Granular Matter

, Volume 16, Issue 3, pp 327–337 | Cite as

Characterisation of the effects of particle shape using a normalised contact eccentricity

Original Paper


In discrete element modelling it is quite common to employ rolling friction models to mimic the effects of particle shape. This paper presents an investigation of the mechanisms at play when using this technique and compares the behaviour of a rolling friction model with various non-spherical particle systems. The motivation behind this work revolves around forming a theoretical framework behind the selection of a coefficient of rolling friction. As a part of this study, we describe an approach where the normalised average contact eccentricity of non-spherical particles (in this case multispheres) is used to characterise the effects of shape. This description is found to capture some aspects of material behaviour reasonably well. When compared to the behaviour of a common rolling friction model, it was found that similar behaviour could be approximated by spheres with a coefficient of rolling friction equal to one half of the normalised eccentricity of non-spherical material. This is approximately in-line with previous studies involving 2D polyhedral particles (Estrada et al. in Phys Rev E 84:011306, 2011).


Granular materials Particle shape  Rolling friction Contact eccentricity 


  1. 1.
    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Géotechnique 29, 47–65 (1979)CrossRefGoogle Scholar
  2. 2.
    Wensrich, C.M., Katterfeld, A.: Rolling friction as a technique for modelling particle shape in DEM. Powder Technol. 217, 409–417 (2012)CrossRefGoogle Scholar
  3. 3.
    Society of Automotive Engineers: SAEJ2452—stepwise coastdown methodology for measuring tire rolling resistance. SAE Standard (1999)Google Scholar
  4. 4.
    Björklund, S., Enblom, R., Iwnicki, S.: Wheel–rail contact mechanics. In: Lewis, R., Olofsson, S. (eds.) Wheel–Rail Interface Handbook. Woodhead Publishing, Cambridge (2009)Google Scholar
  5. 5.
    Wheeler, C.A., Munzenberger, P.J.: Predicting the influence of conveyor belt carcass properties on indentation rolling resistance. Bulk Solids Powder Sci. Technol. 4, 67–74 (2009)Google Scholar
  6. 6.
    Hamrock, B.J., Andreson, W.J.: Rolling element bearings. In: Rothbart, H.A. (ed.) Mechanical Design and Systems Handbook. McGraw Hill, New York (1985)Google Scholar
  7. 7.
    Ai, J., Chen, J.-F., Rotter, J.M., Ooi, J.Y.: Assessment of rolling resistance models in discrete element simulations. Powder Technol. 206, 269–282 (2011)CrossRefGoogle Scholar
  8. 8.
    Iwashita, K., Oda, M.: Rolling resistance at contacts in simulation of shear band development by DEM. J. Eng. Mech. ASCE 124, 285–292 (1998)CrossRefGoogle Scholar
  9. 9.
    Zhu, H.P., Yu, A.B.: A theoretical analysis of the force models in discrete element method. Powder Technol. 161, 122–129 (2006)CrossRefGoogle Scholar
  10. 10.
    Wensrich, C.M.: Stress, stress-asymmetry and contact moments in granular matter. Granul. Matter (2013, submitted)Google Scholar
  11. 11.
    Estrada, N., Azema, E., Radjai, F., Taboada, A.: Identification of rolling resistance as a shape parameter in sheared granular media. Phys. Rev. E 84, 011306 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    Itasca Consultants: PFC3D version 4 user manual (Theory and background) (2011)Google Scholar
  13. 13.
    Wensrich, C.M.: Boundary structure in dense random packing of monosized spherical particles. Powder Technol. 219, 118–127 (2012)CrossRefGoogle Scholar
  14. 14.
    Silbert, L.E., Ertas, D., Grest, G.S., Halsey, T.C., Levine, D.: Geometry of frictionless and frictional packings. Phys. Rev. E 65, 031304 (2002)ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.The University of NewcastleCallaghanAustralia
  2. 2.Otto-von-Guericke UniversitätMagdeburgGermany

Personalised recommendations