A RESHETNYAK-TYPE LOWER SEMICONTINUITY RESULT FOR LINEARISED ELASTO-PLASTICITY COUPLED WITH DAMAGE IN $W^1,n$ - Département de mathématiques appliquées Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2017

A RESHETNYAK-TYPE LOWER SEMICONTINUITY RESULT FOR LINEARISED ELASTO-PLASTICITY COUPLED WITH DAMAGE IN $W^1,n$

Résumé

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 $u_k \rightharpoonup^* u$ 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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Dates et versions

hal-01573938 , version 1 (11-08-2017)

Identifiants

  • HAL Id : hal-01573938 , version 1

Citer

Vito Crismale, Gianluca Orlando. A RESHETNYAK-TYPE LOWER SEMICONTINUITY RESULT FOR LINEARISED ELASTO-PLASTICITY COUPLED WITH DAMAGE IN $W^1,n$. 2017. ⟨hal-01573938⟩
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