Generalized Prandtl-Ishlinskii operators arising from homogenization and dimension reduction
Please always quote using this URN: urn:nbn:de:0296-matheon-8789
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.
| Author: | Alexander Mielke |
|---|---|
| URN: | urn:nbn:de:0296-matheon-8789 |
| Referee: | Carsten Carstensen |
| Language: | English |
| Date of first Publication: | 10.08.2011 |
| Tag: | Gamma convergence; Prandtl-Ishlinskii operator; elastoplasticity; homogenization; hysteresis operators; plastic plate model; play operator; rate-independent systems |
| Institute: | Humboldt-Universität zu Berlin |
| Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) | |
| Project: | C18 Analysis and numerics of multidimensional models for elastic phase transformations in shape-memory alloys |
| MSC-Classification: | 34C55 Hysteresis |
| 47J40 Equations with hysteresis operators [See also 34C55, 74N30] | |
| 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials) | |
| 74K20 Plates | |
| Preprint Number: | Matheon Preprint #813 |


