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arXiv · 2204.04171

Brittle membranes in finite elasticity

Stefano Almi·Dario Reggiani·Francesco Solombrino
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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.

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Stefano Almi, Dario Reggiani, Francesco Solombrino. 2022-09-22. Brittle membranes in finite elasticity. https://arxiv.org/abs/2204.04171

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