Non-unique slipping in the coulomb friction model in two-dimensional linear elasticity

Quarterly Journal of Mechanics and Applied Mathematics

Volumn 57, Issue 2, 2004, Pages 225-235

  Hild, Patrick ^a  

^a UNIVERSITÉ DE FRANCHE COMTÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUUM MECHANICS; EIGENVALUES AND EIGENFUNCTIONS; FRICTION; MATHEMATICAL MODELS; VARIATIONAL TECHNIQUES;

CONTINUUM LINEAR ELASTICITY; COULOMB FRICTION MODEL; STATIC FRICTION PROBLEM;

ELASTICITY;

EID: 3142777170     PISSN: 00335614     EISSN: None     Source Type: Journal    
DOI: 10.1093/qjmam/57.2.225     Document Type: Article

References (13)

1. C. A. de Coulomb, Théorie des machines simples, en ayant égard au frottement de leurs parties et la raideur des cordages. Pièce qui a remporté le Prix double de l'Académie des Sciences pour l'année 1781, In Mémoire des Savants Etrangers X (1785) 163-332. (Reprinted by Bachelier, Paris 1809)
2. A. Signorini, Questioni di elasticità non linearizzata e semilinearizzata, Rend. Mat. e Appl. 18 (1959) 95-139.
3. J. Nečas, J. Jarušek and J. Haslinger, On the solution of the variational inequality to the Signorini problem with small friction, Boll. Unione Mat. Ital. B 17 (1980) 796-811.
4. J. Jarušek, Contact problems with bounded friction. Coercive case, Czech. Math. J. 33 (1983) 237-261.
5. C. Eck and J. Jarušek, Existence results for the static contact problem with Coulomb friction, Math. Models Methods Appl. Sci. 8 (1998) 445-468.
6. P. Hild, Multiple solutions of stick and separation type in the Signorini model with Coulomb friction, submitted.
7. R. Hassani, P. Hild and I. Ionescu, Analysis of eigenvalue problems modelling friction: sufficient conditions of nonuniqueness for the elastic equilibrium, In Contact Mechanics (ed. J. A. C. Martins and M. D. P. Monteiro Marques; Kluwer, Dordrecht 2002) 133-140.
8. R. Hassani, P. Hild and I. Ionescu, Sufficient conditions of nonuniqueness for the Coulomb friction problem, Math. Meth. Appl. Sci. 27 (2004) 47-67.
9. G. Fichera, Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. I 7 (1963/1964) 91-140.
10. A. Klarbring, Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction, Ing. Archiv 60 (1990) 529-541.
11. H. Cho and J. R. Barber, Stability of the three-dimensional Coulomb friction law, Proc. R. Soc. A 455 (1999) 839-861.
12. P. Hild, On finite element uniqueness studies for Coulomb's frictional contact model, Appl. Math. Comp. 12 (2002) 41-50.
13. J. Haslinger, Approximation of the Signorini problem with friction, obeying the Coulomb law, Math. Meth. Appl. Sci. 5 (1983) 422-437.