Using nonsmooth analysis for numerical simulations of contact mechanics

Pierre Alart (1) , David Dureisseix (1) , Mathieu Renouf (1)

1 LMGC - Laboratoire de Mécanique et Génie Civil

Two different approaches for simulation of contact mechanics problems are investigated. First, the equivalence of the Large Time INcrement (LATIN) method for unilateral contact problems, in terms of an augmented Lagrangian approach dedicated to nonsmooth problems, is proved (with the non trivial introduction of two constraints: an equality constraint and an inequality-type constraint). Second, the Finite Element Tearing and Interconnecting method for Contact (FETI-C) is interpreted as a projected gradient with projection, acting on the dual problem. An extension to frictional contact is presented in the context of granular media.

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

Pierre Alart, David Dureisseix, Mathieu Renouf. Using nonsmooth analysis for numerical simulations of contact mechanics. P. Alart, O. Maisonneuve, R.T. Rockafellar. Nonsmooth Mechanics and Analysis: Theoretical and Numerical Advances, Springer, pp.195-207, 2006, Advances in Mechanics and Mathematics, ⟨10.1007/0-387-29195-4_17⟩. ⟨hal-00320246⟩