A predictive, size-dependent continuum model for dense granular flows

Proceedings of the National Academy of Sciences of the United States of America

Volumn 110, Issue 17, 2013, Pages 6730-6735

  Henann, David L ^a   Kamrin, Ken ^a  

^a USA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; EMULSION; FLOW KINETICS; GEOMETRY; GRAIN SIZE DEPENDENT NONLOCAL RHEOLOGY; NONBIOLOGICAL MODEL; PARTICLE SIZE; PRESSURE; PRIORITY JOURNAL; SHEAR FLOW; THREE DIMENSIONAL IMAGING; VISCOSITY;

COMPUTER SIMULATION; MODELS, THEORETICAL; PARTICLE SIZE; RHEOLOGY;

EID: 84876843843     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1219153110     Document Type: Article

References (50)

1. Richard P, Nicodemi M, Delannay R, Ribière P, Bideau D (2005) Slow relaxation and compaction of granular systems. Nat Mater 4(2):121-128.
2. Nedderman RM, Laohakul C (1980) The thickness of the shear zone of flowing granular materials. Powder Technol 25(1):91-100.
3. Mueth DM, et al. (2000) Signatures of granular microstructure in dense shear flows. Nature 406(6794):385-389.
4. Fenistein D, Van Hecke M (2003) Kinematics: Wide shear zones in granular bulk flow. Nature 425(6955):256.
5. Fenistein D, van de Meent JW, van Hecke M (2004) Universal and wide shear zones in granular bulk flow. Phys Rev Lett 92(9):094301.
6. Fenistein D, van de Meent JW, van Hecke M (2006) Core precession and global modes in granular bulk flow. Phys Rev Lett 96(11):118001.
7. Cheng X, et al. (2006) Three-dimensional shear in granular flow. Phys Rev Lett 96(3): 038001.
8. Losert W, Bocquet L, Lubensky TC, Gollub JP (2000) Particle dynamics in sheared granular matter. Phys Rev Lett 85(7):1428-1431.
9. Midi GDR; GDR MiDi (2004) On dense granular flows. Eur Phys J E Soft Matter 14(4): 341-365.
10. Siavoshi S, Orpe AV, Kudrolli A (2006) Friction of a slider on a granular layer: Nonmonotonic thickness dependence and effect of boundary conditions. Phys Rev E Stat Nonlin Soft Matter Phys 73(1 Pt 1):010301.
11. Schoefield A, Wroth P (1968) Critical State Soil Mechanics (Pergamon, Oxford).
12. Nedderman RM (1992) Statics and Kinematics of Granular Materials (Cambridge Univ Press, Cambridge, UK).
13. Jaeger HM, Nagel SR, Behringer RP (1996) Granular solids, liquids, and gases. Rev Mod Phys 68:1259-1273.
14. Halsey T, Mehta A, eds (2002) Challenges in Granular Physics (World Scientific, River Edge, NJ).
15. Bagnold RA (1954) Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc R Soc Lond A Math Phys Sci 225:49-63.
16. da Cruz F, Emam S, Prochnow M, Roux J-N, Chevoir F (2005) Rheophysics of dense granular materials: Discrete simulation of plane shear flows. Phys Rev E Stat Nonlin Soft Matter Phys 72(2 Pt 1):021309.
17. Jop P, Forterre Y, Pouliquen O (2006) A constitutive law for dense granular flows. Nature 441(7094):727-730.
18. Kamrin K (2010) Nonlinear elasto-plastic model for dense granular flow. Int J Plast 26: 167-188.
19. Koval G, Roux J-N, Corfdir A, Chevoir F (2009) Annular shear of cohesionless granular materials: from the inertial to quasistatic regime. Phys Rev E Stat Nonlin Soft Matter Phys 79(2 Pt 1):021306.
20. Jop P (2008) Hydrodynamic modeling of granular flows in a modified Couette cell. Phys Rev E Stat Nonlin Soft Matter Phys 77(3 Pt 1):032301.
21. Kamrin K, Koval G (2012) Nonlocal constitutive relation for steady granular flow. Phys Rev Lett 108(17):178301.
22. Komatsu TS, Inagaki S, Nakagawa N, Nasuno S (2001) Creep motion in a granular pile exhibiting steady surface flow. Phys Rev Lett 86(9):1757-1760.
23. Pouliquen O, Forterre Y (2009) A non-local rheology for dense granular flows. Philos Transact A Math Phys Eng Sci 367(1909):5091-5107.
