A mixed finite element method and solution multiplicity for Coulomb frictional contact

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 41-42, 2003, Pages 4517-4531

  Hassani, Riad ^a   Hild, Patrick ^b   Ionescu, Ioan R ^c   Sakki, Nour Dine ^c  

^a UNIVERSITÉ GRENOBLE ALPES   (France)

^b UNIVERSITÉ DE FRANCHE COMTÉ   (France)

^c UNIVERSITÉ DE SAVOIE   (France)

Author keywords

Contact problem; Coulomb friction; Eigenvalue problem; Mixed finite elements; Solution multiplicity

Indexed keywords

COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; FRICTION;

DISCRETE CONTACT PROBLEMS;

FLUID STRUCTURE INTERACTION;

FINITE ELEMENT METHOD;

EID: 0141680828     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(03)00419-5     Document Type: Article

References (18)

1. Adams R.A. Sobolev Spaces 1975 Academic Press New-York
2. n dans lui même: application à la mécanique du contact Math. Model. Numer. Anal. 27 1993 203-222
3. Ballard P. A counter-example to uniqueness in quasi-static elastic contact problems with small friction Int. J. Engrg. Sci. 37 1999 163-178
4. Cocu M. Pratt E. Raous M. Formulation and approximation of quasistatic frictional contact Int. J. Engrg. Sci. 34 1996 783-798
5. Coorevits P. Hild P. Hjiaj M. A posteriori error control of finite element approximations for Coulomb's frictional contact SIAM J. Sci. Comput. 23 2001 976-999
6. Duvaut G. Lions J.L. Les inéquations en mécanique et en physique 1972 Dunod Paris
7. Eck C. Jarušek J. Existence results for the static contact problem with Coulomb friction Math. Models Methods Appl. Sci. 8 1998 445-468
8. Haslinger J. Approximation of the Signorini problem with friction, obeying the Coulomb law Math. Methods Appl. Sci. 5 1983 422-437
9. Haslinger J. Hlaváček I. Nečas J. Numerical methods for unilateral problems in solid mechanics Ciarlet P.G. Lions J.L. Handbook of Numerical Analysis vol. IV, part 2 1996 313-485 North Holland Amsterdam
10. R. Hassani, P. Hild, I. Ionescu, Sufficient condition of non-uniqueness for the Coulomb friction problem, Math. Methods Appl. Sci. 27 (3) (2004), to be published
11. R. Hassani, P. Hild, I. Ionescu, Analysis of eigenvalue problems modelling friction: sufficient conditions of non-uniqueness for the elastic equilibrium, in: Proceedings of the Third Contact Mechanics International Symposium (CMIS 2001), Peniche, Portugal, June 18-21, 2001, "Solid Mechanics and its Applications" Series of the Kluwer Academic Publishers, 103, 2002, pp. 133-140
12. R. Hassani, P. Hild, I. Ionescu, N.-D. Sakki, Non-uniqueness and dynamic instabilities in the Coulomb friction model, in preparation
13. Hild P. On finite element uniqueness studies for Coulomb's frictional contact model Appl. Math. Comp. 12 2002 41-50
14. Janovský V. Catastrophic features of Coulomb friction model Whiteman J.R. The Mathematics of Finite Elements and Applications 1981 259-264 Academic Press London
15. Jarušek J. Contact problems with bounded friction. Coercive case Czechoslovak. Math. J. 33 1983 237-261
16. Kikuchi N. Oden J.T. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods 1988 SIAM Philadelphia
17. Klarbring A. Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction Ing. Archiv. 60 1990 529-541
18. Nečas J. Jarušek J. Haslinger J. On the solution of the variational inequality to the Signorini problem with small friction Boll. Unione Mat. Ital. 17-B 5 1980 796-811