Can rotational magnetization be theoretically assessed?

We review state-of-the-art modeling of two-dimensional (2D) magnetization process in soft magnets. Emphasis is placed on the phenomenological assessment of the energy losses in steel sheets under rotational field. It is stressed that a general physically based theoretical framework, exploitable for applications in practical materials and machine cores, is not available at present. However, a rational approach to the 2D magnetic losses and their frequency dependence can be pursued. This is based on the separation between quasi-static (hysteresis) and dynamic magnetization processes and the connection with their unidirectional (scalar) counterpart. A number of vector models of the 2D quasi-static hysteresis behavior, typically residing on assessed scalar models, are discussed. They have prevalent formal-mathematical character, and, while being often helpful in numerical calculations, they leave unanswered the quest for solid physical interpretation. The dynamic magnetization process can, on the other hand, rely on a 2D phenomenological extension of the rmly established physical approach to the unidirectional scalar case provided by the statistical theory of losses. This is especially true for isotropic (i.e. nonoriented) magnetic laminations, where both rotational and elliptical flux loci can be conveniently handled. It permits one to achieve general appraisal of the experiments and flexible formulation, useful for numerical applications in machine cores.