Modèles Energétiques d’Hystérésis Magnétique - Développement Théorique et Formulations pour la Méthode des Elements Finis

This work focuses on the development of a highly accurate energy-based hysteresis model for the modeling of magnetic hysteresis phenomena. The model relies on an explicit representation of the magnetic pinning effect as a dry friction-like force acting on the magnetic polarization. Unlike Preisach and Jiles-Atherton models, this model is vectorial from the beginning and derives from thermodynamic first principles. Three approaches are considered: the first one, called vector play model, relies on a simplification that allows an explicit, and thus fast, update rule, while the two others, called the variational and the differential approaches, avoid this simplification, but require a non-linear equation to be solved iteratively. The vector play model and the variational approach were already used by other researchers, whereas the differential approach introduced in this thesis, is a new, more efficient, exact implementation, which combines the efficiency of the vector play model with the accuracy of the variational approach. The three hysteresis implementations lead to the same result for purely unidirectional or rotational excitation cases, and give a rather good approximation in all situations in-between, at least in isotropic material conditions. These hysteresis modeling approaches are incorporated into a finite-element code as a local constitutive relation with memory effect. The inclusion is investigated in detail for two complementary finite-element formulations, magnetic field h or flux density b conforming, the latter requiring the inversion of the vector hysteresis model, naturally driven by h, for which the Newton-Raphson method is used. Then, at the finite-element level, once again, the Newton-Raphson technique is adopted to solve the nonlinear finite-element equations, leading to the emergence of discontinuous differential reluctivity and permeability tensors, requiring a relaxation technique in the Newton-Raphson scheme. To the best of the author’s knowledge, the inclusion of an energy-based hysteresis model has never been successfully achieved in a b-conform finite-element formulation before.FEDO (Free Software for Electric Drive Optimization