Modeling of nonlinear and hysteretic behaviors in the ferroelectric materials under strong electrical and mechanical driving levels

The piezo-ceramics have been using in many piezoelectric applications such as transducers, sensors and actuators. Under high mechanical and electrical strengths, the nonlinear behavior observed on these devices can describe by the second order piezoelectric constitutive equations. However, their hysteretic behavior cannot be described by these equations. In this paper, a more general theoretical model was developed to describe the nonlinear and hysteretic behaviors of the piezo-ceramics under high electrical and mechanical strengths. The model, based on the theory of Landau-Devonshire, can simulate the hysteresis cycles under the combined cyclic electric and static mechanical strengths. It can describe the evolution of the relative dielectric permittivity ε33 as a function of the applied electric field. Using the scaling law, it can also describe the evolution of the piezoelectric coefficient d33 as a function of the applied electric field.