Computational Homogenization in Micro-Magneto-Elasticity

The overall macroscopic response of magneto-mechanically coupled materials stems from complex magnetization evolution and corresponding domain wall motion occurring on a lower length scale. In order to account for such effects we propose a computational homogenization approach that incorporates a ferromagnetic phase-field formulation into a macroscopic Boltzmann continuum. This scale-bridging is obtained by rigorous definition of rate-type and incremental variational principles. An extended version of the classical Hill-Mandel macro-homogeneity condition is obtained as a consequence. In order to satisfy the unity constraint of the magnetization on the micro-scale, an efficient operator-split method is proposed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)