Granular Matter

, 21:43 | Cite as

Capturing the inter-particle force distribution in granular material using LS-DEM

  • Liuchi Li
  • Eloïse Marteau
  • José E. AndradeEmail author
Original Paper


Particle shape, as one of the most important physical ingredients of granular materials, can greatly alter the characteristic of inter-particle force distribution which is of vital importance in understanding the mechanical behavior of granular materials. However, currently both experimental and numerical studies remain limited in this regard. In this paper, we for the first time validate the ability of the level set discrete element method (LS-DEM) on capturing the inter-particle force distribution among particles of arbitrary shape. We first present the technical detail of LS-DEM; we then apply LS-DEM to simulate experiments of shearing granular materials composed of arbitrarily shaped particles. The proposed approach directly links experimentally measured material properties to model parameters such as contact stiffness without any calibration. Our results show that LS-DEM is able to not only capture the macro scale response such as stress and deformation, but also to reproduce the particle scale contact information such as the distribution of contact force magnitude, contact orientation and contact friction mobilization. Our work demonstrates the promising potential of LS-DEM on studying the mechanics and physics of natural granular material and on aiding design granular particle shape for novel macro-scale mechanical property.


Contact forces Discrete element method Validation Force measurement 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Richard, P., Nicodemi, M., Delannay, R., Ribiere, P., Bideau, D.: Slow relaxation and compaction of granular systems. Nat. Mater. 4(2), 121 (2005)ADSCrossRefGoogle Scholar
  2. 2.
    Jaeger, H.M., Nagel, S.R., Behringer, R.P.: The physics of granular materials. Phys. Today 49, 32–39 (1996)CrossRefGoogle Scholar
  3. 3.
    Jaeger, H.M., Nagel, S.R., Behringer, R.P.: Granular solids, liquids, and gases. Rev. Mod. Phys. 68(4), 1259 (1996)ADSCrossRefGoogle Scholar
  4. 4.
    Majmudar, T.S., Behringer, R.P.: Contact force measurements and stress-induced anisotropy in granular materials. Nature 435(7045), 1079 (2005)ADSCrossRefGoogle Scholar
  5. 5.
    Iikawa, N., Bandi, M., Katsuragi, H.: Sensitivity of granular force chain orientation to disorder-induced metastable relaxation. Phys. Rev. Lett. 116(12), 128001 (2016)ADSCrossRefGoogle Scholar
  6. 6.
    Cho, G.-C., Dodds, J., Santamarina, J.C.: Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. J. Geotech. Geoenviron. Eng. 132(5), 591–602 (2006)CrossRefGoogle Scholar
  7. 7.
    Athanassiadis, A.G., Miskin, M.Z., Kaplan, P., Rodenberg, N., Lee, S.H., Merritt, J., Brown, E., Amend, J., Lipson, H., Jaeger, H.M.: Particle shape effects on the stress response of granular packings. Soft Matter 10(1), 48–59 (2014)ADSCrossRefGoogle Scholar
  8. 8.
    Brodu, N., Dijksman, J.A., Behringer, R.P.: Spanning the scales of granular materials through microscopic force imaging. Nat. Commun. 6, 6361 (2015)ADSCrossRefGoogle Scholar
  9. 9.
    Hurley, R., Hall, S., Andrade, J., Wright, J.: Quantifying interparticle forces and heterogeneity in 3d granular materials. Phys. Rev. Lett. 117(9), 098005 (2016)ADSCrossRefGoogle Scholar
  10. 10.
    Hurley, R., Marteau, E., Ravichandran, G., Andrade, J.E.: Extracting inter-particle forces in opaque granular materials: beyond photoelasticity. J. Mech. Phys. Solids 63, 154–166 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    Cundall, P.A., Strack, O.D.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)CrossRefGoogle Scholar
  12. 12.
