Interface design of a neutral spheroidal piezoelectric inhomogeneity in a transversely isotropic piezoelectric matrix

We study the design of a neutral spheroidal piezoelectric inhomogeneity that does not disturb the prescribed uniform axisymmetric electromechanical loading in a piezoelectric matrix. Both the inhomogeneity and the matrix are transversely isotropic. Our design methodology is based on an imperfect interface model with infinitesimal thickness that is spring-type in elasticity and weakly conducting in dielectricity, and is characterized by two non-negative imperfect interface functions which are determined for given material properties of the composite and given geometry of the spheroid. The inhomogeneity is neutral to either a hydrostatic or non-hydrostatic stress field through the interface design. Of particular note is that for the first time, we have achieved the neutrality of a three-dimensional anisotropic piezoelectric inhomogeneity through interface design.