Homogenization for a nonlinear ferroelectric model

Article type: Research Article

Authors: Timofte, Aida

Affiliations: Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania. E-mail: [email protected]

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.

Keywords: homogenization, ferroelectric, energetic formulation, periodic unfolding method

DOI: 10.3233/ASY-2008-0910

Journal: Asymptotic Analysis, vol. 61, no. 3-4, pp. 177-194, 2009