Contact dynamics with Lagrange multipliers

Stephan Brunßen, Stefan Hüeber, Barbara Wohlmuth

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Scopus citations


The efficient modeling of dynamical contact problems with friction is still a callenge in non-linear implicit structural analysis. We employ a mixed formulation in space with the displacement as primal variable and the contact stress as dual variable. For the discretization of the latter we use a discrete Lagrange multiplier space with biorthogonal basis functions. For the treatment of the nonlinear frictional contact conditions semi-smooth Newton methods are applied. To avoid oscillations in the Lagrange multiplier during the solution of dynamical contact problems with mass, we locally under-integrate the mass matrix. We also show the applicability of the mixed formulation to a velocity driven rigid-plastic problem.

Original languageEnglish
Title of host publicationIUTAM Symposium on Computational Methods in Contact Mechanics - Proceedings of the IUTAM Symposium
PublisherSpringer Verlag
Number of pages16
ISBN (Print)9781402064043
StatePublished - 2007
Externally publishedYes
EventIUTAM Symposium on Computational Methods in Contact Mechanics - Hannover, Germany
Duration: 5 Nov 20068 Nov 2006

Publication series

NameSolid Mechanics and its Applications
ISSN (Print)1875-3507


ConferenceIUTAM Symposium on Computational Methods in Contact Mechanics


  • Coulomb friction
  • Energy conservating time integration
  • Non-oscillating Lagrange multiplier
  • Semi-smooth Newton methods


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