Elastic fields due to centers of dilatation and thermal inhomogeneities in plane-layered solids

Abstract

A n image method for obtaining the solution for a center of dilatation in a three-layer elastic solid with planar interfaces is presented. The three-layered elastic solid consists of an elastic slab sandwiched between two semi-infinite elastic solids. The three elastic solids are perfectly bonded together at the two planar interfaces. The solution is given in terms of Galerkin vectors which are in terms of an infinite series of the Newtonian potential function of a mass point at the center of dilatation, its mirror images and their derivatives. As an application, the solution for the center of dilatation is used to obtain the elastic solution due to thermal inhomogeneities. The thermoelastic solution is obtained by a method which is based on the integration of properly weighted centers of dilatation over the volume occupied by the inhomogeneity. The potential functions for the problem solved are the harmonic potential functions of attracting matter filling the volume of the thermal inhomogeneity and its mirror images. The solution for the thermal elastic stresses due to an expanding (or contracting) thermal inhomogeneity (inclusion) of any shape embedded in one of the solids is given as an example. Numerical results for a spherical inclusion with pure dilatation eigenstrain are also presented and discussed.