Modeling of nonlinear piezoelectric behavior

A finite element model for the nonlinear behavior of piezoelectric material is developed. Important issues in modeling the nonlinear behavior of piezoelectric material at micro-scale is discussed and methods to solve such issues are proposed. A procedure is developed to obtain RVE from the simplified microstructure of the material. The RVE is obtained based on a statistical parameter, which is a measure of the degree of heterogeneity at a point. The material properties at the micro-scale are obtained from the macro-scale properties by rule of mixture approach. A finite element iterative solution procedure is then used to model the material behavior by averaging the local response over the entire RVE. Nonlinear behavior of the material is due to the domain switching phenomenon and is simulated based on internal energy density based switching criterion. A numerical example is given for PZT-4 material and the results agree qualitatively with the experimental results.