Solvability of the equivalent inclusion problem for an ellipsoidal inhomogeneity

Abstract

The problem of an elastic ellipsoidal inhomogeneity in an infinite matrix is considered for the case of arbitrary anisotropy. Using the Fourier representation of Hill’s tensor, which we derive directly from the classical Eshelby solution for an ellipsoidal inclusion, and assuming certain conditions on the elasticity tensors, we prove the solvability of the Eshelby equivalent inclusion problem. This justifies a formula for the anisotropic polarization tensor for an ellipsoid.