Uniform Stresses Inside an Elliptical Inhomogeneity With an Imperfect Interface in Plane Elasticity

Abstract

We consider an elliptical inhomogeneity embedded in an infinite isotropic elastic matrix subjected to in-plane deformations under the assumption of remote uniform loading. The inhomogeneity-matrix interface is assumed to be imperfect, which is simulated by the spring-layer model with vanishing thickness. Its behavior is based on the assumption that tractions are continuous but displacements are discontinuous across the interface. We further assume that the same degree of imperfection on the interface is realized in both the normal and tangential directions. We find a form of interface function, which leads to uniform stress field within the elliptical inhomogeneity. The explicit expressions for the uniform stress field within the elliptical inhomogeneity are derived. The obtained results are verified by comparison with existing solutions. The condition under which the internal stress field is not only uniform but also hydrostatic is also presented.