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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.

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Metadaten
Author:Alexander Mielke
URN:urn:nbn:de:0296-matheon-8789
Referee:Carsten Carstensen
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/08/10
Release Date:2011/08/10
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)
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Cxx Qualitative theory [See also 37-XX] / 34C55 Hysteresis
47-XX OPERATOR THEORY / 47Jxx Equations and inequalities involving nonlinear operators [See also 46Txx] (For global and geometric aspects, see 58-XX) / 47J40 Equations with hysteresis operators [See also 34C55, 74N30]
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Cxx Plastic materials, materials of stress-rate and internal-variable type / 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Kxx Thin bodies, structures / 74K20 Plates
Preprint Number:813
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