A thermodynamic consistent material model for hysteresis effects in ferroelectric ceramics and its finite element implementation

Abstract

This paper is concerned with a macroscopic constitutive law for domain switching effects, which occur in piezoelectric ceramics. The thermodynamical framework of the law is based on two scalar valued functions: the electric free Gibbs energy and a switching surface. In common usage, the remanent polarization and the remanent strain are employed as internal variables. The novel aspect of the present work is to introduce an irreversible electric field, which serves besides the irreversible strain as internal variable. The irreversible electric field has only theoretical meaning, but it makes the formulation very suitable for a finite element implementation, where displacements and the electric potential are the nodal degrees of freedom. The constitutive model reproduces the ferroelastic and the ferroelectric hysteresis as well as the butterfly hysteresis and it accounts for the mechanical depolarization effect.