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.
A Reshetnyak-type lower semicontinuity result for linearised elasto-plasticity coupled with damage in W1,n / Crismale, V.; Orlando, G.. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 25:2(2018). [10.1007/s00030-018-0507-9]
A Reshetnyak-type lower semicontinuity result for linearised elasto-plasticity coupled with damage in W1,n
Crismale V.;
2018
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 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.File | Dimensione | Formato | |
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