Riemann solutions and spacetime discontinuous Galerkin method for linear elastodynamic contact

Reza Abedi, Robert B. Haber

Research output: Contribution to journalArticlepeer-review


We derive Riemann solutions for stick, slip and separation contact modes in a linear elastic material with an isotropic Coulomb friction relation and explore their numerical implementation. The Riemann solutions preserve the characteristic structure of the underlying elastodynamic system and imply dynamic contact conditions that are distinct from the quasi-static conditions used in some numerical models. Nonphysical discontinuities in the standard Coulomb model at stick-slip transitions can cause contact-mode chatter in numerical simulations. We restate the Coulomb relation to remove these artificial discontinuities and eliminate the need for algorithmic remedies. Discontinuous response at abrupt separation-to-contact transitions is physically reasonable, and we propose a regularization scheme to address this case. We implement the Riemann contact solutions within an adaptive spacetime discontinuous Galerkin (SDG) code and report numerical results that demonstrate the model's efficacy.

Original languageEnglish (US)
Pages (from-to)150-177
Number of pages28
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Mar 1 2014


  • Contact
  • Coulomb relation
  • Elastodynamics
  • Friction
  • Regularization
  • Riemann solution

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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