Brittle membranes in finite elasticity

Abstract

AbstractThis 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 of functions satisfying a maximal‐rank constraint on the subgradients, which can be approximated by C1‐local immersions on regular subdomains of the cracked set, and (ii) the construction of recovery sequences by means of suitable diffeomorphisms mapping the regular subdomains onto the fractured configuration.