A Local Contact Detection Technique for Very Large Contact and Self-Contact Problems: Sequential and Parallel Implementations

  • V. A. Yastrebov
  • G. Cailletaud
  • F. Feyel
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 58)


The local contact detection step can be very time consuming for large contact problems reaching the order of time required for their resolution. At the same time, even the most time consuming technique all-to-all does not guarantee the correct establishment of contact elements needed for further contact problem resolution. Nowadays the limits on mesh size in the Finite Element Analysis are largely extended by powerful parallelization methods and affordable parallel computers. In the light of such changes an improvement of existing contact detection techniques is necessary. The aim of our contribution is to elaborate a very general, simple and fast method for sequential and parallel detection for contact problems with known a priori and unknown master-slave discretizations. In the proposed method the strong connections between the FE mesh, the maximal detection distance and the optimal dimension of detection cells are established. Two approaches to parallel treatment of contact problems are developed and compared: SDMR/MDMR – Single/Multiple Detection, Multiple Resolution. Both approaches have been successfully applied to very large contact problems with more than 2 million nodes in contact.


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  1. 1.
    Benson, D.J., Hallquist, J.O.: A single surface contact algorithm for the post-buckling analysis of shell structures. Computer Methods in Applied Mechanics and Engineering 78, 141–163 (1990)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Brown, K., Attaway, S., Plimpton, S., Hendrickson, B.: Parallel strategies for crash and impact simulations. Computer Methods in Applied Mechanics and Engineering 184, 375–390 (2000)MATHCrossRefGoogle Scholar
  3. 3.
    Farhat, C., Roux, F.-X.: Implicit parallel processing in structural mechanics. Computational Mechanics Advances 2(1), 1–24 (1994)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Fujun, W., Jiangang, C., Zhenhan, Y.: A contact searching algorithm for contact-impactor problems. Acta Mechanica Sinica (English series) 16(4), 374–382 (2000)Google Scholar
  5. 5.
    Gosselet, P., Rey, C.: Non-overlapping domain decomposition methods in structural mechanics. Archives of Computational Methods in Engineering 13(4), 515–572 (2006)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Griebel, M., Knapek, S., Zumbusch, G.: Numerical Simulation in Molecular Dynamics. Springer, Berlin (2007)MATHGoogle Scholar
  7. 7.
    Konyukhov, A., Schweizerhof, K.: On the solvability of closest point projection procedures in contact analysis: Analysis and solution strategy for surfaces of arbitrary geometry. Computer Methods in Applied Mechanics and Engineering 197(33/40), 3045–3056 (2008)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Pietrzak, G., Curnier, A.: Large deformation frictional contact mechanics: Continuum formulation and augmented Lagrangian treatment. Computer Methods in Applied Mechanics and Engineering 177, 351–381 (1999)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Toselli, A., Widlund, O.: Domain decomposition methods – Algorithms and theory. Springer, Berlin (2005)MATHGoogle Scholar
  10. 10.
    Williams, J.R., O’Connor, R.: Discrete element simulation and the contact problem. Archives of Computational Methods in Engineering 6(4), 279–304 (1999)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Wriggers, P.: Computational Contact Mechanics, 2nd edn. Springer, Berlin (2006)MATHCrossRefGoogle Scholar
  12. 12.
    Wriggers, P., Krstulovic-Opara, L., Korelc, J.: Smooth c1-interpolations for two-dimensional frictional contact problems. International Journal for Numerical Methods in Engineering 51(12), 1469–1495 (2001)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Yang, B., Laursen, T.A.: A contact searching algorithm including bounding volume trees applied to finite sliding mortar formulations. Computational Mechanics 41(2), 189–205 (2008)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Yang, B., Laursen, T.A.: A large deformation mortar formulation of self contact with finite sliding. Computer Methods in Applied Mechanics and Engineering 197(6/8), 756–772 (2008)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Zavarise, G., De Lorenzis, L.: The node-to-segment algorithm for 2D frictionless contact: Classical formulation and special cases. Computer Methods in Applied Mechanics and Engineering 198, 3428–3451 (2009)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • V. A. Yastrebov
    • 1
  • G. Cailletaud
    • 1
  • F. Feyel
    • 2
  1. 1.Centre des MatériauxMines ParisTech, CNRS UMR 7633EvryFrance
  2. 2.ONERAChatillonFrance

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