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A model for the vector magnetization of a distribution of particles with cubic anisotropy is presented. Recent work by the authors modeled the vector magnetization of a distribution of uniaxial particles by decomposing the total magnetization into reversible and irreversible components. In this paper, using an energy approach applicable to a generic plane, the model is extended to include cubic anisotropy projected to the (100) plane. The magnitude of the irreversible component is modeled using a Preisach differential-equation approach; however, other valid models can be used. The direction of the reversible component is modeled using the minimum energy approach of the classical Stoner–Wohlfarth model and taking into account the anisotropy field. The formulation of the generalized model is derived and its results are discussed considering (i) oscillation and rotational modes, (ii) lag angle, and (iii) magnetization trajectories.

In this paper, we discuss a phenomenological approach for the numerical modeling of static hysteresis of grain oriented (GO) steels at macro-magnetic scale. The modeling is inspired to a generalization in 2-d of the Preisach model (this generalization can be easily extended in 3-d, but it is not necessary here), and the magnetization dependent state of the model parameters is represented by two distinct vectors, named the interaction field and the operative field, suitably defined. In this way, the very complex behavior of the GO steel circularly or linearly polarized is reproduced with accuracy, as shown in the numerical tests reported in the paper.