Brittle membranes in finite elasticity

This work is devoted to the variational derivation of a reduced model for brittle membranes in finite elasticity. The main mathematical tools we develop our analysis are: (i) new density result G S B V p $GSBV^{p}$ functions satisfying maximal-rank constraint on subgradients, which can be approximated by C1-local immersions regular subdomains cracked set, and (ii) construction recovery sequences means suitable W 1 , ∞ $W^{1,\infty }$ diffeomorphisms mapping onto fractured configuration.