An unbiased Nitsche's approximation of the frictional contact between two elastic structures

Franz Chouly (1) , Rabii Mlika (2) , Yves Renard (3, 2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
3 MMCS - Modélisation mathématique, calcul scientifique

Most of the numerical methods dedicated to the contact problem involving two elastic bodies are based on the master/slave paradigm. It results in important detection difficulties in the case of self-contact and multi-body contact, where it may be impractical, if not impossible , to a priori nominate a master surface and a slave one. In this work we introduce an unbiased finite element method for the finite element approximation of frictional contact between two elastic bodies in the small deformation framework. In the proposed method the two bodies expected to come into contact are treated in the same way (no master and slave surfaces). The key ingredient is a Nitsche-based formulation of contact conditions. We carry out the numerical analysis of the method, and prove its well-posedness and optimal convergence in the H 1-norm. Numerical experiments are performed to illustrate the theoretical results and the performance of the method.

Mots clés: Finite element method; Tresca friction; Unbiased Master-Slave formulation; Two deformable bodies contact problem; Nitsche's method

Domaines: Mathématiques [math]; Analyse numérique [math.NA]

Franz Chouly, Rabii Mlika, Yves Renard. An unbiased Nitsche's approximation of the frictional contact between two elastic structures. Numerische Mathematik, 2018, 139 (3), pp.593--631. ⟨10.1007/s00211-018-0950-x⟩. ⟨hal-01240068⟩