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Magnetic hysteresis holds significant technical and physical importance in the design of electromagnetic components. Despite extensive research in this area, modeling magnetic hysteresis remains a challenging task that is yet to be fully resolved. The purpose of this paper is to study vector hysteresis play models for anisotropic ferromagnetic materials in a physical, thermodynamical approach.

In this work, hysteresis play models are implemented to interpret magnetic properties, drawing upon classical rate-independent plasticity principles derived from continuum mechanics theory. By conducting qualitative and quantitative verification and validation, various aspects of ferromagnetic vector hysteresis were thoroughly examined. By directly incorporating the hysteresis play models into the primal formulations using fixed point method, the proposed model is validated with measurements in a finite element (FE) environments.

The proposed vector hysteresis play model is verified with fundamental properties of hysteresis effects. Numerical analysis is performed in an FE environment. Measured data from a rotational single sheet tester (RSST) are validated to the simulated results.

The results of this work demonstrates that the essential properties of the hysteresis effects by electrical steel sheets can be represented by the proposed vector hysteresis play models. By incorporation of hysteresis play models into the weak formulations of the magnetostatic problem in the h-based magnetic scalar potential form, magnetic properties of electrical steel sheets can be locally analyzed and represented.

The accurate modeling of magnetic hysteresis in electrical steels is important in several electrical and electronic applications. Numerical models have long been known that can correctly reproduce some typical behaviours of these magnetic materials. Among these, the model proposed by Jiles and Atherton must certainly be mentioned. This model is intuitive and fairly easy to implement and identify with relatively few experimental data. Also, for this reason, it has been extensively studied in different formulations. The developments and numerical tests made on this hysteresis model have indicated that it is able to accurately reproduce symmetrical cycles, especially the major loop, but often it fails to reproduce non-symmetrical cycles. This paper aims to show the positive aspects and highlight the defects of the different formulations in predicting the minor loops of electrical steels excited by non-sinusoidal currents.

The different formulations are applied to different electrical steels, and the data coming from the simulations are compared with those measured experimentally. The direct and inverse Jiles–Atherton models, including the introduction of the dissipative factor approach, are presented, and their limitations are proposed and validated using the measurements of three non-grain-oriented materials. Only the measured major loop is used to identify the parameters of the Jiles–Atherton model. Furthermore, the direct and inverse Jiles–Atherton models were used to simulate the minor loops as well as the hysteresis cycles with direct component (DC) bias excitation. Finally, the simulation results are discussed and compared to measurements for each study case.

The paper indicates that both the direct and the inverse Jiles–Atherton model formulations provide a good agreement with the experimental data for the major loop representation; nevertheless, both models can not accurately predict the minor loops even when the modification approaches proposed in the literature were implemented.

The Jiles–Atherton model and its modifications are widely discussed in the literature; however, some limitations of the model and its modification in the case of the distorted current waveform are not completely highlighted. Furthermore, this paper contains an original discussion on the accuracy of the prediction of minor loops from distorted current waveforms, including DC bias.