Conjugate gradient type algorithms for frictional multi-contact problems: Applications to granular materials

Computer Methods in Applied Mechanics and Engineering

Volumn 194, Issue 18-20, 2005, Pages 2019-2041

  Renouf, Mathieu ^a   Alart, Pierre ^a  

^a UNIVERSITÉ MONTPELLIER 2   (France)

Author keywords

Conjugate gradient; Constraints; Granular media; Multi contact; Optimization

Indexed keywords

ALGORITHMS; FRICTION; GRADIENT METHODS; GRANULAR MATERIALS;

GAUSS-SEIDEL SCHEME; GRADIENT PROJECTIONS; QUASI-OPTIMIZATION PROBLEMS; SINGLE LOOP SCHEME;

PROBLEM SOLVING;

ALGORITHM; CONTACT; GRANULAR MEDIUM;

EID: 14944382723     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2004.07.009     Document Type: Article

References (42)

1. K. Ach P. Alart Numerical simulation of a multi-jointed structure Philos. Trans. Roy. Soc. Lond. A 359 2001 2557-2573
2. n dans lui-même; application à la mécanique du contact Math. Mod. Num. Anal. 27 2 1993 203-222
3. P. Alart Méthode de Newton généralisée en mécanique du contact J. Math. Pures Appl. 76 1997 83-108
4. P. Alart M. Barboteu M. Renouf Parallel computational strategies for multi-contact problems: Applications to cellular and granular media Int. J. Mult. Scales Comput. Engrg. 1 4 2003 419-430
5. P. Alart F. Lebon F. Quittau K. Rey Frictional contact problem in elastostatics: Revisiting the uniqueness condition In: M. Jean M. Raous J.-J. Moreau (Eds.), Contact Mechanics 1995 Plenum Press New York 63-70
6. D. Bonanry F. Daviaud L. Laurent Experimental study of granular surface flows via a fast camera: A continuous description Phys. Fluids 14 5 2002 1666-1673
7. J.-F. Bonnans J.-C. Gilbert C. Lemaréchal C.A. Sugastizàbal Numerical Optimization-Theoretical and Practical Aspect 2003 Springer
8. P.A. Boucard L. Champaney A suitable computational strategy for the parametric analysis of problems with multiple contact Int. J. Numer. Methods Engrg. 57 2003 1259-1281
9. B. Brogliato A.A. ten Dam L. Paoli F. Génot M. Abadie Numerical simulation of finite dimensional multibody nonsmooth mechanical systems Appl. Mech. Rev. 55 2 2002 107-149
10. B. Cambou M. Jean Micromécanique des Matériaux Granulaires 2001 Hermès Science
11. D. Cambou Ph. Dubujet Difficulties and limitation of statistical homogenization in granular materials in: Vermeer et al. (Eds.), Continuous and Discontinuous Modeling of Cohesive Frictional Materials vol. 568 2001 Springer 205-214
12. Z.-H. Cao On the convergence of iterative methods for solving singular linear systems J. Comput. Appl. Math. 145 2002 1-9
13. P. Chabrand F. Dubois M. Raous Various numerical methods for solving unilateral contact problems with friction Math. Comput. Modell. 28 4-8 1999 97-108
14. P.W. Christensen A semi-smooth Newton method for elasto-plastic contact problems Int. J. Solids Struct. 39 2002 2323-2341
15. M. Cocu Existence of solutions of Signorini problems with friction Int. J. Engrg. Sci. 22 5 1984 567-575
16. G. Dilintas P. Laurent-Gengoux D. Trystram A conjugate projected gradient method with preconditioning for unilateral contact problems Comput. Struct. 29 4 1988 675-680
17. F. Dubois, M. Jean, LMGC90 une plateforme de développement dédiée à la modélisation des problèmes d'interaction, in: Actes du sixième colloque national en calcul des structures, vol. 1, CSMA-AFM-LMS, 2003, pp. 111-118
