A condensed approach to model the constitutive behavior of multiphase ferroelectric and multiferroic materials

Ferroelectric as well as ferromagnetic materials are widely used in smart structures and devices as actuators, sensors etc. Most of the developed models, describing the nonlinear behavior, are implemented within the framework of the Finite Element Method. Most investigations, however, are restricted to simple boundary value problems under uniaxial or biaxial loading and their goal is the calculation of hysteresis loops or to determine e.g. electromechanical coupling coefficients. Regarding these circumstances, the so-called condensed method (CM) is introduced to investigate the macroscopic polycrystalline ferroelectric material behavior at a macroscopic material point without any kind of discretization scheme. In the presented paper, the CM is extended towards multiphase ferroelectric material behavior. Moreover, first numerical results of a multiphase ferroelectric material at the morphotropic phase boundary are presented. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)