Eshelby tensor for piezoelectric inclusion and application to modeling of domain switching and evolution Original Research Article

The two-dimensional piezoelectric Eshelby tensor, which relates constrained strains and electric displacement in an elliptic inclusion to specified uniform eigenstrains and eigenelectric displacement therein, is obtained in closed form by using the extended Lekhnitskii’s formalism. The symmetric property of piezoelectric Eshelby tensor is also established. The Eshelby tensor is then used to derive the free energy expression due to the introduction of an elliptic crystallite into a poled ferroelectric matrix. By examining the change of potential energy before and after polarization switching of the crystallite, a domain switching criterion which considers both the interaction of applied electroelastic field with switching strains and switching polarization and the change of electroelastic properties of switched domain is proposed. The derived free energy solution is also applied to study the evolution of 180° and 90° domain nuclei in ferroelectric crystals and the effects of material anisotropy and electromechanical coupling on ferroelectric domain evolution are examined.