Asymptotic Solutions of Penny-Shaped Inhomogeneities in Global Eshelby’s Tensor

Abstract

In this paper, a three-dimensional penny-shaped isotropic inhomogeneity surrounded by unbounded isotropic matrix in a uniform stress field is studied based on Eshelby’s equivalent inclusion method. The solution including the deduced equivalent eigenstrain and its asymptotic expressions is presented in tensorial form. The so-called energy-based equivalent inclusion method is introduced to remove the singularities of the size and eigenstrain of the Eshelby’s equivalent inclusion of the penny-shaped inhomogeneity, and yield the same energy disturbance. The size of the energy-based equivalent inclusion can be used as a generic damage measurement.