| Issue |
ESAIM: M2AN
Volume 46, Number 4, July-August 2012
|
|
|---|---|---|
| Page(s) | 813 - 839 | |
| DOI | https://doi.org/10.1051/m2an/2011072 | |
| Published online | 03 February 2012 | |
A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies
1 Laboratoire LAMSIN, École Nationale d’Ingénieurs de Tunis, Université Tunis El Manar, B.P. 37, 1002 Tunis-Belvédère, Tunisia
Saber.Amdouni@insa-lyon.fr
2 Université de Lyon, CNRS, INSA-Lyon, ICJ UMR5208, 69621 Villeurbanne, France
3 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
4 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
5 Université de Lyon, CNRS, INSA-Lyon, ICJ UMR5208, LaMCoS UMR5259, 69621 Villeurbanne, France
Yves.Renard@insa-lyon.fr
Received: 23 June 2011
Revised: 18 November 2011
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.
Mathematics Subject Classification: 74M15 / 74S05 / 35M85
Key words: Extended finite element method (Xfem) / crack / unilateral contact / Signorini’s problem
© EDP Sciences, SMAI, 2012
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