Granular Matter

, 21:27 | Cite as

Modelling particle kinetic behaviour considering asperity contact: formulation and DEM simulations

  • Can Wang
  • An DengEmail author
  • Abbas Taheri
  • Honghua Zhao
  • Jie Li
Original Paper


A model of formulating particle kinetic behaviour considering surface asperity is presented. The asperity was created by lining up on the surface a set of particles in varying distances. A moving particle was assigned a velocity to travel on the rugged surface where the particle trajectory and mechanical energy were gauged. The results were used to validate a discrete element framework which was developed and applied to examine the effect of surface asperity on the particle kinetic behaviour. Some interesting case studies were designed and simulated. The simulations suggested that the surface roughness influenced the energy dissipation caused in the particle–surface collisions. The research outcomes defined the inter-particle reaction from a micro-scale perspective and helped predict asperity-induced wear.


Surface roughness Collision Contact mechanics Energy dissipation 

List of symbols


Relative distance between the moving disc and base disc at time step t


System mechanical energy


Total energy


Kinetic energy


Dashpot energy loss

Fnd, Fsd

Normal and dashpot force

Fnh, Fsh

Nonlinear normal and shear contact force


Gravity acceleration


Normal stiffness


Relative distance of the collision angle

m1, m2

Mass of the bodies 1 and 2


Mass of the system


Radius of the moving disc


Radius of base disc j


Average radius of the base disc


Distance where the maximum collision angle occurs


Total moving distance


Time step


Time step increment


Time step increment at bounce




Normal velocity before collision


Tangential velocity before collision


Normal velocity after collision

xt, yt

Centre position of the moving disc at time step t


Gravity potential


Restitution coefficient


Damping coefficient


Contact angle


Collision angle

\(\bar{\gamma }^{c}\)

Average collision angle

\(\dot{\delta }_{n}\)

Relative normal translational velocity


Angular velocity


Rotation angle


Disc gap coefficient


Mean of normal distribution


Standard deviation of normal distribution



This study is performed under the supports provided by the Australian Research Council (Project No. DP140103004) and the University of Adelaide. Professional editor, Leticia Mooney, provided copyediting and proofreading services, according to the guidelines laid out in the university-endorsed national ‘Guidelines for editing research theses’.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Research involving human participants and/or animals

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.


