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

Saber Amdouni (1) , Patrick Hild (2) , Vanessa Lleras (3) , Maher Moakher (4) , Yves Renard (1, 5)

1 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
3 I3M - Institut de Mathématiques et de Modélisation de Montpellier
4 ENIT - Ecole Nationale d'Ingénieurs de Tunis
5 ICJ - Institut Camille Jordan

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). This method allows to perform nite-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 nite-element method on the non-cracked domain, avoiding the de nition of a speci c mesh of the crack. Additionally, we present numerical experiments which con rm the e ciency of the proposed method

Domaines: Analyse numérique [math.NA]

Saber Amdouni, Patrick Hild, Vanessa Lleras, Maher Moakher, Yves Renard. A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies. ESAIM: Mathematical Modelling and Numerical Analysis, 2012, 46, pp.813-839. ⟨10.1051/m2an/2011072⟩. ⟨hal-00606313⟩