Numerical representation for anisotropic materials based on coenergy modeling

The aim of this paper is to propose a numerical model of the magnetic behavior law of soft materials based on the equivalence between the vectorial B(H) relationship and a compact representation using the coenergy density w′ as a function of the magnetic field H. The experimental data needed are the B(H) curves in the rolling and transverse directions (respectively x and y). The anisotropic behavior of the sheet is taken into account by a proper modeling of the contours of equal coenergy over the Hx–Hy plan. Then the curves along any direction are derived from the coenergy density. This model is built to reproduce the decoupling of the magnetization processes at low field as well as the emergence of the difficult direction at 54.7° at higher fields, which is a typical behavior of grain-oriented silicon steel sheets. This model has been implemented and tested with experimental data for Goss textured sheets. The B(H) curves in various directions are computed with an error less than 5% over the whole range of magnetization.