A temperature-dependent hysteresis model for relaxor ferroelectric compounds

This paper summarizes the development of a homogenized free energy model which characterizes the temperature-dependent hysteresis and constitutive nonlinearities inherent to relaxor ferroelectric materials. A kernel for the model is developed through mesoscopic energy analysis and extended to provide macroscopic constitutive relations through stochastic homogenization techniques based on the assumption that certain underlying parameters are manifestations of underlying densities rather than constants. Mechanisms characterizing the decrease in hysteresis and saturation polarization polarization as temperatures are increased are constructed using asymptotic properties of the kernel which is derived from statistical mechanics tenets. Attributes of the model are illustrated through comparison with PMN-PT-BT data.