    Jean, M.: The non-smooth contact dynamics method. Comput. Methods Appl. Mech. Eng. 177(3–4), 235–257 (1999)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Da Cruz, F., Emam, S., Prochnow, M., Roux, J.-N., Chevoir, F.: Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72(2), 021309 (2005)ADSCrossRefGoogle Scholar
  14. 14.
    Pazouki, A., Kwarta, M., Williams, K., Likos, W., Serban, R., Jayakumar, P., Negrut, D.: Compliant contact versus rigid contact: a comparison in the context of granular dynamics. Phys. Rev. E 96(4), 042905 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    Radjai, F., Jean, M., Moreau, J.-J., Roux, S.: Force distributions in dense two-dimensional granular systems. Phys. Rev. Lett. 77(2), 274 (1996)ADSCrossRefGoogle Scholar
  16. 16.
    Radjai, F., Wolf, D.E., Jean, M., Moreau, J.-J.: Bimodal character of stress transmission in granular packings. Phys. Rev. Lett. 80(1), 61 (1998)ADSCrossRefGoogle Scholar
  17. 17.
    Azéma, E., Radjai, F., Peyroux, R., Saussine, G.: Force transmission in a packing of pentagonal particles. Phys. Rev. E 76(1), 011301 (2007)ADSCrossRefGoogle Scholar
  18. 18.
    Azéma, E., Radjaï, F.: Stress-strain behavior and geometrical properties of packings of elongated particles. Phys. Rev. E 81(5), 051304 (2010)ADSCrossRefGoogle Scholar
  19. 19.
    Azéma, E., Radjaï, F.: Force chains and contact network topology in sheared packings of elongated particles. Phys. Rev. E 85(3), 031303 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    Azéma, E., Radjai, F., Saussine, G.: Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles. Mech. Mater. 41(6), 729–741 (2009)CrossRefGoogle Scholar
  21. 21.
    Azéma, E., Estrada, N., Radjai, F.: Nonlinear effects of particle shape angularity in sheared granular media. Phys. Rev. E 86(4), 041301 (2012)ADSCrossRefGoogle Scholar
  22. 22.
    Voivret, C., Radjai, F., Delenne, J.-Y., El Youssoufi, M.S.: Multiscale force networks in highly polydisperse granular media. Phys. Rev. Lett. 102(17), 178001 (2009)ADSzbMATHCrossRefGoogle Scholar
  23. 23.
    Staron, L., Vilotte, J.-P., Radjai, F.: Preavalanche instabilities in a granular pile. Phys. Rev. Lett. 89(20), 204302 (2002)ADSCrossRefGoogle Scholar
  24. 24.
    Staron, L., Radjai, F.: Friction versus texture at the approach of a granular avalanche. Phys. Rev. E 72(4), 041308 (2005)ADSCrossRefGoogle Scholar
  25. 25.
    Azéma, E., Preechawuttipong, I., Radjai, F.: Binary mixtures of disks and elongated particles: texture and mechanical properties. Phys. Rev. E 94(4), 042901 (2016)ADSCrossRefGoogle Scholar
  26. 26.
    Ferellec, J.-F., McDowell, G.R.: A method to model realistic particle shape and inertia in dem. Granul. Matter 12(5), 459–467 (2010)zbMATHCrossRefGoogle Scholar
  27. 27.
    Farhadi, S., Behringer, R.P.: Dynamics of sheared ellipses and circular disks: effects of particle shape. Phys. Rev. Lett. 112(14), 148301 (2014)ADSCrossRefGoogle Scholar
  28. 28.
    Kawamoto, R., Andò, E., Viggiani, G., Andrade, J.E.: Level set discrete element method for three-dimensional computations with triaxial case study. J. Mech. Phys. Solids 91, 1–13 (2016)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    Marteau, E., Andrade, J.: Do force chains exist? Effect of grain shape on force transmission and mobilized strength of granular materials. J. Mech. Phys. Solids (2018)Google Scholar
  30. 30.
    Silbert, L.E., Ertaş, D., Grest, G.S., Halsey, T.C., Levine, D., Plimpton, S.J.: Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64(5), 051302 (2001)ADSCrossRefGoogle Scholar
  31. 31.
    Ai, J., Chen, J.-F., Rotter, J.M., Ooi, J.Y.: Assessment of rolling resistance models in discrete element simulations. Powder Technol. 206(3), 269–282 (2011)CrossRefGoogle Scholar