  1. 1.
    Yang, J., Wei, L.: Collapse of loose sand with the addition of fines: the role of particle shape. Géotechnique 62(12), 1111–1125 (2012)CrossRefGoogle Scholar
  2. 2.
    Jensen, R.P., Edil, T.B., Bosscher, P.J., Plesha, M.E., Kahla, N.B.: Effect of particle shape on interface behavior of DEM-simulated granular materials. Int. J. Geomech. 1(1), 1–19 (2001)CrossRefGoogle Scholar
  3. 3.
    Dai, B.B., Yang, J., Zhou, C.Y.: Observed effects of interparticle friction and particle size on shear behavior of granular materials. Int. J. Geomech. 16(1), 04015011 (2015)CrossRefGoogle Scholar
  4. 4.
    Doménech-Carbó, A.: On the independence of friction and restitution: an operational approach. Granul. Matter 18(1), 9 (2016)CrossRefGoogle Scholar
  5. 5.
    Zhai, C.P., Hanaor, D., Gan, Y.X.: Contact stiffness of multiscale surfaces by truncation analysis. Int. J. Mech. Sci. 131, 305–316 (2017). CrossRefGoogle Scholar
  6. 6.
    Holmberg, K., Ronkainen, H., Laukkanen, A., Wallin, K.: Friction and wear of coated surfaces—scales, modelling and simulation of tribomechanisms. Surf. Coat. Technol. 202(4–7), 1034–1049 (2007). CrossRefGoogle Scholar
  7. 7.
    Majumdar, A., Tien, C.L.: Fractal characterization and simulation of rough surfaces. Wear 136(2), 313–327 (1990). CrossRefGoogle Scholar
  8. 8.
    Persson, B.N.J., Albohr, O., Tartaglino, U., Volokitin, A.I., Tosatti, E.: On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion. J Phys Condens. Matter. 17(1), R1–R62 (2005). ADSCrossRefGoogle Scholar
  9. 9.
    Buckley, D.H.: Surface effects in adhesion, friction, wear, and lubrication, vol. 5. Elsevier, London (1981)Google Scholar
  10. 10.
    Tayebi, N., Polycarpou, A.A.: Modeling the effect of skewness and kurtosis on the static friction coefficient of rough surfaces. Tribol. Int. 37(6), 491–505 (2004)CrossRefGoogle Scholar
  11. 11.
    Svahn, F., Kassman-Rudolphi, Å., Wallen, E.: The influence of surface roughness on friction and wear of machine element coatings. Wear 254(11), 1092–1098 (2003)CrossRefGoogle Scholar
  12. 12.
    Zappone, B., Rosenberg, K.J., Israelachvili, J.: Role of nanometer roughness on the adhesion and friction of a rough polymer surface and a molecularly smooth mica surface. Tribol. Lett. 26(3), 191 (2007)CrossRefGoogle Scholar
  13. 13.
    Jensen, R.P., Bosscher, P.J., Plesha, M.E., Edil, T.B.: DEM simulation of granular media—structure interface: effects of surface roughness and particle shape. Int. J. Numer. Anal. Meth. Geomech. 23(6), 531–547 (1999)CrossRefGoogle Scholar
  14. 14.
    Dippel, S., Batrouni, G., Wolf, D.: Collision-induced friction in the motion of a single particle on a bumpy inclined line. Phys. Rev. E 54(6), 6845 (1996)ADSCrossRefGoogle Scholar
  15. 15.
    Jenkins, J.T.: Boundary conditions for plane flows of smooth, nearly elastic, circular disks. J. Fluid Mech. 171, 53–69 (1986). ADSCrossRefzbMATHGoogle Scholar
  16. 16.
    Greenwood, J., Williamson, J.: Contact of nominally flat surfaces, proceedings of the royal society of london. Math. Phys. Eng. Sci. 295(1442), 300–319 (1966)Google Scholar
  17. 17.
    Batrouni, G., Dippel, S., Samson, L.: Stochastic model for the motion of a particle on an inclined rough plane and the onset of viscous friction. Phys. Rev. E 53(6), 6496 (1996)ADSCrossRefGoogle Scholar
  18. 18.
    Henrique, C., Aguirre, M., Calvo, A., Ippolito, I., Dippel, S., Batrouni, G., Bideau, D.: Energy dissipation and trapping of particles moving on a rough surface. Phys. Rev. E 57(4), 4743 (1998)ADSCrossRefGoogle Scholar
  19. 19.
    Valance, A., Bideau, D.: Dynamics of a ball bouncing on a rough inclined line. Phys. Rev. E 57(2), 1886 (1998)ADSCrossRefGoogle Scholar
  20. 20.
    Gollin, D., Berzi, D., Bowman, E.T.: Extended kinetic theory applied to inclined granular flows: role of boundaries. Granul. Matter 19(3), 56 (2017)CrossRefGoogle Scholar
  21. 21.
    Cundall, P.: Computer simulations of dense sphere assemblies. Micromechanics Granul. Mater. 20, 113–123 (1988)Google Scholar
  22. 22.
    Wang, C., Deng, A., Taheri, A.: Three-dimensional discrete element modeling of direct shear test for granular rubber-sand. Comput. Geotech. 97, 204–216 (2018). CrossRefGoogle Scholar
  23. 23.
    Mindlin, R.D., Deresiewicz, H.: Elastic spheres in contact under varying oblique forces. J. Appl. Mech. 20, 327–344 (1953)MathSciNetzbMATHGoogle Scholar
  24. 24.
    Itasca: PFC2D 5.0 User Manual. In. Minneapolis, MN USA (2017)Google Scholar
  25. 25.
    Cundall, P.A., Strack, O.D.: A discrete numerical model for granular assemblies. Géotechnique 29(1), 47–65 (1979)CrossRefGoogle Scholar
  26. 26.
    Becker, V., Schwager, T., Pöschel, T.: Coefficient of tangential restitution for the linear dashpot model. Phys. Rev. E 77(1), 011304 (2008)ADSCrossRefGoogle Scholar
  27. 27.
    Ling, F.: Normal impact model of rough surfaces. J. Tribol. 114(3), 439–447 (1992)CrossRefGoogle Scholar
  28. 28.
    Kawaguchi, T., Tanaka, T., Tsuji, Y.: Numerical simulation of fluidized bed using the discrete element method (the case of spouting bed). Trans. Jp. Soc. Mech. Eng. Ser. B 58(551), 79–85 (1992)Google Scholar
  29. 29.
    Gadelmawla, E., Koura, M., Maksoud, T., Elewa, I., Soliman, H.: Roughness parameters. J. Mater. Process. Technol. 123(1), 133–145 (2002)CrossRefGoogle Scholar
  30. 30.
    Gnecco, E., Bennewitz, R., Gyalog, T., Loppacher, C., Bammerlin, M., Meyer, E., Güntherodt, H.-J.: Velocity dependence of atomic friction. Phys. Rev. Lett. 84(6), 1172 (2000)ADSCrossRefGoogle Scholar
  31. 31.
    Bhushan, B., Israelachvili, J.N., Landman, U.: Nanotribology: friction, wear and lubrication at the atomic scale. Nature 374(6523), 607–616 (1995). ADSCrossRefGoogle Scholar
  32. 32.
    Fujisawa, S., Kishi, E., Sugawara, Y., Morita, S.: Atomic-scale friction observed with a two-dimensional frictional-force microscope. Phys. Rev. B 51(12), 7849 (1995)ADSCrossRefGoogle Scholar
  33. 33.
    Hanaor, D.A.H., Gan, Y.X., Einav, I.: Static friction at fractal interfaces. Tribol. Int. 93, 229–238 (2016). CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Civil Environmental and Mining EngineeringThe University of AdelaideAdelaideAustralia
  2. 2.State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering MechanicsDalian University of TechnologyDalianChina
  3. 3.School of Civil and Infrastructure EngineeringRMIT UniversityMelbourneAustralia

Personalised recommendations