Skip to main content
SpringerLink
Log in

Contact forces of polyhedral particles in discrete element method

  • Original Paper
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

A general contact force law for arbitrarily shaped bodies is presented. At first an advanced contact force law is derived from the well know Hertz contact law. The obtained formulation of the Hertz contact law can be applied to the contact of arbitrarily shaped bodies. In a second step this contact model is applied to the contacts among polyhedral particles. The results are compared to finite element simulations. The model is extended by terms for damping and friction. The behaviour of the damping and friction model are demonstrated with simple examples. The force law is then implemented in the discrete element method (DEM). The application of this DEM is demonstrated by a simulation of the particle movement in a mixer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Carmona, H.A., Wittel, F.K., Kun, F., Herrmann, H.J.: Fragmentation processes in impact of spheres. Phys. Rev. E 77(5), 051302 (2008)

    Google Scholar 

  2. Chen, J., Matuttis, H.G.: Study of quasi two dimensional granular heaps. Theor. Appl. Mech. Jpn. 60, 225–238 (2012)

    Google Scholar 

  3. Chen, J., Schinner, A., Matuttis, H.G.: Discrete element simulation for polyhedral granular particles. Theor. Appl. Mech. Jpn. 59, 335–346 (2011)

    Google Scholar 

  4. Feng, Y.T., Han, K., Owen, D.R.J.: Energy-conserving contact interaction models for arbitrarily shaped discrete elements. Comput. Methods Appl. Mech. Eng. 205–208, 169–177 (2012)

    Article  MathSciNet  Google Scholar 

  5. Fraige, F.Y., Langston, P.A., Chen, G.Z.: Distinct element modelling of cubic particle packing and flow. Powder Technol. 186, 224–240 (2008)

    Article  Google Scholar 

  6. Ghaboussi, J., Barbosa, R.: Three-dimensional discrete element method for granular materials. Int. J. Numer. Anal. Methods Geomech. 14, 451–472 (1990)

    Article  Google Scholar 

  7. Gilardi, G., Sharf, I.: Literature survey of contact dynamics modelling. Mech. Mach. Theor. 37, 1213–1239 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Herrmann, H.J., Luding, S.: Modeling granular media on the computer. Continuum Mech. Thermodyn. 10(4), 189–231 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Hertz, H.: Über die Berührung fester elastischer Körper. J. für die reine und angewandte Math. 92, 156–171 (1881)

    Google Scholar 

  10. Hippmann, G.: Modellierung von Kontakten komplex geformter Körper in der Mehrkörperdynamik. Ph.D. thesis, TU Wien (2004)

  11. Hunt, K.H., Crossley, F.R.E.: Coefficient of restitution interpreted as damping in vibroimpact. J. Appl. Mech. Trans. ASME 42 Ser E(2), 440–445 (1975)

    Article  ADS  Google Scholar 

  12. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985)

    Book  MATH  Google Scholar 

  13. Kloss, C., Goniva, C.: Liggghts a new open source discrete element simulation software. In: Proceedings of The Fifth International Conference on Discrete Element Methods, London, UK (2010)

  14. Lankarani, H.M., Nikravesh, P.E.: Continuous contact force models for impact analysis in multibody systems. Nonlinear Dyn. 5, 193–207 (1994)

    Google Scholar 

  15. MacHado, M., Moreira, P., Flores, P., Lankarani, H.M.: Compliant contact force models in multibody dynamics: evolution of the Hertz contact theory. Mech. Mach. Theor. 53, 99–121 (2012)

    Article  Google Scholar 

  16. Nassauer, B., Liedke, T., Kuna, M.: Polyhedral particles for the discrete element method. Granul. Matter 15(1), 85–93 (2013)

    Article  Google Scholar 

  17. Popov, V.L.: Kontaktmechanik und Reibung. Springer, Berlin (2009)

    MATH  Google Scholar 

  18. Potapov, A.V., Campbell, C.S.: A three-dimensional simulation of brittle solid fracture. Int. J. Mod. Phys. C 7(5), 717–729 (1996)

    Article  ADS  Google Scholar 

  19. Stewart, D.E.: Rigid-body dynamics with friction and impact. SIAM Rev. 42(1), 3–39 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, 09596 , Freiberg, Germany

    Benjamin Nassauer & Meinhard Kuna

Authors
  1. Benjamin Nassauer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Meinhard Kuna
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Benjamin Nassauer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nassauer, B., Kuna, M. Contact forces of polyhedral particles in discrete element method. Granular Matter 15, 349–355 (2013). https://doi.org/10.1007/s10035-013-0417-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-013-0417-9

Keywords

Search

Navigation