Mesoscopic model for ferromagnets with isotropic hardening

Abstract

The proposed model combines tendency for minimization of Gibbs’ magnetic energy with the rate-independent maximum-dissipation mechanism that reflects the macroscopic quantity of energy required to change one pole of a magnet to another. This energy can increase within the evolution which is the effect like hardening in plasticity. The microstructure is described on a “mesoscopic” level in terms of Young measures. Such a mesoscopic, distributed-parameter model is formulated (and, after a suitable regularization), analyzed, discretized, implemented, and eventually tested computationally on a uni-axial magnet. The desired hysteretic “macroscopic” response, including effects as virgin curves and minor loops, is demonstrated.