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


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.

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D t j :

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

E m :

System mechanical energy

E t :

Total energy

E k :

Kinetic energy

E β :

Dashpot energy loss

F d n , F d s :

Normal and dashpot force

F h n , F h s :

Nonlinear normal and shear contact force

g :

Gravity acceleration

k n :

Normal stiffness

L r :

Relative distance of the collision angle

m 1 , m 2 :

Mass of the bodies 1 and 2

m c :

Mass of the system

r :

Radius of the moving disc

r j :

Radius of base disc j

\(\bar{r}\) :

Average radius of the base disc

S γ,max :

Distance where the maximum collision angle occurs

S stop :

Total moving distance

t :

Time step

Δt :

Time step increment

Δt 0 :

Time step increment at bounce

v :


v n :

Normal velocity before collision

v s :

Tangential velocity before collision

v n,r :

Normal velocity after collision

x t , y t :

Centre position of the moving disc at time step t

U :

Gravity potential

α n :

Restitution coefficient

β n :

Damping coefficient

γ :

Contact angle

γ c :

Collision angle

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

Average collision angle

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

Relative normal translational velocity

ω :

Angular velocity

θ :

Rotation angle

η :

Disc gap coefficient

μ :

Mean of normal distribution

σ :

Standard deviation of normal distribution


  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)

    Article  Google 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)

    Article  Google 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)

    Article  Google Scholar 

  4. 4.

    Doménech-Carbó, A.: On the independence of friction and restitution: an operational approach. Granul. Matter 18(1), 9 (2016)

    Article  Google 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).

    Article  Google 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).

    Article  Google Scholar 

  7. 7.

    Majumdar, A., Tien, C.L.: Fractal characterization and simulation of rough surfaces. Wear 136(2), 313–327 (1990).

    Article  Google 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).

    ADS  Article  Google 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)

    Article  Google 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)

    Article  Google 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)

    Article  Google 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)

    Article  Google 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)

    ADS  Article  Google Scholar 

  15. 15.

    Jenkins, J.T.: Boundary conditions for plane flows of smooth, nearly elastic, circular disks. J. Fluid Mech. 171, 53–69 (1986).

    ADS  Article  MATH  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  19. 19.

    Valance, A., Bideau, D.: Dynamics of a ball bouncing on a rough inclined line. Phys. Rev. E 57(2), 1886 (1998)

    ADS  Article  Google 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)

    Article  Google 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).

    Article  Google Scholar 

  23. 23.

    Mindlin, R.D., Deresiewicz, H.: Elastic spheres in contact under varying oblique forces. J. Appl. Mech. 20, 327–344 (1953)

    MathSciNet  MATH  Google Scholar 

  24. 24.

    Itasca: PFC2D 5.0 User Manual. In. Minneapolis, MN USA (2017)

  25. 25.

    Cundall, P.A., Strack, O.D.: A discrete numerical model for granular assemblies. Géotechnique 29(1), 47–65 (1979)

    Article  Google 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)

    ADS  Article  Google Scholar 

  27. 27.

    Ling, F.: Normal impact model of rough surfaces. J. Tribol. 114(3), 439–447 (1992)

    Article  Google 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)

    Article  Google 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)

    ADS  Article  Google 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).

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  33. 33.

    Hanaor, D.A.H., Gan, Y.X., Einav, I.: Static friction at fractal interfaces. Tribol. Int. 93, 229–238 (2016).

    Article  Google Scholar 

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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’.

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Correspondence to An Deng.

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Wang, C., Deng, A., Taheri, A. et al. Modelling particle kinetic behaviour considering asperity contact: formulation and DEM simulations. Granular Matter 21, 27 (2019).

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  • Surface roughness
  • Collision
  • Contact mechanics
  • Energy dissipation