A pragmatic two-scale homogenization technique for ferromagnetic cores at high frequencies

The strong interaction between hysteresis and eddy currents in steel laminations subjected to a time-varying magnetic field cannot be resolved without a coupled finite element modelling at the level of a single lamination. Direct use of such a lamination model into the finite element modelling of an electrical machine, for instance, can be achieved by homogenization methods which, however, make it necessary to modify the finite element code. In this paper, we propose a pragmatic homogenization approach with no implementation required, provided the simulation code at hand has enough flexibility in the description of the material laws. The lamination model is used to identify the parameters of an appropriate macroscopic irreversible material law.