Effective Medium Transformation: The Case of Eddy Currents in Laminated Iron Cores

Effective medium theory replaces a given fine-scale heterostructure with a homogeneous one in such a way that the physically measurable quantities, e.g., reaction fields and losses, remain approximately the same. This article presents a peculiar case where the physical nature of the problem and the type of governing mathematical equations change upon homogenization. We consider a stratified nonlinear magnetic and conducting medium, where a low-frequency excitation induces eddy currents. It is shown that this eddy current problem becomes, upon homogenization, mathematically equivalent to a magnetostatic one and takes eddy currents into account via a complex-valued nonlinear
$B$
–
$H$
-curve. The homogenization procedure is demonstrated for a cylindrical laminated iron core. High accuracy of homogenization, even for the
local
loss distribution, is demonstrated.