A new model for rate-independent hysteresis in permanent magnets

A one-dimensional memory-based model of magnetic materials exhibiting hysteresis loops is proposed here. Mainly, we suggest a modification of the Duhem model investigated by Coleman & Hodgdon in connection with isoperms in order to better fit their real behaviour. Many properties fulfilled by the original model are preserved here. For instance, the presence of the major loop, bounding all hysteresis pathes, the existence and uniqueness of asymptotically stable periodic solutions (primitive loops), the existence of a "universal" demagnetization process (a suitable alternating magnetic field, with slowly decreasing amplitude, reproducing the "virgin state"). On the other hand, a few mathematical features are common to the Preisach model and allow the corresponding hysteretic functional to avoid effects, like self-magnetization, which are typical of the Duhem modelization but physically unsound. In particular, equilibrium states are stable with respect to noises of small amplitude (static vibro-stability).