Calculus of Variations and Geometric Measure Theory

S. Almi - D. Reggiani - F. Solombrino

Brittle membranes in finite elasticity

created by solombrino on 11 Apr 2022
modified on 09 Nov 2023


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

ArXiv: 2204.04171 PDF


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.