Harmonic And Neutral Spherical Elastic Inhomogeneities with A Functionally Graded Interphase Layer

Abstract

Summary We study the elastic field in a three-phase composite composed of an internal spherical homogeneous elastic inhomogeneity, an intermediate functionally graded interphase layer and an outer unbounded homogeneous elastic matrix subjected to an arbitrary uniform remote loading. The shear modulus of the interphase layer obeys a power law distribution along the radial direction. We accomplish the design of harmonic and neutral spherical elastic inhomogeneities. Specifically, the shear modulus of the matrix can be judiciously chosen in such a way that the insertion of the harmonic spherical inhomogeneity does not disturb the original constant mean stress in the surrounding matrix. The shear modulus of the matrix and relative thickness of the interphase can also be suitably chosen such that the insertion of the neutral spherical inhomogeneity does not disturb the original uniform deviatoric stresses in the surrounding matrix.