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Locking-Free Finite Elements for Unilateral CrackProblems in Elasticity

Published online by Cambridge University Press:  27 January 2009

Z. Belhachmi ,
J.-M. Sac-Epée  and
S. Tahir
Z. Belhachmi*
Affiliation:
LMAM UMR7122, Université Paul Verlaine de Metz, Ile du Saulcy, 57045 Metz, France
J.-M. Sac-Epée
Affiliation:
LMAM UMR7122, Université Paul Verlaine de Metz, Ile du Saulcy, 57045 Metz, France
S. Tahir
Affiliation:
LMAM UMR7122, Université Paul Verlaine de Metz, Ile du Saulcy, 57045 Metz, France
*
belhach@univ-metz.fr
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Abstract

We consider mixed and hybrid variational formulations to the linearized elasticity system in domains with cracks. Inequality type conditions are prescribed at the crack faces which results in unilateral contact problems. The variational formulations are extended to the whole domain including the cracks which yields, for each problem, a smooth domain formulation. Mixed finite element methods such as PEERS or BDM methods are designed to avoid locking for nearly incompressible materials in plane elasticity. We study and implement discretizations based on such mixed finite element methods for the smooth domain formulations to the unilateral crack problems. We obtain convergence rates and optimal error estimates and we present some numerical experiments in agreement with the theoretical results.

Keywords

crack problemsvariational inequalitiessmooth domain methodmixed finite elementsa priori estimates
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 1: Modelling and numerical methods in contact mechanics , 2009 , pp. 1 - 20
Copyright
© EDP Sciences, 2009

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