A thermodynamic consistent model for an assumed transversely isotropic piezoceramic with nonlinear ferroelectric hysteresis

Abstract

A characteristic feature of ferroelectric crystals is the appearance of a spontaneous polarisation, where its direction can be reversed by an applied electric field. This quantity, that has a maximum value at high electric-fields, depends on the loading history of the material. In this paper we discuss a thermodynamic consistent phenomenological model for an assumed transversely isotropic ferroelectric crystal, where the history dependency is modelled by internal variables. The anisotropic behaviour is governed by isotropic tensor functions, depending on a finite set of invariants, that satisfy automatically the symmetry relationships of the considered body. The main goal of this investigation is to capture some characteristics of nonlinear ferroelectrica, such as the polarisation-electric-field and the strain-electric-field (butterfly) hysteresis loops.