On the Energy-Based Variational Model for Vector Magnetic Hysteresis

We consider the quasi-static magnetic hysteresis model based on a dry-friction-like representation of magnetization. The model has a consistent energy interpretation, is intrinsically vectorial, and ensures a direct calculation of the stored and dissipated energies at any moment in time, and hence not only on the completion of a closed hysteresis loop. We discuss the variational formulation of this model and derive an efficient numerical scheme, avoiding the usually employed approximation, which can be inaccurate in the vectorial case. The parameters of this model for a nonoriented steel are identified using a set of first-order reversal curves. Finally, the model is incorporated as a local constitutive relation into a 2-D finite-element simulation accounting for both the magnetic hysteresis and the eddy current.