A stress-dependent hysteresis model for PZT

This paper addresses the development of an energy-based characterization framework which quantifies stress-induced dipole switching in ferroelectric materials. Helmholtz and Gibbs energy relations that accommodate 90° and 180° dipole orientations as equilibrium states are constructed at the lattice level. For regimes in which thermal relaxation mechanisms are negligible, minimization of the Gibbs relations provides local polarization and strain relations. Alternatively, behavior such as creep or thermal relaxation can be incorporated by balancing Gibbs and relative thermal energies through Boltzmann principles. In the final step of the development, stochastic homogenization techniques based on the assumption that parameters such as coercive and induced fields are manifestations of underlying distributions are employed to construct macroscopic models suitable for nonhomogeneous polycrystalline compounds. Attributes and limitations of the model are illustrated through comparison with experimental PLZT data.