The coupling of magnetic and electric fields due to the constitutive behavior of a material is commonly denoted as magnetoelectric (ME) effect. In this work, the theoretical background of nonlinear constitutive multifield behavior as well as the Finite Element (FE) implementation are presented. Nonlinear material models describing the magneto-ferroelectric or electro-ferromagnetic behaviors are presented. Both physically and phenomenologically motivated constitutive models have been developed for the numerical calculation of the nonlinear magnetostrictive and ferroelectric behaviors. On this basis, the polarization in the ferroelectric and magnetization in the ferromagnetic respectively magnetostrictive phases are simulated and the resulting effects analyzed. Numerical simulations focus on the prediction of local domain orientations and residual stress going along with the poling process, thus supplying information on favorable electric-magnetic loading sequences. Goals are to improve the efficiency of ME coupling and to reduce damage associated with the poling process. Further, the developed tools enable the prediction of the electromagnetomechanical properties of smart multiferroic composites and supply useful means for their optimization. The resulting final state of a poling simulation can be implemented as a starting condition for approximate linear simulations and multifield homogenization procedures.

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