Generalized Prandtl-Ishlinskii operators arising from homogenization and dimension reduction

We consider rate-independent evolutionary systems over a physical domain Ω that are governed by simple hysteresis operators at each material point. For multiscale systems where ε denotes the ratio between the microscopic and the macroscopic length scale, we show that in the limit ε→0 we are led to systems where the hysteresis operators at each macroscopic point is a generalized Prandtl-Ishlinskii operator.