A Continuation Problem for Computing Solutions of Discretised Evolution Problems. Part II -- Application to Quasi-Static Contact Problems with Friction.

Tomas Ligursky (1) , Yves Renard (2)

1 MAaAM PrF UP - Department of Mathematical Analysis and Applications of Mathematics
2 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]

A continuation problem for finding successive solutions of discretised plane quasi-static contact problems with friction is proposed and studied. Various formulations of the first-order system are derived and results of existence and uniqueness of its solutions are obtained. Conditions guaranteeing continuation of a solution curve along a direction from the first-order system are given. Numerical continuation of solution curves is performed on examples with non-smooth folds.

Mots clés: contact; Coulomb friction; incremental problem; continuation method; first-order system

Domaines: Analyse numérique [math.NA]; Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Tomas Ligursky, Yves Renard. A Continuation Problem for Computing Solutions of Discretised Evolution Problems. Part II -- Application to Quasi-Static Contact Problems with Friction.. 2013. ⟨hal-00877739⟩