Homogenization in gradient plasticity

✍ Scribed by Hauke Hanke

• Book ID: 102217316
• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 107 KB
• Volume: 34
• Category: Article
• ISSN: 0936-7195
• DOI: 10.1002/gamm.201110016

✦ Synopsis

Abstract

This paper yields a two‐scale homogenization result for a rate‐independent elasto‐plastic system. The presented model is a regularization of the classical model of linearized elastoplasticity with hardening, which is extended by a gradient term of the plastic variables. The associated stored elastic energy density has periodically oscillating coefficients, where the period is scaled by ε > 0. The additional gradient term of the plastic variables z is contained in the elastic energy with a prefactor ε^γ^ (γ ≥ 0). We derive different limiting models for ε → 0 in dependence of γ. For γ > 1 the limiting model is the two‐scale model derived in [5], where no gradient term was present. For γ = 1 the gradient term of the plastic variable survives on the microscopic cell problem, while for γ ∈ [0, 1) the limit model is defined in terms of a plastic variable without microsco pic fluctuation. The latter model can be simplified to a purely macroscopic elasto‐plasticity model by homogenization of the elastic part (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)