  32. 32.
    Estrada, N., Azéma, E., Radjai, F., Taboada, A.: Identification of rolling resistance as a shape parameter in sheared granular media. Phys. Rev. E 84(1), 011306 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    Luding, S.: Introduction to discrete element methods: basic of contact force models and how to perform the micro-macro transition to continuum theory. Eur. J. Environ. Civ. Eng. 12(7–8), 785–826 (2008)CrossRefGoogle Scholar
  34. 34.
    Kruggel-Emden, H., Simsek, E., Rickelt, S., Wirtz, S., Scherer, V.: Review and extension of normal force models for the discrete element method. Powder Technol. 171(3), 157–173 (2007)CrossRefGoogle Scholar
  35. 35.
    Kawamoto, R., Andò, E., Viggiani, G., Andrade, J.E.: All you need is shape: predicting shear banding in sand with ls-dem. J. Mech. Phys. Solids 111, 375–392 (2018)ADSCrossRefGoogle Scholar
  36. 36.
    Marteau, E., Andrade, J.: A novel experimental device for investigating the multiscale behavior of granular materials under shear. Granul. Matter 19, 77 (2017)CrossRefGoogle Scholar
  37. 37.
    Lim, K., Kawamoto, R., Andò, E., Viggiani, G., Andrade, J.: Multiscale characterization and modeling of granular materials through a computational mechanics avatar: a case study with experiment. Acta Geotech. 11, 243–253 (2016)CrossRefGoogle Scholar
  38. 38.
    Soille, P.: Morphological Image Analysis: Principles and Applications, 2nd edn. Springer, New York (2003)zbMATHGoogle Scholar
  39. 39.
    Gonzalez, R., Woods, R., Eddins, S.: Digital Image Processing using Matlab. Pearson Prentice Hall, New Jersey (2004)Google Scholar
  40. 40.
    Russ, J.: The Image Processing Handbook, 5th edn. CRC Press, Boca Raton (2007)zbMATHGoogle Scholar
  41. 41.
  42. 42.
    Sutton, M., Orteu, J., Schreier, H.: Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications. Springer, New York (2009)Google Scholar
  43. 43.
    Pan, B., Qian, K., Xie, H., Asundi, A.: Robust full-field measurement considering rotation using digital image correlation. Meas. Sci. Technol. 20, 062001 (2009)ADSCrossRefGoogle Scholar
  44. 44.
    Andrade, J., Avila, C.: Granular element method (gem): linking inter-particle forces with macroscopic loading. Granul. Matter 14, 51–61 (2012)CrossRefGoogle Scholar
  45. 45.
    Christoffersen, J., Mehrabadi, M., Nemat-Nasser, S.: A micromechanical description of granular material behavior. J. Appl. Mech. 48(2), 339–344 (1981)ADSzbMATHCrossRefGoogle Scholar
  46. 46.
    Popov, V.L.: Contact Mechanics and Friction. Springer, Berlin (2010)zbMATHCrossRefGoogle Scholar
  47. 47.
    Lim, K.-W., Andrade, J.E.: Granular element method for three-dimensional discrete element calculations. Int. J. Numer. Anal. Methods Geomech. 38(2), 167–188 (2014)CrossRefGoogle Scholar
  48. 48.
    Hurley, R., Lim, K., Ravichandran, G., Andrade, J.: Dynamic inter-particle force inference in granular materials: method and application. Exp. Mech. 56(2), 217–229 (2016)CrossRefGoogle Scholar
  49. 49.
    Fluoroproducts, D.: Teflon® ptfe fluoropolymer resin: properties handbook. Technical Report, DuPontTM Technical Report H-37051-3 (1996)Google Scholar
  50. 50.
    Clough, R.W., Penzien, J.: Dynamics of Structures. Computers & Structures, Berkeley (1995)zbMATHGoogle Scholar
  51. 51.
    Hunt, M.L., Vriend, N.M.: Booming sand dunes. Ann. Rev. Earth Planet. Sci. 38, 281–301 (2010)ADSCrossRefGoogle Scholar
  52. 52.
    Murphy, K.A., Reiser, N., Choksy, D., Singer, C.E., Jaeger, H.M.: Freestanding loadbearing structures with z-shaped particles. Granul. Matter 18(2), 26 (2016)CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Division of Engineering and Applied ScienceCalifornia Institute of TechnologyPasadenaUSA

Personalised recommendations