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.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Jaeger, H.M., Nagel, S.R.: Physics of the granular state. Science 255(5051), 1523–1531 (1992)
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)
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)
Wood, D.M.: Critical State Soil Mechanics. Cambridge University Press, New York (1990)
Campbell, C.S.: Rapid granular flows. Ann. Rev. Fluid Mech. 22(1), 57–90 (1990)
Goldhirsch, I.: Rapid granular flows. Ann. Rev. Fluid Mech. 35(1), 267–293 (2003)
MiDi, G.D.R.: On dense granular flows. Eur. Phys. J. E 14, 341–365 (2004)
Jop, P., Forterre, Y., Pouliquen, O.: A constitutive law for dense granular flows. Nature 441, 727–730 (2006)
Jutzi, M., Asphaug, E.: Forming the lunar farside highlands by accretion of a companion moon. Nature 476(7358), 69–72 (2011)
Kamrin, K., Koval, G.: Nonlocal constitutive relation for steady granular flow. Phys. Rev. Lett. 108(17), 178301 (2012)
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)
Forterre, Y., Pouliquen, O.: Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 1–24 (2008)
Azéma, E., Radjaï, F.: Internal structure of inertial granular flows. Phys. rev. lett. 112(7), 078001 (2014)
Rothenburg, L., Bathurst, R.J.: Analytical study of induced anistropy in idealized granular materials. Géotechnique 4(1), 601–614 (1989)
Hatano, T., Kuwano, O.: Origin of the velocity-strengthening nature of granular friction. Pure Appl. Geophys. 170(1–2), 3–11 (2013)
Jenkins, J.T.: Dense inclined flows of inelastic spheres. Granul. Matter 10(1), 47–52 (2007)
Sun, Q., Jin, F., Zhou, G.G.D.: Energy characteristics of simple shear granular flows. Granul. Matter 15(1), 119–128 (2013)
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)
Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)
Plimpton, S.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117(1), 1–19 (1995)
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)
Zhang, H.P., Makse, H.A.: Jamming transition in emulsions and granular materials. Phys. Rev. E 72(1), 011301 (2005)
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)
Bridges, F.G., Hatzes, A., Lin, D.N.C.: Structure, stability and evolution of Saturn’s rings. Nature 309, 333–335 (1984)
Brilliantov, N.V., Spahn, F., Hertzsch, J.-M., Pöschel, T.: Model for collisions in granular gases. Phys. Rev. E 53(5), 5382 (1996)
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)
Bagi, K.: Stress and strain in granular assemblies. Mech. Mater. 22(3), 165–177 (1996)
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.
About this article
Cite this article
Hurley, R.C., Andrade, J.E. Friction in inertial granular flows: competition between dilation and grain-scale dissipation rates. Granular Matter 17, 287–295 (2015). https://doi.org/10.1007/s10035-015-0564-2
- Granular materials
- Granular flows
- Dynamic material response