Decomposition contact response (DCR) for explicit finite element dynamics

Fehmi Cirak, Matthew West

Research output: Contribution to journalArticlepeer-review


We propose a new explicit contact algorithm for finite element discretized solids and shells with smooth and non-smooth geometries. The equations of motion are integrated in time with a predictor-corrector-type algorithm. After each predictor step, the impenetrability constraints and the exchange of momenta between the impacting bodies are considered and enforced independently. The geometrically inadmissible penetrations are removed using closest point projections or similar updates. Penetration is measured using the signed volume of intersection described by the contacting surface elements, which is well-defined for both smooth and non-smooth geometries. For computing the instantaneous velocity changes that occur during the impact event, we introduce the decomposition contact response method. This enables the closed-form solution of the jump equations at impact, and applies to non-frictional as well as frictional contact, as exemplified by the Coulomb frictional model. The overall algorithm has excellent momentum and energy conservation characteristics, as several numerical examples demonstrate.

Original languageEnglish (US)
Pages (from-to)1078-1110
Number of pages33
JournalInternational Journal for Numerical Methods in Engineering
Issue number8
StatePublished - Oct 28 2005
Externally publishedYes


  • Contact
  • Explicit dynamics
  • Impact
  • Non-smooth mechanics
  • Shells

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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