Thermoelastic stresses in bimaterials

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Abstract
The recently developed solution of the elastic equations for a bimaterial with an inclusion is used to study the fundamental thermoplastic problem in dissimilar media. The dissimilar medium consists of two semi-infinite isotropic solids of different elastic properties either perfectly bonded together or in frictionless contact with each other at the planar interface. The solutions are obtained by a method which is based on the integration of properly weighted centres of dilatation over the volume occupied by the body. The potential functions for the problem solved are the harmonic potential function of attracting matter filling the element of volume, which is identical to that for the solid of indefinite extent as in Goodier's theory of thermoelastic stress, and its mirror image. The results are applied to the case of an expanding (or contracting) inclusion of any shape embedded in one of the semi-infinite solids near the planar boundary. Numerical results for a spherical inclusion with pure dilatational eigenstrain are presented as an example.

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