Eshelby's conjecture in finite plane elastostatics

We consider an inhomogeneity–matrix system from a particular class of compressible hyper- elastic materials of harmonic type undergoing finiteplane deformations. We discuss the analogue of Eshelby's conjecture for this class of materials. Specifically, we examine whether the stress distribution inside an inhomogeneity is uniform if and only if the inhomogeneity is elliptic when the system is subjected to uniform remote stress.