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.