Spheroidal inhomogeneity in a transversely isotropic piezoelectric medium

Piezoelectric material containing an inhomogeneity with different electroel astic properties is considered. The coupled electroelastic fields within th e inclusion satisfy a system of integral equations solved in a closed form in the case of an ellipsoidal inclusion. The solution is utilized to find t he concentration of the electroelastic fields around an inhomogeneity, and to derive the expression for the electric enthalpy of the electroelastic me dium with an ellipsoidal inclusion that is relevant for various application s. Explicit closed-form expressions are found for the electroelastic fields within a spheroidal inclusion embedded in the transversely isotropic matri x. Results are specialized for a cylinder, a flat rigid disk and a crack. F or a penny-shaped crack, the quantities entering the crack propagation crit erion are found explicitly.