Granular Matter

, Volume 17, Issue 3, pp 287–295 | Cite as

Friction in inertial granular flows: competition between dilation and grain-scale dissipation rates

  • Ryan C. Hurley
  • José E. Andrade
Original Paper


Friction plays an important role in the behavior of flowing granular media. The effective friction coefficient is a description of shear strength in both slow and rapid flows of these materials. In this paper, we study the steady state effective friction coefficient \(\mu \) in a granular material in two steps. First, we develop a new relationship between the steady state effective friction coefficient, the shear rate, the solid fraction, and grain-scale dissipation processes in a simple shear flow. This relationship elucidates the rate- and porosity-dependent nature of effective friction in granular flows. Second, we use numerical simulations to study how the various quantities in the relationship change with shear rate and material properties. We explore how the relationship illuminates the grain-scale dissipation processes responsible for macroscopic friction. We examine how the competing processes of shearing dilation and grain-scale dissipation rates give rise to rate-dependence. We also compare our findings with previous investigations of effective friction in simple shear.


Granular materials Granular flows Friction Dynamic material response Rheology 



Support by the Air Force Office of Scientific Research Grant # FA9550-12-1-0091 through the University Center of Excellence in High-Rate Deformation Physics of Heterogenous Materials is gratefully acknowledged.


  1. 1.
    Jaeger, H.M., Nagel, S.R.: Physics of the granular state. Science 255(5051), 1523–1531 (1992)CrossRefADSGoogle Scholar
  2. 2.
    da Cruz, F., Emam, S., Prochnow, M., Roux, J.-N., Chevoir, F.: Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72(2), 021309 (2005)CrossRefADSGoogle Scholar
  3. 3.
    Savage, S.B., Sayed, M.: Stresses developed by dry cohesionless granular materials sheared in an annular shear cell. J. Fluid Mech. 142, 391–430 (1984)CrossRefADSGoogle Scholar
  4. 4.
    Wood, D.M.: Critical State Soil Mechanics. Cambridge University Press, New York (1990)MATHGoogle Scholar
  5. 5.
    Campbell, C.S.: Rapid granular flows. Ann. Rev. Fluid Mech. 22(1), 57–90 (1990)CrossRefADSGoogle Scholar
  6. 6.
    Goldhirsch, I.: Rapid granular flows. Ann. Rev. Fluid Mech. 35(1), 267–293 (2003)CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    MiDi, G.D.R.: On dense granular flows. Eur. Phys. J. E 14, 341–365 (2004)CrossRefGoogle Scholar
  8. 8.
    Jop, P., Forterre, Y., Pouliquen, O.: A constitutive law for dense granular flows. Nature 441, 727–730 (2006)CrossRefADSGoogle Scholar
  9. 9.
    Jutzi, M., Asphaug, E.: Forming the lunar farside highlands by accretion of a companion moon. Nature 476(7358), 69–72 (2011)CrossRefADSGoogle Scholar
  10. 10.
    Kamrin, K., Koval, G.: Nonlocal constitutive relation for steady granular flow. Phys. Rev. Lett. 108(17), 178301 (2012)CrossRefADSGoogle Scholar
  11. 11.
    Tankeo, M., Richard, P., Édouard, C.: Analytical solution of the \(\mu \)(i)-rheology for fully developed granular flows in simple configurations. Granul. Matter 15(6), 881–891 (2013)CrossRefGoogle Scholar
  12. 12.
    Forterre, Y., Pouliquen, O.: Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 1–24 (2008)CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    Azéma, E., Radjaï, F.: Internal structure of inertial granular flows. Phys. rev. lett. 112(7), 078001 (2014)CrossRefADSGoogle Scholar
  14. 14.
    Rothenburg, L., Bathurst, R.J.: Analytical study of induced anistropy in idealized granular materials. Géotechnique 4(1), 601–614 (1989)CrossRefGoogle Scholar
  15. 15.
    Hatano, T., Kuwano, O.: Origin of the velocity-strengthening nature of granular friction. Pure Appl. Geophys. 170(1–2), 3–11 (2013)CrossRefADSGoogle Scholar
  16. 16.
    Jenkins, J.T.: Dense inclined flows of inelastic spheres. Granul. Matter 10(1), 47–52 (2007)CrossRefMATHGoogle Scholar
  17. 17.
    Sun, Q., Jin, F., Zhou, G.G.D.: Energy characteristics of simple shear granular flows. Granul. Matter 15(1), 119–128 (2013)CrossRefGoogle Scholar
  18. 18.
    Babic, M., Shen, H.H., Shen, H.T.: The stress tensor in granular shear flows of uniform, deformable disks at high solids concentrations. J. Fluid Mech. 219(10), 81–118 (1990)CrossRefADSGoogle Scholar
  19. 19.
    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)Google Scholar
  20. 20.
    Plimpton, S.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117(1), 1–19 (1995)Google Scholar
  21. 21.
    Kloss, C., Goniva, C., Hager, A., Amberger, S., Pirker, S.: Models, algorithms and validation for opensource DEM and CFD-DEM. Prog. Comput. Fluid Dy. 12(2–3):140–152 (2012)Google Scholar
  22. 22.
    Zhang, H.P., Makse, H.A.: Jamming transition in emulsions and granular materials. Phys. Rev. E 72(1), 011301 (2005)CrossRefADSGoogle Scholar
  23. 23.
    Di Renzo, A., Di Maio, F.P.: Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes. Chem. Eng. Sci. 59(3), 525–541 (2004)Google Scholar
  24. 24.
    Bridges, F.G., Hatzes, A., Lin, D.N.C.: Structure, stability and evolution of Saturn’s rings. Nature 309, 333–335 (1984)CrossRefADSGoogle Scholar
  25. 25.
    Brilliantov, N.V., Spahn, F., Hertzsch, J.-M., Pöschel, T.: Model for collisions in granular gases. Phys. Rev. E 53(5), 5382 (1996)CrossRefADSGoogle Scholar
  26. 26.
    Senetakis, K., Coop, M.R., Todisco, M.C.: The inter-particle coefficient of friction at the contacts of leighton buzzard sand quartz minerals. Soils Found. 53(5), 746–755 (2013)CrossRefGoogle Scholar
  27. 27.
    Bagi, K.: Stress and strain in granular assemblies. Mech. Mater. 22(3), 165–177 (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Division of Engineering and Applied ScienceCalifornia Institute of TechnologyPasadenaUSA

Personalised recommendations