Skip to main content
Log in

Temporal variation of contact networks in granular materials

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

Abstract

For analogue granular materials simulated using DEM, contact networks are often drawn by joining the centroids of contacting particles. Although a limited amount of research has been done to characterise the temporal aspects of such contact networks at a micro-scale, many simple questions regarding the duration of contacts in evolving granular systems remain unanswered. This paper addresses this gap in the existing knowledge by using the open-source code LAMMPS to run and analyse nine (3D) triaxial simulations of 20,164 polydisperse spherical particles. Contacts which exist for a long duration are preferentially oriented in the direction of the major principal stress while the fabric anisotropy for contacts with a given duration increases with duration. Regardless of simulation conditions, there is a linear relationship between the percentage of contacts present for a given duration and contact duration, despite the non-linear overall behaviour of the material. The forces transmitted by contacts increase, on average, with increasing duration. The total number of unique contacts which appear during triaxial compression increases linearly after 10 % axial strain, although the number of contacts, both total and subdivided into strong and weak force subnetworks, remains quite stable. The majority of contacts in these evolving granular systems, even those participating in strong force chains, are formed and lost repeatedly.

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

Access this article

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

Instant access to the full article PDF.

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. Hill, S., Agarwal, D.K., Bell, R., Volinsky, C.: Building an effective representation for dynamic networks. J. Comput. Graph. Stat. 15(3), 584–608 (2008)

    Article  MathSciNet  Google Scholar 

  2. Fonseca, J., O’Sullivan, C., Coop, M.R., Lee, P.D.: Quantifying the evolution of soil fabric during shearing using scalar parameters. Géotechnique 63(10), 818–829 (2013)

    Article  Google Scholar 

  3. Hidalgo, R.C., Grosse, C.U., Kun, F., Reinhardt, H.W., Herrmann, H.J.: Evolution of percolating force chains in compressed granular media. Phys. Rev. Lett. 89(205501), 1–4 (2002)

    Google Scholar 

  4. Thornton, C., Barnes, D.J.: Computer simulated deformation of compact granular assemblies. Acta Mech. 64(1–2), 45–61 (1986)

    Google Scholar 

  5. Cundall, P., Strack, O.: The distinct element methods as a tool for research in granular media. Part I, Report to NSF (1978)

  6. Peters, J.F., Muthuswamy, M., Wibowo, J., Tordesillas, A.: Characterization of force chains in granular material. Phys. Rev. E 72(041307), 1–8 (2005)

    Google Scholar 

  7. Pöschel, T., Schwager, T.: Computational Granular Dynamics. Springer, Berlin (2005)

    Google Scholar 

  8. Thornton, C., Antony, S.J.: Quasi-static deformation of particulate media. Phil. Trans. R. Soc. Lond. A 356, 2763–2782 (1998)

    Google Scholar 

  9. Zhang, J., Majumdar, T.S., Tordesillas, A., Behringer, R.P.: Statistical properties of a 2D granular material subjected to cyclic shear. Granul. Matter 12(2), 159–172 (2010)

    Article  Google Scholar 

  10. Walker, D.M., Tordesillas, A.: Taxonomy of granular rheology from grain property networks. Phys. Rev. E 85(011304), 1–11 (2012)

    Google Scholar 

  11. Walker, D.M., Tordesillas, A., Thornton, C., Behringer, R.P., Zhang, J., Peters, J.F.: Percolating contact subnetworks on the edge of isostaticity. Granul. Matter 13(3), 233–240 (2010)

    Article  Google Scholar 

  12. Tordesillas, A., Walker, D.M., Rechenmacher, A.L., Abedi, S.: Discovering community structures and dynamical networks from grain-scale kinematics of shear bands in sand. In: Bonelli, S., Dascalu, C., Nicot, F. (eds.) Advances in Bifurcation and Degradation in Geomaterials (Springer Series in Geomechanics and Geoengineering), vol. 11, pp. 67–73. Springer, The Netherlands (2011)

    Chapter  Google Scholar 

  13. Rognon, P.G., Roux, J.-N., Wolf, D., Naaïm, N., Chevior, F.: Rheophysics of cohesive granular materials. Europhys. Lett. 74(4), 644 (2006)

    Article  ADS  Google Scholar 

  14. Oda, M., Kazama, H.: Microstructure of shear bands and its relation to the mechanism of dilatancy and failure of granular soils. Géotechnique 48(4), 465–481 (1998)

