A multiscale model for magneto-elastic couplings

At the macroscopic scale two different phenomena illustrate the couplings between the elastic and magnetic behaviours of ferromagnetic materials: first, magnetisation induces a deformation mechanism called magnetostriction, and, second, stresses have an effect on the magnetic behaviour. The complexity of the non-linear relations between these phenomena is such that few realistic macroscopic constitutive equations have been proposed to model the coupled magneto-elastic behaviour of magnetic materials. Magnetisation and magnetostriction are macroscopic manifestations of the complex magnetic domain structure that is modified by applied mechanic and magnetic loads. Herein, it is proposed to use homogenisation methods to deduce the macroscopic behaviour of single crystals and polycrystals from a statistical description of the magnetic domain structure. Therefore, the macroscopic couplings naturally arise from the expression of the free energy written at the level of the magnetic domains.