Elastic Energy of an Ellipsoidal Inclusion in an Infinite Solid

Abstract

An exact solution in closed form is presented for the displacements, stresses and total elastic energy for the problem of an ellipsoidal isotropic inclusion bonded to an isotropic body of infinite extent when the inclusion and the infinite solid have uniformly distributed changes in their stress‐free specific volumes. The physically important details of the dependence of the total strain energy of the two materials upon the shape and volume of the inclusion, the elastic moduli of the two isotropic materials and the changes of specific volume, are included. The solution is indicated for the stresses and displacements for the case where the material at infinity is, in addition to the above condition, in a homogeneous state of stress whose principal directions are parallel to the axes of the cavity.