Uniformity of stresses inside a non-elliptical inhomogeneity near an irregularly shaped hole in plane elasticity

Abstract

We analyze the uniformity of stresses inside a non-elliptical elastic inhomogeneity interacting with a nearby irregularly shaped hole when the surrounding matrix is subjected to uniform remote in-plane stresses. Using Muskhelishvili's complex variable formulation and the technique of conformal mapping for a doubly connected domain, we demonstrate that Eshelby's uniformity property is indeed valid when the inhomogeneity and the matrix have the same shear modulus but distinct Poisson's ratios. In this case, the shapes of the inhomogeneity and the hole are completely determined by two material, one loading and three geometric parameters.