    Article  Google Scholar 

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

    Google Scholar 

  16. O’Sullivan, C., Wadee, M.A., Hanley, K.J., Barreto, D.: Use of DEM and elastic stability analysis to explain the influence of the intermediate principal stress on shear strength. Géotechnique 63(15), 1298–1309 (2013)

    Article  Google Scholar 

  17. Thornton, C.: Numerical simulations of deviatoric shear deformation of granular media. Géotechnique 50(1), 43–53 (2000)

    Article  Google Scholar 

  18. Sitharam, T.G., Dinesh, S.V., Shimizu, N.: Micromechanical modelling of monotonic drained and undrained shear behaviour of granular media using three-dimensional DEM. Int. J. Numer. Anal. Met. 26(12), 1167–1189 (2002)

    Article  MATH  Google Scholar 

  19. Cundall, P.: Computer simulations of dense sphere assemblies. In: Satake, M., Jenkins, J. (eds.) Micromechanics of Granular Materials, pp. 113–123. Elsevier, Amsterdam (1988)

    Google Scholar 

  20. Marketos, G., Bolton, M.: Flat boundaries and their effect on sand testing. Int. J. Numer. Anal. Met. 34(8), 821–837 (2010)

    MATH  Google Scholar 

  21. Yang, J., Sze, H.Y.: Cyclic behavior and resistance of saturated sand under non-symmetrical loading conditions. Géotechnique 61(1), 59–73 (2011)

    Article  Google Scholar 

  22. Plimpton, S.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995)

    Article  ADS  MATH  Google Scholar 

  23. Barreto Gonzalez, D.: Numerical and Experimental Investigation into the Behaviour of Granular Materials Under Generalised Stress States. PhD thesis, Imperial College London (2009)

  24. Thornton, C.: The conditions for failure of a face-centered cubic array of uniform rigid spheres. Géotechnique 29(4), 441–459 (1979)

    Article  Google Scholar 

  25. Huang, X., Hanley, K.J., O’Sullivan, C., Kwok, F.: Effect of Sample Size on the Response of DEM Samples with a Realistic Grading. Accepted for publication in Particuology (2013)

  26. Itasca Consulting Group: PFC3D: Particle Flow Code in Three Dimensions. Itasca Consulting Group, Minneapolis (2008)

  27. Roscoe, K.H., Schofield, M.A., Wroth, C.P.: On the yielding of soils. Géotechnique 8(1), 22–53 (1958)

    Article  Google Scholar 

  28. Altuhafi, F.N., Coop, M.R.: Changes to particle characteristics associated with the compression of sands. Géotechnique 61(6), 459–471 (2011)

    Google Scholar 

  29. Potyondy, D.O., Cundall, P.A.: A bonded-particle model for rock. Int. J. Rock Mech. Min. 41(8), 1329–1364 (2004)

    Google Scholar 

  30. Schofield, A., Wroth, C.: Critical State Soil Mechanics. McGraw-Hill, New York (1968)

  31. The MathWorks Inc.: MATLAB version 7.13 R2011b (computer software). Natick, Massachusetts (2011)

  32. Radjai, F., Wolf, D.E., Roux, S., Jean, M., Moreau, J.-J.: Force networks in dense granular media. In: Behringer, R.P., Jenkins, J.T. (eds.) Powders and Grains, vol. 97, pp. 211–214. Balkema, Rotterdam (1997)

    Google Scholar 

  33. Satake, M.: Fabric tensor in granular materials. In: Proceedings IUTAM Conference on Deformation and Failure of Granular Materials, pp. 63–67, Delft (1982)

  34. Barreto, D., O’Sullivan, C.: The influence of inter-particle friction and the intermediate stress ratio on soil response under generalised stress conditions. Granul. Matter 14(4), 505–521 (2012)

    Article  Google Scholar 

Download references

Acknowledgments

K. Hanley would like to acknowledge funding from the Royal Commission for the Exhibition of 1851. Computational time on HECToR, used for code development, was provided as part of Grant EP/I006761/1 from the Engineering and Physical Sciences Research Council.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kevin J. Hanley.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hanley, K.J., Huang, X., O’Sullivan, C. et al. Temporal variation of contact networks in granular materials. Granular Matter 16, 41–54 (2014). https://doi.org/10.1007/s10035-013-0470-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-013-0470-4

Keywords

Navigation