A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies. (English) Zbl 1271.74354

Amdouni, Saber; Hild, Patrick; Lleras, Vanessa; Moakher, Maher; Renard, Yves

ESAIM, Math. Model. Numer. Anal. 46, No. 4, 813-839 (2012).

Summary: 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.

MSC:

74M15	Contact in solid mechanics
74S05	Finite element methods applied to problems in solid mechanics
35M85	Unilateral problems for linear PDEs of mixed type and variational inequalities with partial differential operators of mixed type

Keywords:

extended finite element method (XFEM); crack; unilateral contact; Signorini’s problem