A condensed microelectromechanical approach for modeling tetragonal ferroelectrics

A model for ferroelectric solids with tetragonal unit cells is presented. It is microelectromechanically motivated considering discrete switching on the level of unit cells and quasi-continuous evolution of inelastic fields on the domain wall level. The efficiency of the approach is due to the fact that an implementation within the framework of a numerical discretization scheme is not required to calculate smooth hysteresis loops or residual stresses emanating from strain incompatibilities or charges in a polycrystalline material. The condensed approach, on the other hand, can be combined with the FEM yielding extended elements where each integration point represents a polycrystalline representative volume element. Multiple grain interactions are modeled applying an averaging technique, embedding grains into an effective electromechanical medium. Due to the comparably low implementation effort, the approach is a useful means for the development of a variety of nonlinear constitutive models of functional materials like morphotropic PZT compositions, antiferroelectrics or ferromagnets. The feasibility of the approach is demonstrated by comparison with Finite Element calculations. (C) 2014 Elsevier Ltd. All rights reserved.