Some physical concepts important for a hysteresis model (effective field, anhysteretic magnetization) are discussed on the example of Jiles-Atherton model. The Jiles-Atherton model reveals some drawbacks, which make this model more difficult to be applied in electrical engineering. In particular, it does not describe accurately the magnetization curves after a reversal, moreover complex magnetization cycles are poorly represented. On the other hand, the phenomenological description proposed by Takács seems to be a valuable alternative to the Jiles-Atherton formalism. The concept of effective field may be easily incorporated in the description.

The fixed-point theorem is widely used in different engineering applications. The present paper focuses on its applications in optimisation. A Matlab toolbox, chich implements the branch-and-bound optimisation method based on the fixed-point theorem, is used for solving different real-life test problems, including estimation of model parameters for the Jiles-Atherton model.

An extension of the modified Jiles-Atherton description to include the effect of anisotropy is presented. Anisotropy is related to the value of the angular momentum quantum number J, which affects the form of the Brillouin function used to describe the anhysteretic magnetization. Moreover the shape of magnetization dependent R(m) function is influenced by the choice of the J value.

The paper presents a formula useful for prediction of loss density in soft magnetic materials, which takes into account multi-scale energy dissipation. A universal phenomenological P(Bm, f) relationship is used for loss prediction in chosen soft magnetic materials. A bootstrap method is used to generate additional data points, what makes it possible to increase the prediction accuracy. A substantial accuracy improvement for estimated model parameters is obtained in the case, when additional data points are taken into account. The proposed description could be useful both for device designers and researchers involved in computational electromagnetism.