Hysteresis and phase transitions

Martin Brokate

This monograph contributes to the mathematical analysis of systems exhibiting hysteresis effects and phase transitions. Its main part begins with a detailed study of models for scalar rate independent hysteresis in the form of hysteresis operators. Applications to ferromagnetism, elastoplasticity and fatigue analysis are presented, and two representative distributed systems with hysteresis operator are discussed. The attention then shifts to the mechanisms of energy dissipation and transformation that induce a hysteretic behavior in continuous media undergoing phase transitions. After an introduction to phenomenological thermodynamic theories of phase transitions, in particular, the Landau-Ginzburg theory and phase field models, several specific models are discussed in detail. These include Falk's model for the hysteresis in shape memory alloys and the phase field models due to...

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