Elastic inhomogeneous inclusion and inhomogeneity in bimaterials

Abstract

A method is presented for obtaining the elastic field due to an inhomogeneous inclusion or an inhomogeneity of any shape in two joined semi-infinite isotropic solids (bimaterials) which are either perfectly bonded or in frictionless contact at the planar interface. Eshelby’s equivalent inclusion method and the Galerkin vectors for double forces and double forces with moment in bimaterials are used to obtain the solution. The expression for the equivalent eigenstrains for an inhomogeneous inclusion or an inhomogeneity of arbitrary shape is obtained in terms of a system of singular integral equations which can then be solved numerically. The elastic fields for inhomogeneous inclusions and inhomogeneities are then obtained by treating the problem as a homogeneous inclusion.