24. Aranson IS, Tsimring LS (2002) Continuum theory of partially fluidized granular flows. Phys Rev E Stat Nonlin Soft Matter Phys 65(6 Pt 1):061303.
25. Mohan LS, Rao KK, Nott PR (2002) A frictional Cosserat model for the slow shearing of granular materials. J Fluid Mech 457:377-409.
26. Savage SB (1998) Analyses of slow high-concentration flows of granular materials. J Fluid Mech 377:1-26.
27. Jenkins JT, Berzi D (2010) Dense inclined flows of inelastic spheres: Tests of an extension of kinetic theory. Granul Matter 12(2):151-158.
28. Kamrin K, Bazant MZ (2007) Stochastic flow rule for granular materials. Phys Rev E Stat Nonlin Soft Matter Phys 75(4 Pt 1):041301.
29. Litwiniszyn J (1963) The model of a random walk of particles adapted to researches on problems of mechanics of loose media. Bull Acad Polon Sci 11:61-70.
30. Mullins WW (1972) Stochastic theory of particle flow under gravity. J Appl Phys 43: 665-678.
31. Bocquet L, Colin A, Ajdari A (2009) Kinetic theory of plastic flow in soft glassy materials. Phys Rev Lett 103(3):036001.
32. Goyon J, Colin A, Ovarlez G, Ajdari A, Bocquet L (2008) Spatial cooperativity in soft glassy flows. Nature 454(7200):84-87.
33. Katgert G, Tighe BP, Möbius ME, van Hecke M (2010) Couette flow of two-dimensional foams. Europhys Lett 90(5):54002.
34. Rycroft CH, Kamrin K, Bazant MZ (2009) Assessing continuum postulates in simulations of granular flow. J Mech Phys Solids 57:828-839.
35. Sollich P, Lequeux F, Hébraud P, Cates M (1997) Rheology of soft glassy materials. Phys Rev Lett 78:2020-2023.
36. Dahmen KA, Ben-Zion Y, Uhl JT (2009) Micromechanical model for deformation in solids with universal predictions for stress-strain curves and slip avalanches. Phys Rev Lett 102(17):175501.
37. Dahmen KA, Ben-Zion Y, Uhl JT (2011) A simple analytic theory for the statistics of avalanches in sheared granular materials. Nat Phys 7:554-557.
38. Picard G, Ajdari A, Lequeux F, Bocquet L (2005) Slow flows of yield stress fluids: Complex spatiotemporal behavior within a simple elastoplastic model. Phys Rev E Stat Nonlin Soft Matter Phys 71(1 Pt 1):010501.
39. Lois G, Carlson JM (2007) Force networks and the dynamic approach to jamming in sheared granular media. Europhys Lett 80(5):58001.
40. Lemaître A, Caroli C (2009) Rate-dependent avalanche size in athermally sheared amorphous solids. Phys Rev Lett 103(6):065501.
41. Abaqus (2010) Abaqus Reference Manuals, Version 6.10 (Dassault Systèmes Simulia, Providence, RI).
42. Unger T, Török J, Kertész J, Wolf DE (2004) Shear band formation in granular media as a variational problem. Phys Rev Lett 92(21):214301.
43. Depken M, Lechman JB, van Hecke M, van Saarloos W, Grest GS (2007) Stresses in smooth flows of dense granular media. Europhys Lett 78:58001.
44. Török J, Unger T, Kertész J, Wolf DE (2007) Shear zones in granular materials: Optimization in a self-organized random potential. Phys Rev E Stat Nonlin Soft Matter Phys 75(1 Pt 1):011305.
45. Luding S (2008) The effect of friction on wide shear bands. Particul Sci Technol 26: 33-42.
46. Sakaie K, Fenistein D, Carroll TJ, van Hecke M, Umbanhowar P (2008) MR imaging of Reynolds dilatancy in the bulk of smooth granular flows. Europhys Lett 84(3):38001.
47. Dijksman JA, van Hecke M (2010) Granular flows in split-bottom geometries. Soft Matter 6:2901-2907.
48. Jop P, Forterre Y, Pouliquen O (2005) Crucial role of sidewalls in granular surface flows: Consequences for the rheology. J Fluid Mech 541:167-192.
49. Staron L, Lagrée P-Y, Popinet S (2012) The granular silo as a continuum plastic flow: The hour-glass vs the clepsydra. Phys Fluids 24:103301.
50. Pouliquen P (1999) Scaling laws in granular flows down rough inclined planes. Phys Fluids 11:542-548.