A Hybrid Analytical/Numerical Model of Piezoelectric Stack Actuators Using a Macroscopic Nonlinear Theory of Ferroelectricity and a Preisach Model of Hysteresis

Hysteretic behavior of polarized piezoelectric materials is of importance in the context of high power electro-mechanical transduction. The main goal of this article is to combine the Tiersten theory of electroelasticity and a Preisach model of hysteresis to model a simple force loaded piezoelectric actuator. The proposed theory of piezo-ferro-elasticity extends the derivation of Tiersten and Huang to the case of an arbitrary polarization direction in the ferroelectric domain. The general model is subsequently reduced to a mono-dimensional stack actuator under low operating voltage; therefore, the modeling focuses on minor loop modeling around the initial state of polarization. The model of hysteresis between polarization and electric field proposed here takes into account the nonlocal (macroscopic) memory of a piezoelectric ceramic by the use of a Preisach model. The Preisach model of hysteresis and the set of new ferro-electro-elastic constants that account for the irreversible relation between electric field and polarization are identified through experiments. The nonlinear model successfully reproduces the nonlinear dependence of generated displacements and forces as a function of applied electric field. Possible applications of this work involve nonlinear actuator behavior in the active control of vibration.