The elastic field of an inclusion in an anisotropic medium

Abstract
A new general method of solving problems of anisotropic elasticity, by successive approximations, is applied to find the elastic field of a basic physical problem. In this problem an arbitrary part of an unbounded homogeneous anisotropic medium is a misfitting inclusion that would undergo an arbitrary uniform strain if its surrounding material was absent. An inclusion of ellipsoidal shape is particularly considered; a convergent series of successive approximations is used to generate, and bound as restrictively as desired, the resulting uniform strain in this inclusion. Detailed bounds are given for a spherical inclusion in a medium of cubic anisotropy. Some applications are mentioned, especially the determination of the elastic field when the material in the ellipsoidal inclusion differs from that in its surroundings.

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