On energy dissipation and hysteresis of materials in electromagnetic formulations, the dilemma of heterogeneity, local non linear properties, and fields coupling

Most soft materials used in power electrical devices adopt more or less organized small structures with domains and walls. Microscopic eddy currents are therefore induced with time varying fields, they give rise to excess losses and dynamic hysteresis. In this paper, we first introduce magnetic and electric dynamic properties and dedicated formulations usable within numerical simulation tools. We then argue the use of local homogeneous parameters, which is closely linked to the choice of fields coupling at each border of a given region.