A differential algebraic approach for the modeling of polycrystalline ferromagnetic hysteresis with minor loops and frequency dependence

In the current paper, a nonlinear differential algebraic approach is proposed for the modeling of hysteretic dynamics of polycrystalline ferromagnetic materials. The model is constructed by employing a phenomenological theory to the magnetization orientation switching. For the modeling of hysteresis in polycrystalline ferromagnetic materials, the single crystal model is applied to each magnetic domain along its own principal axis. The overall dynamics of the polycrystalline materials is obtained by taking a weighted combination of the dynamics of all magnetic domains. The weight function for the combination is taken as the distribution function of the principal axes. Numerical simulations are performed and comparisons with its experimental counterparts are presented. The hysteretic dynamics caused by orientation switching processes is accurately captured by the proposed model. Minor hysteresis loops associated with partial-amplitude loadings are also captured. Rate dependence of the hysteresis loops are inherently incorporated into the model due to its differential nature.