Generalized Prandtl--Ishlinskii operators arising from homogenization and dimension reduction
- Mielke, Alexander
2010 Mathematics Subject Classification
- 34C55 47J40 774Qxx 74C05 74K20
- Hysteresis operators, play operator, Prandtl-Ishlinskii operator, Gamma convergence, rate-independent system, homogenization, elastoplasticity, plastic plate model
We consider rate-independent evolutionary systems over a physically 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
- Phys. B, 407 (2012) pp. 1330--1335.