On energy consistent vector hysteresis operators

TL;DR

This paper introduces an energy-based representation of vector hysteresis operators in magnetic materials, facilitating magnetic field computations via scalar and vector potentials, supported by numerical finite element simulations.

Contribution

It provides an equivalent energy-based formulation of vector hysteresis operators using convex duality, enhancing computational approaches in magnetic field modeling.

Findings

Demonstrates equivalence between energy-based and existing hysteresis models

Develops inverse hysteresis operator for vector potential computations

Provides numerical validation through finite element simulations

Abstract

Incremental models for magnetic vector hysteresis have been developed in previous works in accordance with basic principles of thermodynamics. In this paper, we present an equivalent representation of the associated hysteresis operator in terms of a co-energy functional which is useful for magnetic field computations based on a scalar potential. Using convex duality, we further define the corresponding energy functional and the associated inverse hysteresis operator which is required for computations based on the vector potential. The equivalence of the two representations with the energy-based hysteresis models proposed in earlier works is demonstrated and numerical results for some typical test problems are presented obtained by finite element simulation of corresponding scalar and vector potential formulations.