This paper summarizes the development of a homogenized free energy model which
characterizes the temper- ature-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.
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