An Effective Material Approach for the Nonlinear Eddy Current Problem for a Laminated Open Core Including Stray Fields

Effective materials are an efficient way to solve the eddy current problem for devices consisting of many thin steel sheets. They allow to replace the fine-structured geometry by a bulk medium that is cheap to resolve in the finite element mesh. The parameters of this effective material are obtained using a suitable cell problem. By utilizing a complex permeability, the effective formulation becomes a static one, requiring only a magnetic scalar potential, which further reduces both the required memory and the computation time. However, conventional effective material theory requires the magnetic flux to be aligned with the sheets, i.e. stray fields cannot be accounted for. This paper presents a way to include stray fields in an effective material in an efficient way. A numerical example using an open core shows very satisfying results at the cost of only a single additional scalar potential restricted to the bulk medium.