Electromagnetic phenomena in heterogeneous media: Effective properties and local behavior

Abstract

The purpose of this paper is the use of a mathematical homogenization approach based on the multiple scale expansion theory for modeling the electromagnetic phenomena arising in heterogeneous media under an imposed magnetic flux. The attention is focused on the analysis and discussion of the merits and limits of this theoretical approach in reproducing not only the effective macroscopic properties but also the local behavior, under a wide frequency range and considering different constitutive and geometrical parameters. The results show that the proposed method is able to predict local and integral physical quantities, ranging from a substantially global behavior in the whole media to significantly localized effects determined by the microscopic structure.

Connection between microstructure and magnetic properties of soft magnetic materials

“…In this case too, a direct connection between excess loss and hysteresis loss is found. A detailed analysis of the residual role played by eddy currents in soft ferrites can be carried out by appropriate homogenization techniques [49,50] applied to the heterogeneous microstructure of the ferrite core, consisting of grains and inter-grain layers. This approach permits one, in particular, to determine the conditions associated with qualitatively different dynamical regimes, one where closed eddy current flow patterns are present inside each individual grain, and the other where eddy currents flow across inter-grain layers and generate patterns extending over the entire ferrite core.…”

Magnetic loss, permeability dispersion, and role of eddy currents in Mn–Zn sintered ferrites

“…The problem associated with the electrical conduction process and its dependence on f in the heterogeneous ferrite structure has been solved by numerical methods, emulating such a structure with a regular array of identical cubic grains of side /sS with intervening dielectric layer [8]. A great simplification is obtained by adopting a mathematical homogenization technique [9]. This permits one to make an estimate of thickness, permittivity, and resistivity of the boundary layers and resistivity of the grains, starting from the experimentally known /sS, R s (f), and X s (f) values.…”

“…is then calculated through the governing Maxwell's equation and the so-called classical energy loss (including the dielectric losses) W cl (J p , f) is obtained [9]. W cl is in fact the result expected for a perfectly homogeneous material.…”

A multiscale approach to the analysis of magnetic grid shields and its validation

“…Being inconceivable to directly solve the problem with heterogeneous grid structures, the analysis can be advantageously handled by adopting a mathematical homogenization technique, which replaces the heterogeneous structure with an equivalent homogeneous one. This method, also suitable for the analysis of composite material sheets, is found to be able to well reproduce the electromagnetic field behaviour without unacceptable computational burdens [8].…”