Elastic behavior of inhomogeneities with size and shape different from their hosting cavities

In this paper we consider an application of the Eshelby theory concerning the elastic behavior of prestrained or prestressed inhomogeneities. The theory, in its original version, deals with a configuration where both the ellipsoidal particle and the surrounding matrix are in elastostatic equilibrium if no external loads are applied to the system. Here, we consider slightly different shapes and sizes for the particle and the hosting cavity (whose surfaces are firmly bonded together) and, therefore, we observe a given state of strain (or stress) even without externally applied loads. We develop a complete procedure able to determine the uniform elastic field induced in an arbitrarily prestrained particle subjected to arbitrary remote loadings.