The translation of a rigid ellipsoidal inclusion embedded in an anisotropic piezoelectric medium

A rigid ellipsoidal inclusion is perfectly bonded to a surrounding piezoelectric medium of infinite extent, and is translated infinitesimally by an externally imposed force. We show that the resulting exterior fields are equivalent to those induced by a layer of body force and electric charge applied over the ellipsoidal surface. Without having to solve the governing equations of equilibrium, we find directly the relation between the force and translation vectors, together with the stress, strain, rotation tensor and electric fields just outside the inclusion. Gaussian double quadratures with variable station points are employed in the numerical computations. Results are presented for two piezoelectric ceramics, GaAs and PZT-6B, to show the effect of the aspect ratio of the spheroid on the translational stiffness. This work extends the results of Walpole L. J. (1991b) Proc. R. Soc. London A434, 571-585 to piezoelectric media.