A domain evolution model for hysteresis in piezoceramic materials

In this paper, we use a circular distribution to quantify certain domain properties and model the hysteresis behavior of piezoceramic materials. The model is constructed by bridging the characteristics of microscopic domain distribution into the macroscopic (or bulk) behavior. Contributions, other than those associated with the polarization of domains, to bulk quantities are also counted. A domain orientation distribution function is first selected and the corresponding distribution function parameters are chosen as the internal state variables. For the two-dimensional model, a von Mises-Fisher circular distribution is used. Instead of micromechanical analysis of domain motions that would involve large computation efforts, the delineation of domain evolution is simplified by considering the evolution of the domain orientation distribution, which is determined by the dynamic variations of the internal state variables. We also develop a procedure to identify the material constants introduced in the constitutive equations. The models are used to quantitatively characterize various hysteresis loops observed in piezoceramic materials.