Abstract The aim of this paper is to extend recent works devoted to the study of the effect of 3 D pores of concave shape embedded in isotropic matrix to the case of transversely isotropic (TI) matrix. In the first part of the paper, approximate relations for the compliance contribution tensor of pores of two reference shapes, supersphere and axisymmetrical superspheroid, are developed on the basis of 3 D Finite Element Modelling, recently presented in a companion paper, and known exact solutions for the limiting cases of spherical pores and circular crack. In the second part application to effective elastic coefficients of transversely isotropic materials such as clay rocks, in the frame of homogenization theory is presented to illustrate the impact of concavity parameter on overall properties.

中文翻译：

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具有凹孔的横向各向同性材料的有效弹性特性

摘要 本文的目的是将最近致力于研究嵌入各向同性基质中的凹形 3D 孔对横向各向同性 (TI) 基质的影响的工作扩展。在论文的第一部分中，基于 3D 有限元建模开发了两种参考形状（超球体和轴对称超球体）的孔的柔度贡献张量的近似关系，该模型最近在一篇配套论文中提出，并且已知精确解对于球形孔和圆形裂纹的极限情况。第二部分对粘土岩等横向各向同性材料的有效弹性系数的应用，在均质化理论的框架下，阐述了凹度参数对整体性能的影响。