Brittle membranes in finite elasticity

Abstract

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