The determination of the elastic and electric fields in a piezoelectric inhomogeneity

The transformed inclusion problem in a piezoelectric solid of general anisotropy is studied. An anisotropic piezoelectric medium contains a subregion Ω of a different piezoelectric solid which undergoes constant eigenstresses and spontaneous electric polarizations. An analytical solution is constructed for ellipsoidal shapes Ω in an unbounded surrounding matrix. A related problem is that in which no eigenstresses and polarizations are prescribed anywhere, but instead the inhomogeneity‐matrix assembly is subjected to an external electromechanical loading. The electric and elastic fields in this case are shown to follow from the solution of the transformed inclusion problem.