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

A rigid ellipsoidal inclusion is embedded in a homogeneous piezoelectric matrix and is rotated infinitesimally, about an axis through its center, by an imposed couple. Without having to solve the governing equations of equilibrium, we find directly the relation between the couple and rotation vectors, together with the stress, strain, rotation tensor and electric fields just outside the ellipsoidal surface. In addition, we establish boundary integral formulae for evaluation of the fields in the matrix. Gaussian quadrature formulae with variable station points are employed in the numerical computations. Results are presented for a piezoelectric ceramic PZT-6B to show the effect of the aspect ratio of the spheroid on the rotational stiffness. This work extends the results of Walpole (Proc.R. Soc. London A433, 179-207, 1991) to piezoelectric media.