Statistical Properties of Dense Granular Matter

  • R.P. Behringer
  • E. Clément
  • J. Geng
  • R. Hartley
  • D. Howell
  • G. Reydellet
  • B. Utter
Conference paper

Summary

We review recent work characterizing force fluctuations and transmission in dense granular materials. These forces are carried preferentially on filimentary structures known as force chains. When a system is deformed, these chains tend to resist further deformation; with continued deformation, chains break and rearrange, leading to large spatio-temporal fluctuations. We first consider experiments on force fluctuations, diffusion and mobility under steady-state shear. We then turn to force transmission in static systems as determined by the response to a small point force. These experiments show that the packing structure and friction play important roles in determining the force transmission. Disordered highly frictional packings have responses that are similar to that of an elastic solid. Ordered packings show responses that may be described either by anisotropic elasticity or by a wave-like description.

Keywords

Fluctuations Granular Materials Force Transmission 

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References

  1. 1.
    G.W. Baxter, R. Leone, G.A. Johnson, and R.P. Behringer. Time-dependence and pattern formation in flowing sand. Eur. J. Mech. B: Fluids, 10:181, 1991.Google Scholar
  2. 2.
    G.W. Baxter, R. Leone, and R.P. Behringer. Experimental test of time scales in flowing sand. Europhys. Lett., 21(5):569–574, 1993.CrossRefGoogle Scholar
  3. 3.
    J. Geng, D. Howell, E. Longhi, R.P. Behringer, G. Reydellet, L. Vanel, E. Clément, and S. Luding. Footprints in sand: The response of a granular material to local perturbations. Phys. Rev. Lett., 87:035506, 2001.CrossRefGoogle Scholar
  4. 4.
    R.R. Hartley and R.P. Behringer. Logarithmic rate dependence of force networks in sheared granular materials. Nature, 421(6926):928–931, 2003.CrossRefGoogle Scholar
  5. 5.
    B. Miller, C. O’Hern, and R.P. Behringer. Stress fluctuations for continously sheared granular materials. Phys. Rev. Lett., 77:3110–3113, 1996.CrossRefGoogle Scholar
  6. 6.
    J. Geng, R.P. Behringer, G. Reydellet, and E. Clément. Green’s function measurements in 2d granular materials. Physica D, 182:274–303, 2003.MATHCrossRefGoogle Scholar
  7. 7.
    B. Utter and R.P. Behringer. Self-diffusion in dense granular shear flows. Phys. Rev. E, 69:031308, 2004.CrossRefGoogle Scholar
  8. 8.
    D. Howell, R.P. Behringer, and C. Veje. Stress fluctuations in a 2D granular Couette experiment: A continuous transition. Phys. Rev. Lett., 82(26):5241–5244, 1999.CrossRefGoogle Scholar
  9. 9.
    G. Reydellet and E. Clement. Green’s function probe of a static granular piling. 2001.Google Scholar
  10. 10.
    M. Da Silva and J. Rajchenbach. Stress transmission through a model system of cohesionless elastic grains. Nature, 406:708–XXX, 2000.CrossRefGoogle Scholar
  11. 11.
    J-P. Bouchaud, P. Claudin, D. Levine, and M. Otto. Force chain splitting in granular materials: A mechanism for large-scale pseudo-elastic behavior. Euro. Phys. J., E4:451, 2001.Google Scholar
  12. 12.
    J.E.S. Socolar, D.G. Schaeffer, and P. Claudin. Directed force chain networks and stress response in static granular materials. Euro. Phys. J., E7:353, 2002.Google Scholar
  13. 13.
    C. Goldenberg and I. Goldhirsch. Elasticity of microscopically inhomogeneous systems: The one-dimensional case. preprint, 2000.Google Scholar
  14. 14.
    A.V. Tkachenko and T.Q. Witten. Stress propagation through frictionless granular material. Phys. Rev. E, 60:687, 1999.CrossRefGoogle Scholar
  15. 15.
    A.V. Tkachenko and T.Q. Witten. Stress in frictionless granular material: Adaptive network simulations. Phys. Rev. E, 62:2510, 2000.CrossRefGoogle Scholar
  16. 16.
    N.W. Mueggenburg, H.M. Jaeger, and S.R. Nagel. Stress transmission through three-dimensional ordered granular arrays. Phys. Rev. E, 66:031304, 2002.CrossRefGoogle Scholar
  17. 17.
    R.M. Nedderman and C. Laohakul. The thickness of the shear zone of flowing granular material. Powder Technol., 25:91, 1980.CrossRefGoogle Scholar
  18. 18.
    C.H. Liu, S.R. Nagel, D.A. Schecter, S.N. Coppersmith, S. Majumdar, O. Narayan, and T.A. Witten. Force fluctuations in bead packs. Science, 269:513, 1995.CrossRefGoogle Scholar
  19. 19.
    J.-P. Bouchaud, M.E. Cates, and P. Claudin. Stress distribution in granular media and nonlinear wave equation. J. Phys. I, 5:639–656, 1995.CrossRefGoogle Scholar
  20. 20.
    P. Claudin and J.-P. Bouchaud. Stick-slip transition in the scalar arching model. In H.J. Herrmann, J.-P. Hovi, and S. Luding, editors, Physics of Dry Granular Media, page 129, Dordrecht, 1998. Kluwer Academic Publishers.Google Scholar
  21. 21.
    M.E. Cates, J.P. Wittmer, J.-P. Bouchaud, and P. Claudin. Jamming, force chains, and fragile matter. Phys. Rev. Lett., 81(9):1841–1844, 1998.CrossRefGoogle Scholar
  22. 22.
    O. Straußand S. Luding. Granular Gases. Springer-Verlag, 2000.Google Scholar
  23. 23.
    L. Landau and E. Lifschitz. Theory of elasticity. MIR, Moscow, 1967.Google Scholar
  24. 24.
    R. Albert, M.A. Pfeifer, A.L. Barabási, and P. Schiffer. Slow drag in a granular medium. Phys. Rev. Lett., 82:205, 1999.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • R.P. Behringer
    • 1
  • E. Clément
    • 2
  • J. Geng
    • 1
  • R. Hartley
    • 1
  • D. Howell
    • 1
  • G. Reydellet
    • 2
  • B. Utter
    • 1
  1. 1.Dept. of PhysicsDuke UniversityDurhamUSA
  2. 2.Université Pierre et Marie CurrieParisFrance

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