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

Abstract

The ferroelectric materials have been used in several piezoelectric sensors and actuators applications. Under strong mechanical and electrical driving levels, the nonlinear behavior of these ferroelectric materials can be described by the second order piezoelectric constitutive equations. However, their hysteretic behavior cannot be modeled by these equations. In this paper, a novel phenomenological model was developed to describe the nonlinear and hysteretic behaviors of the ferroelectrics subjected to strong electrical and mechanical strengths. The model, based on the theory of Landau-Devonshire, can simulate the polarization/electric field hysteretic cycles of the ferroelectrics under mechanical compressive stress. It can also describe the evolutions of relative permittivity/electric field and piezoelectric coefficient/electric field of the ferroelectric materials under compressive stress. Simulated behaviors are finally compared with experimental data obtained for a soft PZT and good agreements were found.