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Existence Results for Unilateral Quasistatic Contact Problems With Friction and Adhesion

Published online by Cambridge University Press:  15 April 2002

Marius Cocu  and
Rémi Rocca
Marius Cocu
Affiliation:
Université de Provence et Laboratoire de mécanique et d'acoustique, CNRS, 31 chemin J. Aiguier, 13402 Marseille Cedex 20, France. (cocu@lma.cnrs-mrs.fr)
Rémi Rocca
Affiliation:
Laboratoire de mécanique et d'acoustique, CNRS, 31 chemin J. Aiguier, 13402 Marseille Cedex 20, France. (rocca@lma.cnrs-mrs.fr)
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Abstract

We consider a two dimensional elastic body submitted to unilateral contact conditions, local frictionand adhesion on a part of his boundary. After discretizing the variational formulation with respectto time we use a smoothing technique to approximate the friction term by an auxiliary problem. A shiftingtechnique enables us to obtain the existence of incremental solutions with bounds independent of the regularization parameter. We finally obtain the existence of a quasistatic solution by passing to thelimit with respect to time.

Keywords

Frictionadhesionlocal Coulomb lawunilateral contactquasistatic problem.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 5 , September 2000 , pp. 981 - 1001
Copyright
© EDP Sciences, SMAI, 2000

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References

L. Cangémi, Frottement et adhérence: modèle, traitement numérique et application à l'interface fibre matrice. PhD thesis, University of Aix-Marseille II (1997).
M. Raous, L. Cangémi and M. Cocu, Un modèle couplant adhérence et frottement pour le contact unilatéral entre deux solides déformables. C. R. Acad. Sci., Paris, Série II b, t. 325 (1997) 503-509.
Raous, M., Cangémi, L. and Cocu, M., A consistent model coupling adhesion friction and unilateral contact. Comput. Methods Appl. Mech. Engrg. 177 (1999) 383-399. CrossRef
R. Rocca, Existence of a solution for a quasistatic problem of unilateral contact with local friction. C. R. Acad. Sci., Paris, Série I. 328 (1999) 1253-1258.
R. Rocca and M. Cocu, Existence and approximation of a solution to quasistatic Signorini problem with local friction. Int. J. Engrg. (to appear).
R. Rocca, Analyse mathématique et numérique de problèmes quasi statique de contact unilatéral avec frottement local de Coulomb en élasticité, Ph.D. Thesis. Université d'Aix Marseille I (2000).
Andersson L.-E, Existence results for quasistatic contact problems with Coulomb friction. Appl. Math. Optim. (to appear).
Cocu, M., Pratt, E. and Raous, M., Formulation and approximation of quasistatic frictional contact. Int. J. Engrg. Sci. 34 (1996) 783-798. CrossRef
Jaru, J.šek, Contact problems with bounded friction coercive case. Czechoslovak Math. J. 33 (1983) 237-261.
C. Eck and J. Jarušek, Existence results for the static contact problem with Coulomb friction, Math. Models Methods Appl. Sci. 8(1998) 445-468.
R.A. Adams, Sobolev spaces. Academic Press, New York (1975).
J.L. Lions and E. Magenes, Problèmes aux limites non homogènes, Vol. I. Dunod, Paris (1967).
E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. I. Springer Verlag, New York (1993).