Efficient Modeling of Ferroelectric Behavior for the Finite Element Analysis of Piezoelectric Actuators

This work proposes a method of efficiently modeling the hysteresis of ferroelectric materials, such that the finite element analysis of complex structures will be possible. Our approach includes the additive combination of a reversible and an irreversible portion of the polarization and strain, respectively. Whereas the reversible parts correspond to the common piezoelectric linear equations, the irreversible parts are modeled by hysteresis operators. These operators are based on Preisach and Jiles-Atherton hysteresis models which are well-established tools in ferromagnetic modeling. In contrast to micro-mechanical approaches, a Preisach or a Jiles-Atherton hysteresis operator can be efficiently numerically evaluated. A comparison of the resulting simulations to measured data concludes the paper.