On eigenstresses in dissimilar media

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Abstract
Prompted by possible applications to situations in geological investigations dealing with surfaces of displacement discontinuity near the interface between layers of rock strata, an analysis of the problem of a transforming sphere completely embedded in an isotropic elastic half-space in perfect contact with a dissimilar half-space is presented here. The analysis stays wholly within the framework of classical elastostatics and furnishes a general solution in a compact form in terms of the Papkovitch-Neuber potentials. It is found that a simple relationship exists between the potentials for the homogeneous whole space and those for the bonded dissimilar half-spaces. This relationship has application to the study of the stress field in problems involving distributed forces and continuous dislocations on a surface located in one of the dissimilar solids. The image system due to Stokeslets and sources in the interior of one of two mutually immiscible semi-infinite incompressible viscous fluids is also recoverable by appropriate specialization of the relationship.

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