Elastic field in joined semi-infinite solids with an inclusion

Abstract

A general method is presented to obtain the elastic field in two joined semi-infinite isotropic solids due to an inclusion of any shape which undergoes a spontaneous change of shape and is located anywhere within one of the semi-infinite solids. The inclusions change of shape is such that, were the surrounding material absent, it would result from some prescribed stress free transformation strain (eigenstrain). The two semi-infinite solids can be either perfectly bonded or in frictionless contact at the planar interface. Examples are given for the inclusion with eigenstrains of practical interest. For the case where the inclusion is an ellipsoid and the given eigenstrain is uniform, the solution can be expressed in terms of well-known elliptic integrals. It is shown that existing solutions for the ellipsoidal inclusion in a semi-infinite solid are special cases of the present general solution.