Constitutive modeling of polycrystalline multiconstituent and multiphase ferroic materials based on a condensed approach

The constitutive behavior of polycrystalline ferroelectric or ferromagnetic materials is essentially determined by ferroelectric domain and ferromagnetic Bloch or Neel wall motions, respectively, on the one hand and grain interactions on the other. In physically motivated models, domain switching and the rotation of elementary magnets, respectively, are directly considered coping with the first issue. In phenomenological macroscale approaches, both domain processes and grain interactions are merged in one constitutive model. The implementation of constitutive equations into a finite element code provides intrinsic interactions due to the coupling of physical quantities on the node- and element-level. The condensed approach is based on microphysical considerations of domains and accounts for grain interaction on the level of generalized residual stresses due to mismatches of individual grains and the associated effective medium. The approach is first applied to the prediction of magnetoelectric coupling in a multiferroic ferroelectric–ferromagnetic compound, where its basic idea is translated to model interactions of the constituents without going back to any discretization scheme. Second, a tetragonal–rhombohedral ferroelectric composition is considered with associated interactions in multiphase grains.