On the Energy-Based Variational Model for Vector Magnetic Hysteresis

TL;DR

This paper introduces an energy-based variational model for vector magnetic hysteresis that provides accurate energy calculations and an efficient numerical scheme, validated through parameter identification and finite element simulations.

Contribution

It presents a novel energy-based variational formulation for vector magnetic hysteresis with an efficient numerical scheme and practical parameter identification.

Findings

Accurate energy computation at any time during hysteresis cycles.

Efficient numerical scheme avoiding common approximations.

Successful integration into 2D finite element simulations.

Abstract

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 2D finite element simulation accounting for both the magnetic hysteresis and the eddy current.