Dynamic Contact Problems With Slip-Dependent Friction in Viscoelasticity

• Autorzy: Ionescu I. R. , Nguyen Q. L.
• Języki publikacji: EN

Abstrakty

EN

The dynamic evolution with frictional contact of a viscoelastic body is considered. The assumptions on the functions used in modelling the contact are broad enough to include both the normal compliance and the Tresca models. The friction law uses a friction coefficient which is a non-monotone function of the slip. The existence and uniqueness of the solution are proved in the general three-dimensional case.

Słowa kluczowe

EN

slip-dependent friction; dynamic viscoelasticity; Tresca contact; normal compliance; existence and uniqueness

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2002
• Tom: Vol. 12, no 1
• Strony: 71--80
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Ionescu I. R.

• Laboratoire de Mathématiques, CNRS and Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France

autor

Nguyen Q. L.

• National Polytechnic Institute, Ho-Shi-Minh, 143/2D Xo Viet nghe Tinh (he m), P25, Q.BT, Ho-Shi-Minh, Vietnam

Bibliografia

• [1] Duvaut G. and Lions J.L. (1976): Inequalities in Mechanics and Physics. - Berlin: Springer.
• [2] Campillo M. and Ionescu I.R. (1997): Initiation of antiplane shear instability under slip dependent friction. - J. Geophys. Res., Vol. 122, No. B9, pp. 20363-20371.
• [3] Corneschi C., Hoarau-Martel T.-H. and Sofonea M. (2002): A quasistatic contact problem with slip dependent coefficient of friction for elastic materials. - J. Appl. Anal. (to appear).
• [4] Dascalu C., Ionescu I.R. and Campillo M. (2000): Fault finiteness and initiation of dynamic shear instability. - Earth Planet. Sci. Lett., No. 177, pp. 163-176.
• [5] Dieterich J.H. (1994): A constitutive law for rate of earthquake production and its application to earthquake clustering. - J. Geophys. Res., Vol. 99, No. B2, pp. 2601-2618.
• [6] Favreau P., Campillo M. and Ionescu I.R. (1991): Initiation of inplane shear instability under slip dependent friction. - Bull. Seism. Soc. Amer., Vol. 89, No. 5, pp. 1280-1295.
• [7] Favreau P., Ionescu I.R. and Campillo M. (1991b): On the dynamic sliding with rate and state dependent friction laws. - Geophys. J., Vol. 139, pp. 671-678.
• [8] Ionescu I.R. (2001): Viscosity solutions for dynamic problems with slip-rate dependent friction. - Quart. Appl. Math. (to appear).
• [9] Ionescu I.R. and Campillo M. (1999): The influence of the shape of the friction law and fault finiteness on the duration of initiation. - J. Geophys. Res., Vol. 104, No. B2, pp. 3013-3024.
• [10] Ionescu I.R. and Paumier J.C. (1993): Dynamic stick-slip motions with sliding velocity-dependent friction. - Comptes Rendus de l’Acad. Sci. Paris, S. I, Vol. 316, pp. 121-125.
• [11] Ionescu I.R. and Paumier J.C. (1994): On the contact problem with slip rate dependent friction in elastodynamics. - Europ. J. Mech., A-Solids, Vol. 13, No. 4, pp. 556-568.
• [12] Ionescu I.R. and Paumier J.C. (1996): On the contact problem with slip displacement dependent friction in elastostatics. - Int. J. Eng. Sci., Vol. 34, No. 4, pp. 471-491.
• [13] Kuttler K.L. (1997): Dynamic friction contact problems for general normal and friction laws. - Nonlin. Anal., Vol. 28, No. 3, pp. 559-575.
• [14] Kuttler K.L. and Shillor K.L. (1999): Set-valued pseudomonotone maps and degenerate evolution inclusions. - Commun. Contemp. Math., Vol. 1, pp. 87-123.
• [15] Martins J.A.C. and Oden J.T. (1987): Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface law. - Nonlin. Anal., Vol. 11, No. 3, pp. 407-428.
• [16] Oden J.T. and Martins J.A.C. (1985): Models and computational methods for dynamic friction phenomena. - Comp. Math. Appl. Mech. Eng., Vol. 52, pp. 527-634.
• [17] Ohnaka Y., Kuwahara Y. and Yamamoto K. (1987): Constitutive relations between dynamic physical parameters near a tip of the propagation slip during stick-slip shear failure. - Tectonophysics, Vol. 144, pp. 109-125.
• [18] Perrin G., Rice J.R. and Zheng G. (1995): Self-healing slip pulse on a frictional surface. - J. Mech. Phys. Solids, Vol. 43, No. 9, pp. 1461-1495.
• [19] Rabinowicz E. (1951): The nature of the static and kinetic coefficients of friction. - J. Appl. Phys., Vol. 22. No. 11, pp. 13730-1379.
• [20] Rice J.R. and Ruina A.L. (1983): Stability of steady frictional slipping. - J. Appl. Mech., Vol. 50, pp. 343-349.
• [21] Ruina A.L. (1983): Slip instabilities and state variable friction laws. - J. Geophys. Res., Vol. 88, No. B12, pp. 10359-10370.
• [22] Scholz C.H. (1990): The Mechanics of Earthquakes and Faulting. - Cambridge: Cambridge University Press.