Published Paper
Inserted: 11 apr 2022
Last Updated: 9 nov 2023
Journal: Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
Volume: 103
Number: 11
Pages: 29
Year: 2023
Doi: 10.1002/zamm.202200525
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 $GSBV^{p}$ 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.