Convergence of a Neumann-Dirichlet algorithm for two-body contact problems with non local Coulomb's friction law
ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 2, pp. 243-262.

In this paper, the convergence of a Neumann-Dirichlet algorithm to approximate Coulomb's contact problem between two elastic bodies is proved in a continuous setting. In this algorithm, the natural interface between the two bodies is retained as a decomposition zone.

DOI : 10.1051/m2an:2008003
Classification : 65N30, 65N55, 65K05
Mots-clés : domain decomposition methods, contact problems, convergence 
@article{M2AN_2008__42_2_243_0,
     author = {Bayada, Guy and Sabil, Jalila and Sassi, Taoufik},
     title = {Convergence of a {Neumann-Dirichlet} algorithm for two-body contact problems with non local {Coulomb's} friction law},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {243--262},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {2},
     year = {2008},
     doi = {10.1051/m2an:2008003},
     mrnumber = {2405147},
     zbl = {1133.74042},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an:2008003/}
}
TY  - JOUR
AU  - Bayada, Guy
AU  - Sabil, Jalila
AU  - Sassi, Taoufik
TI  - Convergence of a Neumann-Dirichlet algorithm for two-body contact problems with non local Coulomb's friction law
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 2008
SP  - 243
EP  - 262
VL  - 42
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/m2an:2008003/
DO  - 10.1051/m2an:2008003
LA  - en
ID  - M2AN_2008__42_2_243_0
ER  - 
%0 Journal Article
%A Bayada, Guy
%A Sabil, Jalila
%A Sassi, Taoufik
%T Convergence of a Neumann-Dirichlet algorithm for two-body contact problems with non local Coulomb's friction law
%J ESAIM: Modélisation mathématique et analyse numérique
%D 2008
%P 243-262
%V 42
%N 2
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/m2an:2008003/
%R 10.1051/m2an:2008003
%G en
%F M2AN_2008__42_2_243_0
Bayada, Guy; Sabil, Jalila; Sassi, Taoufik. Convergence of a Neumann-Dirichlet algorithm for two-body contact problems with non local Coulomb's friction law. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 2, pp. 243-262. doi : 10.1051/m2an:2008003. http://www.numdam.org/articles/10.1051/m2an:2008003/

[1] P. Alart, M. Barboteu, P. Le Tallec and M. Vidrascu, Méthode de Schwarz additive avec solveur grossier pour problèmes non symétriques. C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 399-404. | MR | Zbl

[2] L. Baillet and T. Sassi, Simulations numériques de différentes méthodes d'éléments finis pour les problèmes contact avec frottement. C. R. Acad. Sci. Paris Sér. II B 331 (2003) 789-796. | Zbl

[3] L. Baillet and T. Sassi, Mixed finite element method for the Signorini problem with friction. Numer. Methods Partial Differential Equations 22 (2006) 1489-1508. | MR | Zbl

[4] G. Bayada, J. Sabil and T. Sassi, Algorithme de Neumann-Dirichlet pour des problèmes de contact unilatéral: résultat de convergence. C. R. Math. Acad. Sci. Paris 335 (2002) 381-386. | MR | Zbl

[5] A.B. Chandhary and K.J. Bathe, A solution method for static and dynamic analysis of three-dimensional contact problems with friction. Comput. Struc. 24 (1986) 855-873. | Zbl

[6] P.W. Christensen, A. Klarbring, J.S. Pang and N. Strömberg, Formulation and comparison of algorithms for frictional contact problems. Internat. J. Numer. Methods Engrg. 42 (1998) 145-173. | MR | Zbl

[7] G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique, Travaux et Recherches Mathématiques 21. Dunod, Paris (1972). | MR | Zbl

[8] C. Eck and B. Wohlmuth, Convergence of a contact-Neumann iteration for the solution of two-body contact problems. Math. Models Methods Appl. Sci. 13 (2003) 1103-1118. | MR | Zbl

[9] C. Farhat and F.X. Roux, Implicit parallel processing in structural mechanics. Computational Mechanics Advances 1 (1994) 1-124. | MR | Zbl

[10] R. Glowinski, J.-L. Lions and R. Trémolières, Numerical analysis of variational inequalities, Studies in Mathematics and its Applications 8. North-Holland Publishing Co., Amsterdam (1981). Translated from the French. | MR | Zbl

[11] J. Haslinger, Z. Dostál and R. Kučera, On a splitting type algorithm for the numerical realization of contact problems with Coulomb friction. Comput. Methods Appl. Mech. Engrg. 191 (2002) 2261-2281. | MR | Zbl

[12] N. Kikuchi and J.T. Oden, Contact problems in elasticity: a study of variational inequalities and finite element methods, SIAM Studies in Applied Mathematics 8. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1988). | MR | Zbl

[13] R. Kornhuber and R. Krause, Adaptive multigrid methods for Signorini's problem in linear elasticity. Comput. Vis. Sci. 4 (2001) 9-20. | MR | Zbl

[14] R.H. Krause, Monotone multigrid methods for Signorini's problem with friction. Ph.D. thesis, University of Berlin, Germany (2001).

[15] R.H. Krause and B.I. Wohlmuth, Nonconforming domain decomposition techniques for linear elasticity. East-West J. Numer. Math. 8 (2000) 177-206. | MR | Zbl

[16] R.H. Krause and B.I. Wohlmuth, A Dirichlet-Neumann type algorithm for contact problems with friction. Comput. Vis. Sci. 5 (2002) 139-148. | MR | Zbl

[17] P. Le Tallec, Domain decomposition methods in computational mechanics. Comput. Mech. Adv. 1 (1994) 121-220. | MR | Zbl

[18] L. Lusternik and V. Sobolev, Précis d'analyse fonctionnelle. MIR, Moscow (1989).

[19] B.F. Smith, P.E. Bjørstad and W.D. Gropp, Domain decomposition, Parallel multilevel methods for elliptic partial differential equations. Cambridge University Press, Cambridge (1996). | MR | Zbl

[20] G. Zavarise and P. Wriggers, A superlinear convergent augmented Lagrangian procedure for contact problems. Engrg. Comput. 16 (1999) 88-119. | Zbl

Cité par Sources :