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On Abstract Variational Inequalities in Viscoplasticity with Frictional Contact

Author

Listed:
  • M. Delost

    (Observatoire Ocanologique)

  • C. Fabre

    (Université Paris Sud)

Abstract

In this paper, we study quasistatic abstract variational inequalities with time-dependent constraints. We prove existence results and present an approximation method valid for nonsmooth constraints. Then, we apply our results to the approximation of the quasistatic evolution of an elastic body in bilateral contact with a rigid foundation. The contact involves viscous friction of the Tresca or Coulomb type. We prove existence results for approximate problems and give a full asymptotic analysis, proving strong or weak convergence results. Our work is motivated by the numerical study in the paper [Delost, M.: Quasistatic Problem with Frictional Contact: Comparison between Numerical Methods and Asymptotic Analysis Related to Semi Discrete and Fully Discrete Approximations. University of Nice, Nice (2007, to appear)] and explains the choice of the approximation made in it.

Suggested Citation

  • M. Delost & C. Fabre, 2007. "On Abstract Variational Inequalities in Viscoplasticity with Frictional Contact," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 131-150, May.
    • Handle: RePEc:spr:joptap:v:133:y:2007:i:2:d:10.1007_s10957-007-9176-2
    DOI: 10.1007/s10957-007-9176-2
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    References listed on IDEAS

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    1. A. Amassad & C. Fabre, 2003. "Analysis of a Viscoelastic Unilateral Contact Problem Involving the Coulomb Friction Law," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 465-483, March.
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