A fictitious domain method for frictionless contact problems in elasticity using Nitsche's method

Mathieu Fabre; Jérôme Pousin; Yves Renard

doi:10.5802/smai-jcm.8

A fictitious domain method for frictionless contact problems in elasticity using Nitsche's method

Mathieu Fabre ¹ Jérôme Pousin ¹ Yves Renard ^{2, 3, 1}

1 ICJ - Institut Camille Jordan [Villeurbanne]

2 MMCS - Modélisation mathématique, calcul scientifique

ICJ - Institut Camille Jordan [Villeurbanne]

3 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]

Abstract : In this paper, we develop and analyze a finite element fictitious domain approach based on Nitsche's method for the approximation of frictionless contact problems of two deformable elastic bodies. In the proposed method, the geometry of the bodies and the boundary conditions, including the contact condition between the two bodies, are described independently of the mesh of the fictitious domain. We prove that the optimal convergence is preserved. Numerical experiments are provided which confirm the correct behavior of the proposed method.

Keywords : Fictitious domain Nitsche's method Stabilisation elasticity finite element method Unilateral contact

Document type :

Journal articles

Domain :

Mathematics [math] / Numerical Analysis [math.NA]

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https://hal.archives-ouvertes.fr/hal-00960996
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