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Variational–hemivariational inequality for a class of dynamic nonsmooth frictional contact problems

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  • Migórski, Stanisław
  • Gamorski, Piotr

Abstract

In this paper, a dynamic frictional contact problem for viscoelastic materials with long memory is studied. The contact is modeled by a multivalued normal damped response condition with the Clarke generalized gradient of a locally Lipschitz superpotential and the friction is described by a version of the Coulomb law of dry friction with the friction bound depending on the regularized normal stress. The weak formulation of the contact problem is a history-dependent variational–hemivariational inequality for the velocity. A result on the unique weak solvability to this inequality is proved through a recent contribution on evolutionary subdifferential inclusions and a fixed point approach.

Suggested Citation

  • Migórski, Stanisław & Gamorski, Piotr, 2019. "Variational–hemivariational inequality for a class of dynamic nonsmooth frictional contact problems," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 465-479.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:465-479
    DOI: 10.1016/j.amc.2018.10.011
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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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    1. 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.

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