A quasistatic contact problem with slip dependent coefficient of friction for elastic materials

• Autorzy: Corneschi, C. , Hoarau-Mantel T.-V. , Sofonea, M.
• Języki publikacji: EN

Abstrakty

EN

We consider a mathematical model which describes the frictional contact between a deformable body and an obstacle, say a foundation. The body is assumed to be linear elastic and the contact is modeled with a version of Coulomb's law of dry friction in which the normal stress is prescribed on the contact surface. The novelty consists here in the fact that we consider a slip dependent coefficient of friction and a quasistatic process. We present two alternative yet equivalent formulations of the problem and establish existence and uniqueness results. The proofs are based on a new result obtained in [10] in the study of evolutionary variational inequalities.

Słowa kluczowe

PL

elastyczny materiał; przemiana quasi-statyczna; prawo Coulomba; poślizg zależny od tarcia; nierówności wariacyjne; słabe rozwiązanie

EN

elastic material; quasistatic process; Coulomb`s law; slip dependent friction; variational inequality; weak solution

• Czasopismo: Journal of Applied Analysis
• Rocznik: 2002
• Tom: Vol. 8, nr 1
• Strony: 63-82
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Corneschi, C.

• Departement of Mathematics University "Al. I. Cuza" Bd. Carol No. 11, 6600 Iasi Romania

autor

Hoarau-Mantel T.-V.

• Laboratoire de Théorie des Systèmes, Universitéde Perpignan, 52 Avenue de Villeneuve, 66860 Perpignan, France

autor

Sofonea, M.

• Laboratoire de Théorie des Systèmes, Universitéde Perpignan, 52 Avenue de Villeneuve, 66860 Perpignan, France

Bibliografia

• [1] Andersson, L.-E., A quasistatic frictional problem with normal compliance, Nonlinear Anal. 16 (1991), 407-428.
• [2] Andersson, L.-E., A global existence result for a quasistatic contact problem with friction, Adv. Math. Sci. Appl. 5 (1995), 249-286.
• [3] Cocu, M., Pratt, E., and Raous, M., Formulation and approximation of quasistatic frictional contact, Internat. J. Engrg. Sci. 34 (1996), 783-798.
• [4] Duvaut, G. and Lions, J. L., Inequalities in Mechanics and Physics, Springer-Verlag, Berlin, 1976.
• [5] Ionescu, I. R. and Paumier, J. C., On the contact problem with slip rate dependent friction in elastodynamics, European J. Mech. A Solids 13 (1994), 555-568.
• [6] Ionescu, I. R. and Paumier, J. C., On the contact problem with slip dependent friction in elastostatics, Internat. J. Engrg. Sci. 34 (1996), 471-491.
• [7] Ionescu, I. R. and Sofonea, M., Functional and Numerical Methods in Viscoplasticity, Oxford University Press, Oxford, 1993.
• [8] Kikuchi, N. and Oden, J. T., Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM Stud. Appl. Math. 8, Philadelphia, 1988.
• [9] Klarbring, A., Mikelic, A. and Shillor, M., Frictional contact problems with normal compliance, Internat. J. Engrg. Sci. 26 (1988), 811-832.
• [10] Motreanu, D. and Sofonea, M., Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials, Abstr. Appl. Anal. 4 (1999), 255-279.
• [11] Necas, J. and Hlavacek, I., Mathematical Theory of Elastic and Elastoplastic Bodies: An Introduction, Elsevier, Amsterdam, 1981.
• [12] Oden, J. T. and Martins, J. A. C., Models and computational methods for dynamic friction phenomena, Comput. Methods Appl. Mech. Engrg. 52 (1985), 527-634.
• [13] Panagiotopoulos, P. D., Inequality Problems in Mechanical and Applications, Birkhauser, Basel, 1985.
• [14] Rabinowicz, E., Friction and Wear of Materials, Wiley, New York, 1965.
• [15] Raous, M., Jean, M., and Moreau, J. J. (eds.), Contact Mechanics, Plenum Press, New York, 1995.
• [16] Scholz, C. H., The Mechanics of Earthquakes and Faulting, Cambridge Univ. Press, Cambridge, 1990.
• [17] Shillor, M. (ed.), Recent advances in contact mechanics, Math. Comput. Modelling 28(4-8) (1998).