*Published Paper*

**Inserted:** 13 jul 2017

**Last Updated:** 21 feb 2019

**Journal:** NoDEA Nonlinear Differential Equations Appl.

**Volume:** 25

**Pages:** Article 25:16

**Year:** 2018

**Doi:** 10.1007/s00030-018-0507-9

**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 $u_k\stackrel{*}\rightharpoonup u$ 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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