An Irreversible Thermodynamic Model of Nonlinearities and Hysteresis in Piezoceramics

Abstract

In this paper, a simple irreversible thermodynamic model that uses the concepts of the internal variable theory is developed to describe nonlinear material behavior of piezoceramics beyond the linear approximation region, which exhibit the following nonlinear characteristics: dielectric hysteresis, ferroelastic hysteresis, butterfly hysteresis, phase transition and depolarization. At each instant, the local state of a material point is described by a set of classical state variables and internal state variables that integrate the microstructure effects. Instead of micromechanical modeling of domains and their motions that would involve large computation efforts, a proper domain orientation distribution is assumed, in which the corresponding distribution parameters are chosen as the internal state variables. The Von Mises-Fisher circular distribution and the Fisher spherical distribution are chosen for 2-D and 3-D model, respectively. The distribution parameters are the concentration parameter κ, and the mean domain orientation that includes one polar angle θ for the 2-D model and two spherical orientation angles φ , θ for the 3-D model. The delineation of domain evolvements is simplified by the evolutions of domain orientation distribution, which is determined by the evolutions of the corresponding internal variables.