The Eshelby tensor

The problem of the existence of a tensor that is inverse to the well-known Eshelby tensor, which connects the free homogeneous and hindered strains of an ellipsoidal elastic inclusion undergoing transformation, is investigated. It is shown that this tensor exists for inclusions in the form of oblate and prolate spheroids in isotropic elastic space. Certain applications are considered, in particular problems of determining the stresses in ellipsoidal rigid and rigid plastic inclusions.