Homogenization for a nonlinear ferroelectric model

Abstract

We prove homogenization results for a class of rate-independent, nonlinear ferroelectric models. The PDE system defining the model is restated in terms of a stability condition and an energy balance law using an energy-storage functional and a dissipation functional. By the method of weak and strong two-scale convergence via periodic unfolding, we show that the solutions of the problem with periodicity converge to the energetic solution of the homogenized problem associated with the corresponding Γ-limits of the functionals. The main difficulties are the nonlinearity of the model, as well as the general form considered for the stored energy, which is neither convex nor quadratic.