On numerical evaluation of Eshelby tensor for superspherical and superellipsoidal inclusions in isotropic elastic material

Abstract 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.