WIAS Preprint No. 1612, (2011)

Generalized Prandtl--Ishlinskii operators arising from homogenization and dimension reduction


  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

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

Appeared in

  • Phys. B, 407 (2012) pp. 1330--1335.

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