Abstract The present study is on the analytical solution for the elastic field due to a cuboidal inclusion of uniform eigenstrain within a transversely isotropic full-space material, and a numerical method to model inclusions of any arbitrary shapes and with any eigenstrain distributions as the integration of a set of such cuboidal inclusions. The fast Fourier transform (FFT) is applied for efficient computation. The developed method and results are implemented to analyze the elastic field in a transversely isotropic full-space material containing inclusions of different shapes, different eigenstrain distributions, and multiple cuboids of different densities. Furthermore, the effect of material anisotropy on the stress field subjected to a spherical inclusion with pure dilatant eigenstrains is explored by comparing the behavior of a transversely isotropic material with that of a corresponding isotropic one. The numerical results show that the induced stresses are drastically influenced by the Young’s moduli of transversely isotropic materials, and that material constant C 33 has a large influence on normal stress σ 33 .

中文翻译：

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由任意夹杂物引起的横向各向同性全空间弹性场的有效方法

摘要 本研究是关于由于横向各向同性全空间材料中均匀本征应变的立方体包裹体引起的弹性场的解析解，以及一种将任意形状和任何本征应变分布的包裹体建模为积分的数值方法。一组这样的立方体包裹体。快速傅立叶变换 (FFT) 用于高效计算。所开发的方法和结果用于分析包含不同形状、不同本征应变分布和多个不同密度长方体的横向各向同性全空间材料中的弹性场。此外，通过比较横向各向同性材料与相应各向同性材料的行为，探讨了材料各向异性对受具有纯剪胀本征应变的球形夹杂物影响的应力场的影响。数值结果表明，横向各向同性材料的杨氏模量对诱导应力的影响很大，材料常数C 33 对法向应力σ 33 的影响很大。