Mathematical 3D models of irreversible polarization processes of a ferroelectrics and ferroelastics polycrystal

A review of three-dimensional mathematical models describing the irreversible processes of polarization of polycrystalline ferroelectrics is given. Experimental works and most frequently used models for describing hysteresis properties are considered. These include well-known phenomenological and micromechanical models. Some of them allow describing the nonlinear response under the action of electrical and mechanical loads. For each of the models, physical and mathematical features, basic formulas and calculating algorithms are presented. The main advantages and disadvantages of each of the presented models are noted. Large and small loops of dielectric and deformation hysteresis are shown. A conclusion is drawn about the unresolved problems in the field of modeling of polycrystalline ferroelectrics – ferroelastics. The list of works on the review topic is given.