Development of mathematical models, which describe nonlinear processes, is a relevant problem of practical importance. The present article concentrates on the approach to modeling polarization of polycrystalline ferroelectric materials subjected to high electric field in the case of plane strain. The model employed here is based on the Jiles-Atherton model. It is important to emphasize that this Jiles-Atherton model, designed for one-dimensional case, is generalized here on a two-dimensional case, taking into account the influence of the neighborhood electrical domains on the process of their switching. In the first step, polarization of the representative volume element is defined without including mutual interaction between the neighbor domains. There’s introduced a new notion of ideal polarization, which takes place in the ideal case, when the influence of neighboring domains on the dipoles’ switching is ignored. In the second step, the correction of the model is carried out through the consideration of domain wall dynamics and the influence of neighboring domains on it. The convergence method is suggested to solve this system. The article presents a broad range of computational experiments for the determination of the model parameters. The practical application of this model lies in the introduction of the elaborated algorithm into the finite element package ACELAN.

Представлена двумерная математическая модель поляризации сегнетоэлектрических поликристаллических материалов в сильных внешних электрических полях на основе теории запертой стенки. Предложен метод численного решения полученных уравнений в дифференциалах методом последовательных приближений. Построены петли диэлектрического гистерезиса.