on structural wave propagation behavior.

^{[3]}

这种统一的求解框架为更复杂的弹性问题提供了一种简单的解决方法，例如功能梯度固体中的热弹性问题。

^{[1]}具体来说，我们 (i) 通过在广泛的材料级配分布和方向上进行数值实验，深入了解 FGM 的裂纹扩展阻力，(ii) 准确再现在分级光降解共聚物和玻璃填充环氧树脂 FGM 中观察到的裂纹轨迹， (iii) 用替代数值方法的结果对我们的预测进行基准测试，以及 (iv) 对三维功能梯度固体中的复杂裂纹路径和失效进行建模。

^{[2]}结果证明了本方法对轴对称功能梯度固体中弹性波传播分析的有效性，材料成分变化对结构波传播行为有重要影响。

^{[3]}