On hysteresis in elasto-plasticity and in ferromagnetism

We define hysteresis as rate-independent memory, illustrate some of its properties, and review some scalar models of elasto-plasticity: the stop, the play, the Prandtl=Ishlinskii models. In particular we study the Prager model of linear kinematic hardening, which encompasses stops and plays. We then couple the latter model with the dynamic equation for a one-dimensional system, show existence of a weak solution, and deal with its homogenization. We also discuss the extension to tensors and to three-dimensional systems. We then deal with ferromagnetic hysteresis. We review the classic Preisach model and a vector extension. Finally, we formulate a model of vector ferromagnetic hysteresis, couple it with the magnetostatic equations, and discuss its homogenization. The latter consists in a two-length-scale model, and corresponds to a variant of the vector Preisach model. (C) 2002 Elsevier Science Ltd. All rights reserved.