An inclusion in one of two joined isotropic elastic half-spaces

Two dissimilar, homogeneous and isotropic, elastic half-spaces are bonded together over their infinite plane of contact. An arbitrarily shaped finite part of one of them (an inclusion) tends spontaneously to undergo a uniform infinitesimal strain, but, as it remains attached to and restrained by the surrounding material, an equilibrated state of stress and strain is established everywhere instead. By adopting a convenient expression for the fundamental field of a point force, we construct the full elastic field of a layer of body force and hence of the transformed inclusion. For a general shape of the inclusion and for particular spherical and finite cylindrical shapes in detail, we consider the evaluation of the elastic strain energy, especially of the interaction term which depends on the location of the inclusion and both pairs of elastic moduli, and which is of great significance in physical applications.