  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 $GSBV^{p}$ 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.
