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A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies

Published online by Cambridge University Press:  03 February 2012

Saber Amdouni ,
Patrick Hild ,
Vanessa Lleras ,
Maher Moakher  and
Yves Renard
Saber Amdouni
Affiliation:
Laboratoire LAMSIN, École Nationale d’Ingénieurs de Tunis, Université Tunis El Manar, B.P. 37, 1002 Tunis-Belvédère, Tunisia. Saber.Amdouni@insa-lyon.fr ; maher.moakher@enit.rnu.tn Université de Lyon, CNRS, INSA-Lyon, ICJ UMR5208, 69621 Villeurbanne, France
Patrick Hild
Affiliation:
Laboratoire de Mathématiques de Besançon, CNRS UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France; patrick.hild@univ-fcomte.fr
Vanessa Lleras
Affiliation:
Institut de Mathématiques et de Modélisation de Montpellier, CNRS UMR 5149, Université de Montpellier 2, Case courrier 51, Place Eugène Bataillon, 34095 Montpellier Cedex, France; vlleras@math.univ-montp2
Maher Moakher
Affiliation:
Laboratoire LAMSIN, École Nationale d’Ingénieurs de Tunis, Université Tunis El Manar, B.P. 37, 1002 Tunis-Belvédère, Tunisia. Saber.Amdouni@insa-lyon.fr ; maher.moakher@enit.rnu.tn
Yves Renard
Affiliation:
Université de Lyon, CNRS, INSA-Lyon, ICJ UMR5208, LaMCoS UMR5259, 69621 Villeurbanne, France; Yves.Renard@insa-lyon.fr
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Abstract

The purpose of this paper is to provide a priori error estimates on the approximation of contact conditions in the framework of the eXtended Finite-Element Method (XFEM) for two dimensional elastic bodies. This method allows to perform finite-element computations on cracked domains by using meshes of the non-cracked domain. We consider a stabilized Lagrange multiplier method whose particularity is that no discrete inf-sup condition is needed in the convergence analysis. The contact condition is prescribed on the crack with a discrete multiplier which is the trace on the crack of a finite-element method on the non-cracked domain, avoiding the definition of a specific mesh of the crack. Additionally, we present numerical experiments which confirm the efficiency of the proposed method.

Keywords

Extended finite element method (Xfem)crackunilateral contactSignorini’s problem
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 4 , July 2012 , pp. 813 - 839
Copyright
© EDP Sciences, SMAI, 2012

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