Rate-dependent projection operators for frictional contact constraints

Y. Araki, K. D. Hjelmstad

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We develop rate-dependent regularization approaches for three-dimensional frictional contact constraints based on the Kelvin and Maxwell viscoelastic constitutive models. With the present regularization schemes, we aim to provide a basis to better model friction and to stabilize the contact analysis while keeping the contact model as simple as possible. The key feature of the regularization approaches, implemented using an implicit time integrator, is that one can recover in the limit the widely used rate-independent elastoplastic regularization framework without encountering numerical difficulties. Intermediate contact tractions are defined in terms of the relative displacement, the relative velocity, and the regularization parameters. The projection operators operate on the intermediate tractions and yield contact tractions that satisfy all the discretized contact constraints. The use of projection operators allows a systematic implementation of the present regularization schemes. Through numerical simulations, we observed that the Maxwell-type regularization effectively avoids convergence problems, even for relatively large time step sizes, while the Kelvin-type regularization does not.

Original languageEnglish (US)
Pages (from-to)923-954
Number of pages32
JournalInternational Journal for Numerical Methods in Engineering
Issue number7
StatePublished - Jun 21 2003
Externally publishedYes


  • Finite element
  • Frictional contact
  • Implicit time integrator
  • Projection operator
  • Rate-dependent regularization
  • Viscoelasticity

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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