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Quasistatic Viscoelastic Contact with Normal Compliance and Friction

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Abstract

We prove the existence of a unique weak solution to the quasistatic problem of frictional contact between a deformable body and a rigid foundation. The material is assumed to have nonlinear viscoelastic behavior. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We establish the continuous dependence of the solution on the normal compliance function. Moreover, we prove the existence of a unique solution to the problem of sliding contact with wear.

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References

  1. R.S. Adams, Sobolev Spaces, Academic Press, New York, 1975.

    MATH  Google Scholar 

  2. A. Ait Moussa, Modelisation et Etudes des Singularities de Contraintes d'un Joint Colle Tres Mince. Thesis, University of Montpelier-2, (1989).

  3. A. Amassad and M. Sofonea, Analysis of a quasistatic viscoplastic problem involving Tresca friction law, to appear in Discrete and Continuous Dynamical Systems.

  4. L.-E. Andersson, A quasistatic frictional problem with normal compliance, Nonlin. Anal. 16(4) (1991) 347-370.

    Article  MATH  MathSciNet  Google Scholar 

  5. K.T. Andrews, A. Klarbring, M. Shillor and S. Wright, A dynamical thermoviscoelastic contact problem with friction and wear. Int. J. Engng. Sci. 35(14) (1997) 1291-1309.

    Article  MATH  MathSciNet  Google Scholar 

  6. K.T. Andrews, K.L. Kuttler and M. Shillor, On the dynamic behavior of a thermoviscoelastic body in frictional contact with a rigid obstacle. Euro. J. Appl. Math. 8(1997) 417-436.

    MATH  MathSciNet  Google Scholar 

  7. M. Cocu, E. Pratt and M. Raous, Formulation and approximation of quasistatic frictional contact. Int. J. Engng. Sci. 34(7) (1996) 783-798.

    Article  MATH  MathSciNet  Google Scholar 

  8. G. Duvaut and J.L. Lions, Les Inéquations en Mécanique et en Physique. Dunod, Paris, 1972.

    MATH  Google Scholar 

  9. I. Hlaváček and J. Nečas, Mathematical Theory of Elastic and Elastoplastic Bodies: an Introduction, Elsevier, Amsterdam, 1981.

    Google Scholar 

  10. I.R. Ionescu and M. Sofonea, Functional and Numerical Methods in Viscoelasticity. Oxford University Press, Oxford, 1993.

    Google Scholar 

  11. J. Jarusek, Contact problems with bounded friction, coercive case, Czech. Math. J. 33(108) (1983) 237-261.

    MATH  MathSciNet  Google Scholar 

  12. L. Johansson and A. Klarbring, Thermoelastic frictional contact problems: Modelling, finite element approximation and numerical realization. Comp. Meth. Appl. Mech. Eng. 105(1993) 181-210.

    Article  MATH  MathSciNet  Google Scholar 

  13. N. Kikuchi and T.J. Oden, Contact Problems in Elasticity. SIAM, Philadelphia, 1988.

    MATH  Google Scholar 

  14. A. Klarbring, A. Mikelic and M. Shillor, Frictional contact problems with normal compliance. Int. J. Engng. Sci. 26(8) (1988) 811-832.

    Article  MATH  MathSciNet  Google Scholar 

  15. A. Klarbring, A. Mikelic and M. Shillor, A global existence result for the quasistatic frictional contact problem with normal compliance. Unilateral Problems in Structural Analysis, Vol. 4, Eds. G. DelPiero and F. Maceri, Birkhauser, Boston (1991) 85-111.

    Google Scholar 

  16. A. Klarbring, A. Mikelic and M. Shillor, The rigid punch problem with friction. Int. J. Engng. Sci. 29(6) (1991) 751-768.

    Article  MATH  MathSciNet  Google Scholar 

  17. C. Licht, Un problème d'élasticité avec frottement visqueux non linéaire. J. Méc. Th. Appl. 4(1) (1985) 15-26.

    MATH  MathSciNet  Google Scholar 

  18. C. Licht, private communication.

  19. J.A.C. Martins and T.J. Oden, Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws. Nonlin. Anal. 11(3) (1987) 407-428.

    Article  MATH  MathSciNet  Google Scholar 

  20. J. Necas, J. Jarusek and J. Haslinger, On the solution of the variational inequality to the Signorini problem with small friction. Boll. U.M.I. 17(5) (1980) 796-811.

    MATH  MathSciNet  Google Scholar 

  21. P.D. Panagiotopoulos, Inequality Problems in Mechanics and Applications. Birkhauser, Basel, 1985.

    MATH  Google Scholar 

  22. M. Raous, M. Jean and J.J. Moreau, Contact Mechanics. Plenum Press, New York (1995).

    Google Scholar 

  23. M. Rochdi, Analyse Variationnelle de Quelques Problèmes aux Limites en Viscoplasticité, Ph.D. Thesis, University of Perpignan, France (1997).

    Google Scholar 

  24. M. Rochdi and M. Sofonea, On frictionless contact between two elastic-viscoplastic bodies. QJMAM 11(3) (1997), 481-496.

    MathSciNet  Google Scholar 

  25. M. Shillor and M. Sofonea, A quasistatic viscoelastic contact problem with friction, to appear in JMAA.

  26. M. Sofonea, On a contact problem for elastic-viscoplastic bodies. Nonlin. Anal. 29(9) (1997) 1037-1050.

    Article  MATH  MathSciNet  Google Scholar 

  27. N. Strömberg, Continuum Thermodynamics of Contact, Friction and Wear. Ph.D. Thesis, Linköping University, Sweden (1995).

    Google Scholar 

  28. N. Strömberg, L. Johansson and A. Klarbring, Derivation and analysis of a generalized standard model for contact friction and wear. Int. J. Solids Structures 33(13) (1996) 1817-1836.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Théorie des Systèmes, University of Perpignan, 52 Avenue de Villeneuve, 66860, Perpignan, France

    M. Rochdi & M. Sofonea

  2. Department of Mathematical Sciences–Oakland, University Rochester, MI, 48309, USA

    M. Shillor

Authors
  1. M. Rochdi
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  2. M. Shillor
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  3. M. Sofonea
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Rochdi, M., Shillor, M. & Sofonea, M. Quasistatic Viscoelastic Contact with Normal Compliance and Friction. Journal of Elasticity 51, 105–126 (1998). https://doi.org/10.1023/A:1007413119583

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  • DOI: https://doi.org/10.1023/A:1007413119583

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