In this article we propose a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic formulation. In particular, the stored magnetic energy and the dissipated energy are known at all times, and not solely after the completion of closed hysteresis loops as is usually the case. The obtained incremental formulation is variationally consistent, i.e., all internal variables follow from the minimization of a thermodynamic potential. This variational approach is directly inspired from the kinematic hardening theory of plasticity, which opens the door for novel energy-consistent coupled mechanical/electromagnetic models.
Energy-Consistent Finite Element Modelling of Ferromagnetic Hysteresis
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Geuzaine, C, Stainier, L, & Henrotte, F. "Energy-Consistent Finite Element Modelling of Ferromagnetic Hysteresis." Proceedings of the ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. Volume 4: Advanced Manufacturing Processes; Biomedical Engineering; Multiscale Mechanics of Biological Tissues; Sciences, Engineering and Education; Multiphysics; Emerging Technologies for Inspection and Reverse Engineering; Advanced Materials and Tribology. Nantes, France. July 2–4, 2012. pp. 319-320. ASME. https://doi.org/10.1115/ESDA2012-82050
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