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Approximation Results for a Class of Quasistatic Contact Problems Including Adhesion and Friction

  • M. Cocu
  • L. Cangemi
  • M. Raous
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 66)

Abstract

This paper is concerned with a continuum thermodynamic and mathematical formulation of an interface law including unilateral contact, adhesion and friction. The model is based on the notion of material boundary associated to the interface and its derivation follows from the principle of virtual power and the principles of thermodynamics (Cangémi et al., 1996 a). Adhesion and friction are strongly coupled and adhesion is characterized by a new variable, the intensity of adhesion β introduced by Prémond. We consider a quasistatic unilateral contact problem for which we present a variational formulation. A time discretization is adopted and we prove that if the friction coefficient is sufficiently small then the incremental formulation that can be derived from this discretization has a unique solution. Finally an application to an indentation problem is mentioned.

Keywords

Contact Problem Quasi Variational Inequality Incremental Formulation Unilateral Contact Virtual Power 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Cangémi, L., Cocu, M. and Raous, M. (1996a) Adhesion and friction model for the fiber/matrix interface of a composite, Proceedings ESDA′96-ASME, July 1-4, Montpellier.Google Scholar
  2. Cangémi, L., Cocu, M. and Raous, M. (1996) Adhérence et frottement, une nouvelle approche pour les interfaces fibre/mat rice, Actes des 10 éme Journées Nationales sur les Composites, Paris 29-31 Octobre, EN S AM.Google Scholar
  3. Cocu, M., Pratt E. and Raous M. (1996) Formulation and approximation of quasistatic fractional contact, Int. J. Engng. Sci., Vol. 34, pp. 783–798.MathSciNetCrossRefzbMATHGoogle Scholar
  4. Frémond, M. (1987) Adhérence des solides, J. Méc. Théor. et Appl.,Vol. 6, pp. 383–407.zbMATHGoogle Scholar
  5. Klarbring, A. (1990) Derivation and analysis of rate boudary-value problems of frictional contact, European Journal of Mechanics, A/Solids, Vol. 9, no. 1, pp. 53–85.MathSciNetzbMATHGoogle Scholar
  6. Raous, M., Chabrand P. and Lebon, F. (1988) Numerical methods for frictional contact problems and applications, J. Méc. Théor. et Appl., special issue, supplement no. 1 to Vol. 6, pp. 111–128.MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • M. Cocu
    • 1
  • L. Cangemi
    • 2
  • M. Raous
    • 2
  1. 1.L.M.A. — C.N.R.S. and Université de ProvenceFrance
  2. 2.Laboratoire de Mécanique et d’Acoustique — C.N.R.S.Marseille Cedex 20France

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