Uniqueness of the shape of neutral inhomogeneities with interface effects in anisotropic plane elasticity

Abstract

In the context of classical interface elasticity theory, the existence and uniqueness of elliptical neutral inhomogeneities in an isotropic plane have been verified in the literature for plane deformation when the interface effects are described by variable interface parameters and the matrix is subjected to a uniform external loading. In this paper, we examine similar existence and uniqueness of neutral inhomogeneities in an anisotropic plane under the same conditions. We show that for an anisotropic inhomogeneity-matrix system under plane deformation and uniform external in-plane loadings, (i) the inhomogeneity is necessarily elliptical to achieve neutrality even if the interface parameters are allowed to vary at the interface, and (ii) the inhomogeneity must be circular to ensure its neutrality when the interface parameters keep constant on the entire interface.