Nitsche-based finite element method for contact with Coulomb friction

Franz Chouly (1, 2) , Patrick Hild (3) , Vanessa Lleras (4) , Yves Renard (5, 6, 7, 8)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 UBFC - Université Bourgogne Franche-Comté [COMUE]
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 IMAG - Institut Montpelliérain Alexander Grothendieck
5 INSA Lyon - Institut National des Sciences Appliquées de Lyon
6 ICJ - Institut Camille Jordan
7 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
8 MMCS - Modélisation mathématique, calcul scientifique

The aim of this paper is to provide some mathematical results for the discrete problem associated to contact with Coulomb friction, in linear elasticity, when finite elements and Nitsche method are considered. We consider both static and dynamic situations. We establish existence and uniqueness results under appropriate assumptions on physical (friction coefficient) and numerical parameters. These results are complemented by a numerical assessment of convergence.

Domaines: Analyse numérique [math.NA]

Franz Chouly, Patrick Hild, Vanessa Lleras, Yves Renard. Nitsche-based finite element method for contact with Coulomb friction. European Conference on Numerical Mathematics and Advanced Applications ENUMATH 2017, University of Bergen, Sep 2017, Voss, Norway. pp.839-847, ⟨10.1007/978-3-319-96415-7_79⟩. ⟨hal-01654487⟩