Skip to main content
SpringerLink
Log in

An efficient algorithm for granular dynamics simulations with complex-shaped objects

  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

One of the most difficult aspect of the realistic modeling of granular materials is how to capture the real shape of the particles. Here we present a method to simulate two-dimensional granular materials with complex-shaped particles. The particle shape is represented by the classical concept of a Minkowski sum, which permits the representation of complex shapes without the need to define the object as a composite of spherical or convex particles. A well defined interaction force between these bodies is derived. The algorithm for identification of neighbor particles reduces force calculations to O(N), where N is the number of particles. The method is much more efficient, accurate and easier to implement than other models. We prove that the algorithm is consistent with energy conservation, which is numerically verified using non-dissipative granular dynamics simulations. Biaxial test simulations on dissipative granular systems demonstrate the relevance of shape in the strength and stress fluctuations at the critical state.

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

Similar content being viewed by others

References

  1. Carlson H., McCammon A.: Accommodating protein flexibility in computational drug design. Mol. Pharmacol. 57(2), 213–218 (2000)

    Google Scholar 

  2. Darve F., Laouafa F.: Instabilities in granular materials and application to landslides. Mech. Cohesive-Frictional Mater. 5, 627–652 (2000)

    Article  Google Scholar 

  3. Pöschel T., Luding S.: Granular Gases. Springer, Berlin (2000)

    Google Scholar 

  4. Alonso-Marroquin F., Vardoulakis I., Herrmann H.J., Weatherley D., Mora P.: Effect of rolling on dissipation in fault gouges. Phys. Rev. E 74, 031306 (2006)

    Article  ADS  Google Scholar 

  5. Ting J., Khwaja M., Meachum L., Rowell J.: An ellipse-based discrete element model for granular materials. Int. J. Numer. Anal. Methods Geomech. 17(9), 603–23 (1993)

    Article  MATH  Google Scholar 

  6. Lin X., Ng T.: A three-dimensional discrete element model using arrays of ellipsoids. Geotechnique 47(2), 319–329 (1997)

    Google Scholar 

  7. Mustoe G., Miyata M.: Material flow analyses of noncircular-shaped granular media using discrete element methods. J. Eng. Mech. 127(10), 1017–1026 (2001)

    Article  Google Scholar 

  8. Cheng Y., Nakata Y., Bolton M.: Discrete element simulation of crushable soil. Geotechnique 53(7), 633–641 (2003)

    Article  Google Scholar 

  9. McDowell G.R., Bolton M.D., Robertson D.: The fractal crushing of granular materials. J. Mech. Phys. Solids 44(12), 2079–2102 (1996)

    Article  ADS  Google Scholar 

  10. Alonso-Marroquin F., Herrmann H.J.: Calculation of the incremental stress-strain relation of a polygonal packing. Phys. Rev. E 66, 021301 (2002)

    Article  ADS  Google Scholar 

  11. Matuttis H.-G., Luding S., Herrmann H.J.: Discrete element methods for the simulation of dense packings and heaps made of spherical and non-spherical particles. Powder Technol. 109, 278–292 (2000)

    Article  Google Scholar 

  12. Mirghasemi A.A., Rothenburg L., Matyas E.L.: Influence of particle shape on engineering properties of assemblies of two-dimensional polygon-shaped particles. Geotechnique 52(3), 209–217 (2002)

    Article  Google Scholar 

  13. Müller, D., Liebling, T.M.: Detection of collisions of polygons by using a triangulation. In: Contact Mechanics, Proceedings of the 2nd Contact Mechanics International Symposium, pp. 369–372. Carry-le-Rouet, France (1994)

  14. Müller, D.: Techniqes informatiques efficaces pour la simulation de milieux granulaires pare des méthodes d’éléments distinct, thesis no. 1545, Ph.D. thesis, École Polytechnique Fédérale de Lausanne (1996)

  15. Mirtich B.: V-clip: fast and robust polyhedral collision detection. ACM Trans. Graph. (TOG) 15(3), 177–208 (1998)

    Article  Google Scholar 

  16. Cundall P.: Formulation of a three-dimensional distinct element model–Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int. J. Rock Mech. Min. Sci. Geomech. Abstr 25(3), 107–116 (1988)

    Google Scholar 

  17. McNamara S., Luding S.: Energy flows in vibrated granular media. Phys. Rev. E 58, 813–822 (1998)

    Article  ADS  Google Scholar 

  18. Jean M.: The non-smooth contact dynamics method. Comput. Methods Appl. Mech. Eng. 177(3–4), 235–257 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  19. McNamara S., García-Rojo R., Herrmann H.: Indeterminacy and the onset of motion in a simple granular packing. Phys. Rev. E 72(2), 21304 (2005)

    Article  ADS  Google Scholar 

  20. Alonso-Marroquin F., Luding S., Herrmann H., Vardoulakis I.: Role of the anisotropy in the elastoplastic response of a polygonal packing. Phys. Rev. E 51, 051304 (2005)

