Brittle membranes in finite elasticity

2022/04/08 by Almi, Stefano, Reggiani, Dario, Solombrino, Francesco · 3 citations
#49J45 #74K15 #74R10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2204.04171

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 C¹-local immersions on regular subdomains of the cracked set, and (ii) the construction of recovery sequences by means of suitable W^1,∞ diffeomorphisms mapping the regular subdomains onto the fractured configuration.

Cited by

• Derivation of variational membrane models in the context of anisotropic nonlocal hyperelasticity
• The effects of pressure loads in the dimension reduction of elasticity models
• Derivation of Kirchhoff-type plate theories for elastic materials with voids

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