Microstructure evolution model in micromagnetics

Abstract

The proposed model combines tendency for minimization of Gibbs’ magnetic energy with the rate-independent maximum-dissipation mechanism that reflects the macroscopical quantity of energy required to change one pole of a magnet to another. The microstructure is described on a “mesoscopical” level in terms of Young measures. Such mesoscopical, distributed-parameter model is formulated (and, after a suitable regularization), analyzed, discretized, implemented, and eventually tested computationally on a uni-axial magnet. The desired hysteresis “macroscopical” response is demonstrated together with the influence of material properties.