Modeling the constitutive behavior of ferroelectric,ferromagnetic and multiferroic materials by using the condensed method (CM)

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)