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2002 | 12 | 1 | 41-50

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On finite element uniqueness studies for Coulombs frictional contact model


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We are interested in the finite element approximation of Coulomb's frictional unilateral contact problem in linear elasticity. Using a mixed finite element method and an appropriate regularization, it becomes possible to prove existence and uniqueness when the friction coefficient is less than Cε^{2}|log(h)|^{-1}, where h and ε denote the discretization and regularization parameters, respectively. This bound converging very slowly towards 0 when h decreases (in comparison with the already known results of the non-regularized case) suggests a minor dependence of the mesh size on the uniqueness conditions, at least for practical engineering computations. Then we study the solutions of a simple finite element example in the non-regularized case. It can be shown that one, multiple or an infinity of solutions may occur and that, for a given loading, the number of solutions may eventually decrease when the friction coefficient increases.








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  • Laboratoire de Mathématiques, Université de Savoie, CNRS UMR 5127, 73376 Le Bourget-du-Lac, France


  • Adams R.A. (1975): Sobolev Spaces. - New-York: Academic Press.
  • Alart P. (1993): Critères d'injectivite et de surjectivite pourcertaines applications de R^n dans lui même: application à la mecanique du contact. - Math. Model. Numer. Anal., Vol. 27, No. 2, pp. 203-222.
  • Ben Belgacem F. (2000): Numerical simulation of some variational inequalities arisen fromunilateral contact problems by the finite element method. - SIAM J. Numer. Anal., Vol. 37, No. 4, pp. 1198-1216.
  • Ciarlet P.G. (1991): The finite element method for elliptic problems, In: Handbook of Numerical Analysis, Volume II (P.G. Ciarlet and J.L. Lions, Eds.). - Amsterdam: North Holland, pp.17-352.
  • Coorevits P., Hild P., Lhalouani K. and Sassi T. (2002): Mixed finite element methods for unilateral problems: convergence analysis and numerical studies. - Internal report of Laboratoire de Mathematiques de l'Universite de Savoie n^o 00-01c, to appear in Mathematics of Computation (published online May 21, 2001).
  • Duvaut G. and Lions J.-L. (1972): Les Inequations en Mecanique et en Physique. - Paris: Dunod.
  • Eck C. and Jarušek J. (1998): Existence results for the static contact problem with Coulomb friction. - Math. Mod. Meth. Appl. Sci., Vol. 8, No. 3, pp. 445-468.
  • Haslinger J. (1983): Approximation of the Signorini problem with friction, obeying the Coulomb law. - Math. Meth. Appl. Sci., Vol. 5, No. 3, pp. 422-437.
  • Haslinger J. (1984): Least square method for solving contact problems with friction obeying Coulomb's law. - Apl. Mat., Vol. 29, No. 3, pp. 212-224.
  • Haslinger J., Hlavaček I. and Nečas J. (1996): Numerical methods for unilateral problems in solid mechanics, In: Handbook of Numerical Analysis, Vol. IV (P.G. Ciarlet and J.L. Lions, Eds.). - Amsterdam: North Holland, pp. 313-485.
  • Hassani R., Hild P. and Ionescu I. (2001): On non-uniqueness of the elastic equilibrium with Coulomb friction: A spectral approach. - Internal report of Laboratoire de Mathematiques de l'Universite de Savoie no. 01-04c. Submitted.
  • Janovsky V. (1981): Catastrophic features of Coulomb friction model, In: The Mathematics of Finite Elements and Aplications (J.R. Whiteman, Ed.). - London: Academic Press, pp.259-264.
  • Jarušek J. (1983): Contact problems with bounded friction. Coercive case. - Czechoslovak. Math. J., Vol. 33, No. 2, pp. 237-261.
  • Kato Y. (1987): Signorini's problem with friction in linear elasticity. - Japan J. Appl. Math., Vol. 4, No. 2, pp. 237-268.
  • Klarbring A. (1990): Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction. - Ing. Archiv, Vol. 60, pp. 529-541.
  • Nečas J., Jarušek J. and Haslinger J. (1980): On the solution of the variational inequality to the Signorini problem with small friction. - Boll. Unione Mat. Ital., Vol. 17-B(5), No. 2, pp. 796-811.

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