The role of elastic contrast on the strain energy and the stress state of a spheroidal inclusion with a general eigenstrain state

Based on a recent contribution by two of the authors [Fischer FD, Bohm HJ. Acta Mater 2005;53:367-74] exact analytical relations are presented for the strain energy density and selected values of the stress components for a class of inhomogeneous spheroidal inclusions that are subjected to general normal and shear eigenstrain states. Among the inclusion shapes covered are discs, spheres and cylinders ("needles"). The reported relations can be used for the understanding of the eigenstrain state on the development of a wide field of inclusions (precipitates).