18. G. Duvaut Loi de frottement non locale J. Méc. Th. et Appl. numro spécial 1982 73-78
19. E. Gondet P.-F. Lavallee Couts OpenMP. IDRIS September 2000
20. M. Jean The non-smooth contact dynamics method Comput. Methods Appl. Mech. Engrg. 177 1999 235-257
21. F. Jourdan P. Alart M. Jean A Gauss-Seidel like algorithm to solve frictional contact problem Comput. Methods Appl. Mech. Engrg. 155 1998 31-47
22. Y. Kishino Mechanics of Granular Materials: An Introduction 2000 Balkema 147-159
23. Y. Kishino, H. Akaizawa, K. Kaneko, On the plastic flow of granular materials, in: Y. Kishino (Ed.), Powder and Grains, 2001, pp. 199-202
24. P. Ladevèze A. Nouy O. Loiseau A multiscale computational approach for contact problems Comput. Methods Appl. Mech. Engrg. 43 2002 4869-4891
25. T.A. Laursen J.C. Simo Algorithmic symmetrization of Coulomb frictional problems using augmented Lagrangians Comput. Methods Appl. Mech. Engrg. 108 1993 133-146
26. H.-O. May The conjugate gradient method for unilateral problems Comput. Struct. 12 4 1986 595-598
27. F. Mehrez, Modélisation du Contact-Frottement dans la simulation numérique de I'emboutissage des tales, Ph.D. thesis, Université Pierre et Marie Curie, Paris 6, juin 1991
28. J.-J. Moreau Unilateral contact and dry friction in finite freedom dynamics in: J.-J. Moreau P.-D. Panagiotopoulos (Eds.), Non Smooth Mechanics and Applications CISM Courses and Lectures vol. 302 1998 Springer-Verlag Wien, New York 1-82
29. J.-J. Moreau. Indétermination liée au frottement sec dans le calcul des granulats, in: Actes du Sixieme Collogue National en Calcul des Structures, vol. 3, CSMA-AFM-LMS, 2003, pp. 465-472
30. J.J. Moreau Numerical aspects of sweeping process Comput. Methods Appl. Mech. Engrg. 177 1999 329-349
31. J. Necas J. Jarusek J. Haslinger On the solution of the variational inequality to the Signorini problem with small friction Bolletino U.M.I. 5 17.B 1980 796-811
32. S. Nemat-Nasser J. Zhang Constitutive relations for cohesionless frictional granular materials Int. J. Plast. 18 2002 531-547
33. J.-S. Pang Newton's method for B-differentiable equations Math. Op. Res. 15 1990 311-341
34. F. Radjai D.E. Wolf M. Jean J.-I. Moreau Bimodal character of stress transmission in granular packings Phys. Rev. Lett. 80 1 1998 61-64
35. J. Rajchenbach Granular flows Adv. Phys. 49 2 2000 229-256
36. M. Raous, S. Barbarin, Conjugate gradient for frictional contact, in: A. Curnier (Ed.), Proc. Contact Mechanics Int. Symp., PPUR, 1992, pp. 423-432
37. M. Renouf P. Alart Solveurs paralleles pour la simulation de systèmes multi-contacts Rev. Eur. Elem. Finis. 13 5-7 2004 691-702
38. M. Renouf F. Dubois P. Alart A parallel version of the non smooth contact dynamics algorithm applied to the simulation of granular media J. Comput. Appl. Math. 168 2004 375-382
39. J.B. Rosen The gradient projection method for nonlinear programming. Part 1 - linear constraints J. Soc. Indust. Appl. Math. 8 1 1960 181-217
40. J.B. Rosen The gradient projection method for nonlinear programming. Part 2 - Non-linear constraints J. Soc. Indust. Appl. Math. 9 4 1961 514-532
41. H. Troadec F. Radjai S. Roux J.C. Charmet Model for granular texture with steric exclusion Phys. Rev. E 66 2002 041305
42. P. Wriggers Finite element algorithms for contact problems Arch. Comput. Meth. Engrg. 2 1995 1-49