    Article  ADS  Google Scholar 

  21. Poeschel T., Schwager T.: Computational Granular Dynamics. Springer, Berlin (2004)

    Google Scholar 

  22. Pournin, L., Liebling, T.: A generalization of distinct element method to tridimentional particles with complex shapes. In: Powders & Grains 2005, pp. 1375–1478. Leiden, Balkema (2005)

  23. Pournin, L.: On the behavior of spherical and non-spherical grain assemblies, its modeling and numerical simulation. Ph.D. thesis, École Polytechnique Fédérale de Lausanne (2005)

  24. Alonso-Marroquin F.: Spheropolygons: a new method to simulate conservative and dissipative interactions between 2d complex-shaped rigid bodies. Europhys. Lett. 83(1), 14001 (2008)

    Article  ADS  Google Scholar 

  25. Pournin L., Weber M., Tsukahara M., Ferrez J.-A., Ramaioli M., Liebling T.M.: Three-dimensional distinct element simulation of spherocylinder crystallization. Granul. Matter 7(2–3), 119–126 (2005)

    Article  MATH  Google Scholar 

  26. Franklin, R.: How do I find if a point lies within a polygon. In: comp.graphics.algorithms FAQ, www.faqs.org/faqs/graphics/algorithms-faq/, p. Subject 2.03 (1994)

  27. Josuttis N.: The C++ Standard Library: A Tutorial and Reference. Addison-Wesley Professional, USA (1999)

    Google Scholar 

  28. García-Rojo R., Alonso-Marroquín F., Herrmann H.: Characterization of the material response in granular ratcheting. Phys. Rev. E 72(4), 41302 (2005)

    Article  ADS  Google Scholar 

  29. Sibille L., Froiio F.: A numerical photogrammetry technique for measuring microscale kinematics and fabric in Schneebeli materials. Granul. Matter 9(3), 183–193 (2007)

    Article  Google Scholar 

  30. Wood, D.M.: Soil Behaviour and Critical State Soil Mechanics. ISBN: 0-521-33782-8, Cambridge (1990)

  31. Vardoulakis I., Georgopoulos I.O.: The stress-dilatancy hypothesis revisited: shear-banding related instabilities. Soils & Foundations 45, 61–76 (2005)

    Google Scholar 

  32. Adjemian F., Evesque P., Jia X.: Ultrasonic experiment coupled with triaxial test for micro-seismicity detection in granular media. In: García-Rojo, R., Herrmann, H., McNamara, S. (eds) Powders and Grains 2005, pp. 281–285. Balkema, Leiden (2005)

    Google Scholar 

  33. Pena A., Lizcano A., Alonso-Marroquin F., Herrmann H.J.: Biaxial test simulations using a packing of polygonal particles. Int. J. Numer. Anal. Meth. Geomech. 32(2), 143 (2008)

    Article  Google Scholar 

  34. Tordesillas A.: Force chain buckling, unjamming transitions and shear banding in dense granular assemblies. Philos. Mag. 87(32), 4987–5016 (2007)

    Article  ADS  Google Scholar 

  35. Herrmann H., Hansen A., Roux S.: Fracture of disordered, elastic lattices in two dimensions. Phys. Rev. B 39(1), 637–648 (1989)

    Article  ADS  Google Scholar 

  36. Tordesillas, A., Alonso-Marroquin, F.: On the connection between aspect ratio and rolling resistance (in preparation)

  37. Cleary P.W., Sinnott M.D., Morrison R.D.: DEM prediction of particle flows in grinding processes. Int. J. Numer. Meth. Fluids 58, 319–353 (2008)

    Article  MATH  Google Scholar 

  38. Muth, B., Eberhard, P., Luding, S.: Collisions between particles of complex shape. In: Powders & Grains 2005, pp. 1379–1383. Leiden, Balkema (2005)

  39. Muth, B., Muller, M., Eberhard, P., Luding, S.: Collision detection and administration methods for many particles with different sizes. In: DEM07 Proceedings CD, pp. 1–18. www2.msm.ctw.utwente.nl/sluding/PAPERS/dem07.pdf

  40. Wang Y., Abe S., Latham S., Mora P.: Implementation of particle-scalerotation in the 3-D lattice solid model. Pure Appl. Geophys. 163(9), 1769–1785 (2006)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. MoSCoS, School of Mathematics and Physics, The University of Queensland, St Lucia, Brisbane, QLD, 4072, Australia

    Fernando Alonso-Marroquín

  2. CSIRO Exploration and Mining, Technology Court, Pullenvale, QLD, 4069, Australia

    Yucang Wang

  3. PO Box 883, Kenmore, QLD, 4069, Australia

    Yucang Wang

Authors
  1. Fernando Alonso-Marroquín
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yucang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fernando Alonso-Marroquín.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alonso-Marroquín, F., Wang, Y. An efficient algorithm for granular dynamics simulations with complex-shaped objects. Granular Matter 11, 317–329 (2009). https://doi.org/10.1007/s10035-009-0139-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-009-0139-1

Keywords

Search

Navigation