A free energy model for piezoceramic materials

This paper addresses the development of a free energy model for quantifying the hysteresis and constitutive nonlinearities inherent to piezoceramic materials. In the first step of the development, free energy relations for a single crystal with uniform lattice are considered and used to construct evolution equations which quantify the polarization as a function of the applied field. The effects of nonuniform lattice structures, nonhomogeneous effective fields and polycrystalline materials are then incorporated through the use of appropriate distributions in the free energy formulation. The resulting model, which is an extension of the Müller-Achenbach-Seelecke theory for shape memory alloys, is low-order and hence highly efficient to implement. Attributes of the model are illustrated through comparison with experimental data.