The recent development of nanoscience and nanotechnology enables the synthesis of nano-particles of non-ellipsoidal shape. In this study, to tackle the various inclusion topologies in the framework of micromechanics, the numerical surface integration was used to evaluate the volume-averaged Eshelby tensor for superspheral and superellipsoidal inclusions in isotropic elastic material. By taking advantage of the available solutions and the characteristics of the Eshelby tensor, the effectiveness of numerical surface integration was systematically investigated. It was found that the singularity associated with Green's function can be treated with the non-linear transformation. The invariants of the Eshelby tensor for superellipsoidal inclusion were also confirmed, and they can be conveniently employed for efficient numerical evaluation.

纳米科学和纳米技术的最新发展使得能够合成非椭圆形的纳米颗粒。在这项研究中，为了解决微力学框架中的各种夹杂物拓扑问题，数值表面积分被用于评估各向同性弹性材料中超球形和超椭圆形夹杂物的体积平均Eshelby张量。通过利用可用的解决方案和Eshelby张量的特性，系统地研究了数值表面积分的有效性。发现与格林函数有关的奇异性可以用非线性变换来处理。还确定了超椭圆体包含的Eshelby张量不变量，可以方便地将其用于有效的数值评估。