Stresses in two-dimensional isostatic granular systems: Exact solutions

New Journal of Physics

Volumn 9, Issue , 2007, Pages

  Blumenfeld, Raphael ^a,b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; GRANULAR MATERIALS; STATISTICAL METHODS; TENSORS;

FLUCTUATIONS DECAY; FORCE CHAINS; ISOSTATIC GRANULAR SYSTEMS; STRESS TRANSMISSION;

STRESS ANALYSIS;

EID: 34250167888     PISSN: 13672630     EISSN: None     Source Type: Journal    
DOI: 10.1088/1367-2630/9/6/160     Document Type: Article

References (51)

1. Sokolowskii V V 1995 Statics of Granular Materials (Oxford: Pergamon)
2. Brown R L and Richards J C 1966 Principles of Powder Mechanics (New York: Pergamon)
3. Nedderman R M 1992 Statics and Kinematics of Granular Materials (Cambridge: Cambridge University Press)
4. Jaeger H M, Nagel S R and Behringer R P 1996 Rev. Mod. Phys. 68 1259
5. de Gennes P G 1999 Rev. Mod. Phys. 71 S374
6. Kadanoff L P 1999 Rev. Mod. Phys. 71 435
7. Aranson I S and Tsimring L 2006 Rev. Mod. Phys. 78 641
8. Smid J and Novosad J 1981 Ind. Chem. Eng. Symp. 63 D3/V/1
9. Brockbank B, Huntley J M and Ball R C 1997 J. Phys. II (France) 7 1521
10. Vanel L, Howell D W, Clark D, Behringer R P and Clement E 1999 Phys. Rev. E 60 R5040
11. Atman A P F, Brunet P, Genbg J, Reydellet G, Claudin P, Behringer R P and Clement E 2005 Eur. Phys. J. E 17 93
12. Luding S 1997 Phys. Rev. E 55 4720
13. Silbert L E, Grest G S and Landry J W 2002 Phys. Rev. E 66 061303
14. Snoeijer J H, Vlugt T J H, van Hecke M and van Saarloos W 2004 Phys. Rev. Lett. 92 054302
15. Ostojic S, Somfai E and Nienhuis B 2006 Nature 439 828
16. Wittmer J P, Claudin P, Cates M E and Bouchaud J-P 1996 Nature 382 336
17. Wittmer J P, Cates M E and Claudin P 1997 J. Phys. I (France) 1 39
18. Cates M E, Wittmer J P, Bouchaud J-P and Claudin P 1998 Phys. Rev. Lett. 81 1841
19. Edwards S F and Oakeshott R B 1989 Physica D 38 88
20. Edwards S F and Oakeshott R B 1989 Physica A 157 1080
21. Mehta A and Edwards S F 1989 Physica A 157 1091
22. Edwards S F and Mounfield C C 1996 Physica A 226 1
23. Edwards S F and Mounfield C C 1996 Physica A 226 12
24. Edwards S F and Mounfield C C 1996 Physica A 226 25
25. Bouchaud J-P, Cates M E and Claudin P J 1995 J. Phys. I (France) 5 639
26. Edwards S F and Grinev D V 1999 Phys. Rev. Lett. 82 5397
27. Ball R C 1999 Structures and Dynamics of Materials in the Mesoscopic Domain ed M Lal, R A Mashelkar, B D Kulkarni and V M Naik (London: Imperial College Press)
28. Savage S B 2002 Physics of Dry Granular Media (NATO ASI Series vol 25) ed H J Herrmann, J P Hovi and S Luding (Amsterdam: Kluwer)
29. Goldenberg C and Goldhirsch 12002 Phys. Rev. Lett. 89 084302
30. Blumenfeld R 2005 Stress transmission and isostatic states of non-rigid particulate systems Modeling of Soft Matter IMA Volume in Mathematics and its Applications vol 141, ed M C T Calderer and E M Terentjev (Berlin: Springer)
31. Henkes S and Chakraborty B 2005 Phys. Rev. Lett. 95 198002
32. Blumenfeld R 2004 Phys. Rev. Lett. 93 108301
33. Ball R C and Blumenfeld R 2002 Phys. Rev. Lett. 88 115505
34. Muskhelishvili N I 1963 Some Basic Problems of the Mathematical Theory of Elasticity (Groningen: P Noordhoff)
35. Blumenfeld R 2004 Physica A 336 361
36. Gerritsen M 2007 private communication
37. Gerritsen M, Kreiss G and Blumenfeld R Exact stress chain solutions in two-dimensional isostatic granular systems: fabric-dependent trajectories and branching, in preparation
38. Liu C-h, Nagel S R, Schecter D A, Coppersmith S N, Majumdar S, Narayan O and Witten T 1995 Science 269513
39. Bouchaud J-P, Claudin P, Levinev and Otto M 2001 Eur. Phys. J. E 4 451457
40. Ostjic S, Somfar E and Nienhuis B 2006 Nature 439 828
41. Kreiss H-O and Lorenz J 2004 Initial-Boundary Problems and the Navier-Stokes Equation (Philadelphia: SIAM)
42. Blumenfeld R, Edwards S F and Ball R C 2005 J. Phys.: Condens. Matter 17 S2481-S2487
43. Radjai F, Jean M, Moreau J-J and Roux S 1996 Phys. Rev. Lett. 77 274
44. Sexton M G, Socolar J E S and Schaeffer D G 1999 Phys. Rev. E 60 1999
45. Edwards S F and Grinev D V 2003 Granular Matter 4 147
46. Snoeijer J H, Vlugt T J H, van Hecke M and van Saarloos W 2004 Phys. Rev. Lett. 92 054302
47. Snoeijer J H, van Hecke M, Somfai E and van Saarloos W 2004 Phys. Rev. E 70 011301
48. Metzger P T 2004 Phys. Rev. E 70 051303
49. Ostojic S, Somfai E and Nienhuis B 2006 Nature 439 828
50. Muthuswamy M and Tordesillas A 2006 J. Stat. Mech. P09003
51. Blumenfeld R and Edwards S F Compactivity and angoricity: granular microstates and their statistics, in preparation