A Reshetnyak-type lower semicontinuity result for linearised elasto-plasticity coupled with damage in W1,n

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 αkEuk with respect to the weak convergence αk⇀ α in W1,n(Ω) and the weak∗ convergence uk⇀ ∗ u in BD(Ω) , E denoting the symmetrised gradient. A concentration compactness argument shows that the limit has the form αEu+η, with η supported on an at most countable set.