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A Reshetnyak-type lower semicontinuity result for linearised elasto-plasticity coupled with damage in \(W^{1,n}\)

  • Vito Crismale
  • Gianluca Orlando
Article
  • 39 Downloads

Abstract

In this paper we prove a lower semicontinuity result of Reshetnyak type for a class of functionals which appear in models for small-strain elasto-plasticity coupled with damage. To do so we characterise the limit of measures \(\alpha _k\,{\mathrm {E}}u_k\) with respect to the weak convergence \(\alpha _k\rightharpoonup \alpha \) in \(W^{1,n}(\Omega )\) and the weak\(^*\) convergence \(u_k{\mathop {\rightharpoonup }\limits ^{*}}u\) in \(BD(\Omega )\), \({\mathrm {E}}\) denoting the symmetrised gradient. A concentration compactness argument shows that the limit has the form \(\alpha \,{\mathrm {E}}u+\eta \), with \(\eta \) supported on an at most countable set.

Keywords

Reshetnyak theorem Lower semicontinuity Elasto-plasticity Damage 

Mathematics Subject Classification

49J45 74G65 35B33 74C05 74R99 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CMAP, École Polytechnique, UMR CNRS 7641Palaiseau CedexFrance
  2. 2.TUMGarching bei MünchenGermany

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