Uniform electroelastic field within a spheroidal inhomogeneity imperfectly bonded to an infinite transversely isotropic piezoelectric matrix

We consider a transversely isotropic piezoelectric spheroidal inhomogeneity embedded in an infinite transversely isotropic piezoelectric matrix subjected to a uniform remote axisymmetric electromechanical loading. The inhomogeneity-matrix interface is spring-type in elasticity and weakly conducting in dielectricity. The same degree of interface imperfection in elasticity is realized in both the normal and tangential directions and the interface is characterized by two imperfect interface functions. We identify the two interface functions leading to a uniform interior electroelastic field within the spheroidal inhomogeneity. Explicit expressions for the internal uniform stresses and electric displacement within the inhomogeneity are presented and illustrated. The uniformity property within an imperfectly bonded spheroidal piezoelectric inhomogeneity under a uniform remote antisymmetric electromechanical loading is also proved and illustrated.