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.
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Crismale, V., Orlando, G. A Reshetnyak-type lower semicontinuity result for linearised elasto-plasticity coupled with damage in \(W^{1,n}\). Nonlinear Differ. Equ. Appl. 25, 16 (2018). https://doi.org/10.1007/s00030-018-0507-9
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DOI: https://doi.org/10.1007/s00030-018-0507-9