An elastic singularity in a spherical inclusion: the Green tensor

A spherical inclusion of one homogeneous isotropic elastic medium is bonded to an unbounded matrix of a different such medium. An arbitrary elastic singularity is located within the inclusion and an equilibrated elastic field is induced consequently at all points. Given the primary elastic field of the singularity in a completely homogeneous medium, we offer a full determination of the field in the two-phase structure. Our main application is to a point force in order to determine an explicit expression for, and examine the immediate properties of, the fundamental elastic Green's tensor.