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Macroscopic properties of ferroelectrics are controlled by processes on the microscale, in particular the switching of crystal unit cells and the movement of domain walls, respectively. Besides these microscopic levels, the grains of a polycrystalline material constitute the mesoscopic scale. Interactions of grains with statistically distributed orientations, as a consequence of mechanical and electrostatic mismatch, give rise to for example, residual stress which in turn affects domain switching. A multiscale modeling thus has to incorporate at least three interacting scales. In this context, the condensed method has recently been elaborated as an efficient tool with low computational cost and effort of implementation. It is extended toward statistical distributions of grain sizes in a representative material volume element and amended with regard to the modeling of domain evolution. Each of the few parameters of the constitutive approach has a unique physical meaning and is adapted to available experimental values of macroscopic quantities of barium titanate taken from various sources.

Due to the multifunctional applicability, smart materials are of particular interest in the field of material modeling. Most of the developed models, describing the nonlinear behavior, are implemented within the framework of the Finite Element Method (FEM). However, most investigations are restricted to simple boundary value problems (BVP) under uniaxial loading and their goal is the calculation of hysteresis loops. Regarding this circumstance, the so‐called condensed method (CM) is introduced to investigate the macroscopic polycrystalline ferroelectric material behavior at a global material point without any kind of discretization scheme. In the presented paper, the CM is extended towards ferromagnetic and multiferroic material behavior. Moreover, numerical results for a pure ferromagnetic behavior and a comparison between the magnetoelectric coupling coefficient calculated by the FEM and the CM are presented. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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A condensed model for ferroelectric solids with tetragonal unit cells is presented. The approach is microelectromechanically and physically motivated, considering discrete switching processes on the level of unit cells and quasi-continuous evolution of inelastic fields on the domain wall level. To calculate multiple grain interactions an interaction tensor is introduced. Hysteresis loops are simulated for pure electric and electromechanical loading, demonstrating e.g. the influence of a compressive preload on the poling process and interaction between statistically arranged crystallits. The residual stresses and the corresponding principle stresses are used to simulate fatigue damage in ferroelectric materials.

This research is about determining the effects of phase transitions in lead zirconate titanate. Transformations between tetragonal and rhombohedral phases have been implemented using an adapted evolution law. Predictions concering polycrystalline material behavior are made by the condensed method. Stresses and strains under electric loads are considered to investigate upcoming effects near the morphotropic phase boundary. An interpretation concerning actuator applications will be provided.