Brittle membranes in finite elasticity

TL;DR

This paper develops a variational framework for modeling brittle membranes under finite elasticity, introducing new mathematical tools to handle crack constraints and construct recovery sequences.

Contribution

It introduces a novel density result in $GSBV^{p}$ with maximal-rank constraints and constructs recovery sequences using $W^{1,inity}$ diffeomorphisms, advancing the mathematical modeling of brittle membranes.

Findings

New density result in $GSBV^{p}$ with maximal-rank constraint

Construction of recovery sequences via $W^{1,inity}$ diffeomorphisms

Mathematical framework for brittle membranes in finite elasticity

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.