Linearized elasticity as Mosco limit of finite elasticity in the presence of cracks-Reference-Cited by-同舟云学术

Linearized elasticity as Mosco limit of finite elasticity in the presence of cracks

Published:2020-01-01 Issue:1 Volume:13 Page:33-52
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
language:
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Author:

Gussmann Pascal¹,Mielke Alexander²

Affiliation:

1. Weierstrass-Institut, Mohrenstrasse 39, 10117Berlin, Germany

2. Weierstrass-Institut, Mohrenstrasse 39, 10117Berlin, Germany; and Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Germany

Abstract

AbstractThe small-deformation limit of finite elasticity is considered in presence of a given crack. The rescaled finite energies with the constraint of global injectivity are shown to Γ-converge to the linearized elastic energy with a local constraint of non-interpenetration along the crack.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2017-0010/pdf

Reference34 articles.

1. Injectivity and self-contact in nonlinear elasticity;Arch. Ration. Mech. Anal.,1987

2. Linearized plasticity is the evolutionary Γ-limit of finite plasticity;J. Eur. Math. Soc. (JEMS),2013

3. Ground states in complex bodies;ESAIM Control Optim. Calc. Var.,2009

4. Linearized elasticity as Γ-limit of finite elasticity;Set-Valued Anal.,2002

5. Injectivity and self-contact in nonlinear elasticity;Arch. Ration. Mech. Anal.,1987

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