Brittle membranes in finite elasticity
Stefano Almi, Dario Reggiani, Francesco Solombrino · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2023
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 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.