An accurate Local Average Contact (LAC) method for nonmatching meshes in 2D and 3D

Guillaume Drouet (1, 2) , Patrick Hild (2)

1 LAMSID - UMR 8193 - Laboratoire de Mécanique des Structures Industrielles Durables
2 IMT - Institut de Mathématiques de Toulouse UMR5219

The present paper deals with linear and quadratic finite element approximations of the two and three-dimensional unilateral contact problems between two elastic bodies with non-matching meshes. We propose a simple noninterpenetration condition (on the displacements) which is local (as the well known node-on-segment and node-on-face conditions) and accurate (like the mortar approach). This condition consists of averaging locally on a few elements the noninterpenetration. We achieve the corresponding optimal convergence analysis in 2D and 3D using various linear and quadratic elements and the computations of the Taylor patch test and Hertzian contact.

Mots clés: mortar contact; Local Average Contact condition; nonmatching meshes; Unilateral contact; a priori error estimates; Local Average Contact (LAC) condition; node-on-segment contact; node-on-face contact

Domaines: Analyse numérique [math.NA]

Guillaume Drouet, Patrick Hild. An accurate Local Average Contact (LAC) method for nonmatching meshes in 2D and 3D. Numerische Mathematik, 2017, 136 (2), pp.467-502. ⟨10.1007/s00211-016-0846-6⟩. ⟨hal-01143753v2⟩