Constitutive Law for Ferroelastic and Ferroelectric Piezoceramics

Abstract

The focus of this paper is to investigate the nonlinear behavior exhibited by ferroelectric and ferroelastic ceramics under high electromechanical loading. External loads, such as electric field and stress, can induce a remanent strain or polarization due to domain switching. Two internal variables are introduced in order to capture the history dependance and dissipation that characterize ferroelectricity and ferroelasticity. Two loading surfaces are introduced so that associated flow rules provide the evolution laws of the internal variables. In addition, these variables must verify kinematical constraints that may depend on the stress state since experiments indicate that tensile and compressive states have to be considered in this order. Then, dielectric, butterfly, and ferroelastic hysteresis are represented. Mechanical depolarization is also captured. All the tangent operators are expressed so that a resolution with a finite element method can be achieved.