Regularized frictional contact problems with the interior point method

Houssam Houssein (1) , Simon Garnotel (2) , Frédéric Hecht (3)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 Airthium SAS
3 LJLL - Laboratoire Jacques-Louis Lions

The aim of this paper is to present an algorithm to solve frictional contact problems by considering the Coulomb's criterion. As it is known, the frictional contact problem using Coulomb's criterion has no minimization principle behind. However in order to use algorithms based on minimization methods, the frictional contact problem is written as an optimization one, more specifically as a sequence of Tresca contact problems. Moreover a family of regularization functions is introduced in order to regularize the non-smooth character of the Tresca criterion, which in some cases can have an experimental justifications. As each minimization problem becomes smooth enough, the interior point method is used to solve the generated optimization problem.

Mots clés: Frictional contact; regularization; optimization; fixed point; interior point method; symmetric algorithm

Domaines: Mathématiques [math]; Mécanique des solides [physics.class-ph]

Houssam Houssein, Simon Garnotel, Frédéric Hecht. Regularized frictional contact problems with the interior point method. 2021. ⟨hal-03483991⟩