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 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,W-infinity diffeomorphisms mapping the regular subdomains onto the fractured configuration.

Automated summary

This work focuses on deriving a simplified model for brittle membranes in finite elasticity through variational methods. The main mathematical tools used in this analysis include: (i) a new density result in GSBV(P) for functions that satisfy 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 using suitable W-1, W-infinity diffeomorphisms that map the regular subdomains onto the fractured configuration.