Experimental Mechanics

, Volume 56, Issue 2, pp 217–229 | Cite as

Dynamic Inter-Particle Force Inference in Granular Materials: Method and Application

  • R.C. Hurley
  • K.W. Lim
  • G. Ravichandran
  • J.E. Andrade


Inter-particle force transmission in granular media plays an important role in the macroscopic static and dynamic behavior of these materials. This paper presents a method for inferring inter-particle forces in opaque granular materials during dynamic experiments. By linking experimental measurements of particle kinematics and volume-averaged strains to forces, the method provides a new tool for quantitatively studying force transmission and its relation to macroscopic behavior. We provide an experimental validation of the method, comparing inter-particle forces measured in a simple impact test on two-dimensional rubber grains to a finite-element simulation. We also provide an application of the method, using it to study inter-particle forces during impact of an intruder on a granular bed. We discuss the current challenges for applying the method to both model materials and real geologic materials.


Granular materials Inter-particle forces Inverse problems Dynamic material response 



Support by the Air Force Office of Scientific Research Grant # FA9550-12-1-0091 through the University Center of Excellence in High-Rate Deformation Physics of Heterogenous Materials is gratefully acknowledged.


  1. 1.
    Bathurst RJ, Rothenburg L (1990) Observations on stress-force-fabric relationships in idealized granular materials. Mech Mater 9(1):65–80CrossRefGoogle Scholar
  2. 2.
    Christoffersen J, Mehrabadi MM, Nemat-Nasser S (1981) A micromechanical description of granular material behavior. J Appl Mech 48(2):339–344CrossRefMATHGoogle Scholar
  3. 3.
    Radjai F, Wolf DE, Jean M, Moreau JJ (1998) Bimodal character of stress transmission in granular packings. Phys Rev Lett 80(1):61–64CrossRefGoogle Scholar
  4. 4.
    Rothenburg L, Bathurst RJ (1989) Analytical study of induced anistropy in idealized granular materials. Géotechnique 39(4):601–614CrossRefGoogle Scholar
  5. 5.
    Somfai E, Roux J-N, Snoeijer JH, van Hecke M, van Saarloos W (2005) Elastic wave propagation in confined granular systems. Phys Rev E 72:021301CrossRefGoogle Scholar
  6. 6.
    da Cruz F, Emam S, Prochnow M, Roux J-N, Chevoir F (2005) Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys Rev E 72(2):021309CrossRefGoogle Scholar
  7. 7.
    Liu C-h, Nagel SR, Schecter DA, Coppersmith SN, Majumdar S, Narayan O, Witten TA (1995) Force fluctuations in bead packs. Science 269(5223):513–515CrossRefGoogle Scholar
  8. 8.
    Mueth DM, Jaeger HM, Nagel SR (1998) Force distribution in a granular medium. Phys Rev E 57 (3):3164CrossRefGoogle Scholar
  9. 9.
    Ciamarra MP, Lara AH, Lee AT, Goldman DI, Vishik I, Swinney HL (2004) Dynamics of drag and force distributions for projectile impact in a granular medium. Phys Rev Lett 92(19): 194301CrossRefGoogle Scholar
  10. 10.
    Coppersmith SN, Liu C-h, Majumdar S, Narayan O, Witten TA (1996) Model for force fluctuations in bead packs. Phys Rev E 53(5):4673CrossRefGoogle Scholar
  11. 11.
    Clark AH, Petersen AJ, Behringer RP (2014) Collisional model for granular impact dynamics. Phys Rev E 89(1):012201CrossRefGoogle Scholar
  12. 12.
    Drescher A, de Josselin de Jong G (1972) Photoelastic verification of a mechanical model for the flow of a granular material. J Mech Phys Solids 20:337–340CrossRefGoogle Scholar
  13. 13.
    Howell D, Behringer RP, Veje C (1999) Stress fluctuations in a 2d granular couette experiment, A continuous transition. Phys Rev Lett 82:5241–5244CrossRefGoogle Scholar
  14. 14.
    Majmudar TS, Behringer RP (2005) Contact force measurements and stress-induced anisotropy in granular materials. Nature 435(1079):1079–1082CrossRefGoogle Scholar
  15. 15.
    Clark AH, Kondic L, Behringer RP (2012) Particle scale dynamics in granular impact. Phys Rev Lett 238302:109Google Scholar
  16. 16.
    Hurley R, Marteau E, Ravichandran G, Andrade JE (2014) Extracting inter-particle forces in opaque granular materials: beyond photoelasticity. J Mech Phys Solids 63:154–166CrossRefGoogle Scholar
  17. 17.
    Jongchansitto P, Balandraud X, Grédiac M, Beitone C, Preechawuttipong I (2014) Using infrared thermography to study hydrostatic stress networks in granular materials. Soft matter 10(43):8603–8607CrossRefGoogle Scholar
  18. 18.
    Saadatfar M, Sheppard AP, Senden TJ, Kabla AJ (2012) Mapping forces in a 3d elastic assembly of grains. J Mech Phys Solids 60(1):55–66CrossRefMATHGoogle Scholar
  19. 19.
    Alshibli KA, Reed AH (2010) Applications of X-ray Microtomography to Geomaterials, 1st edn. Wiley-ISTEGoogle Scholar
  20. 20.
    Desrues J, Viggiani G, Bésuelle P (eds) (2006) Advances in X-ray Tomography for Geomaterials. Wiley-ISTEGoogle Scholar
  21. 21.
    Wang JY, Park L, Fu Y (2007) Representation of real particles for dem simulation using x-ray tomography. Constr Build Mater 21(2):338–346CrossRefGoogle Scholar
  22. 22.
    Sutton MA, Orteu JJ, Schreier H (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. SpringerGoogle Scholar
  23. 23.
    Hall S, Wright J, Pirling T, Andò E, Hughes D, Viggiani G (2011) Can intergranular force transmission be identified in sand Granul Matter 13:251–254CrossRefGoogle Scholar
  24. 24.
    Martins RV, Margulies L, Schmidt S, Poulsen HF, Leffers T (2004) Simultaneous measurement of the strain tensor of 10 individual grains embedded in an al tensile sample. Mater Sci Eng: A 387–389(0):84–88Google Scholar
  25. 25.
    Oddershede J, Schmidt S, Poulsen HF, Sørensen OH, Wright J, Reimers W (2010) Determining grain resolved stresses in polycrystalline materials using three-dimensional X-ray diffraction. J Appl Crystallogr 43 (3):539–549CrossRefGoogle Scholar
  26. 26.
    Poulsen HF (2004) Three-dimensional X-ray diffraction microscopy: mapping polycrystals and their dynamics. Springer, New YorkCrossRefGoogle Scholar
  27. 27.
    Boyd S, Vandenberghe L (2004) Convex Optimization. Cambridge University Press, New YorkCrossRefMATHGoogle Scholar
  28. 28.
    Dassault Systèmes Simulia (2011) Abaqus 6.11 Analysis User’s ManualGoogle Scholar
  29. 29.
    Vic-2D Users’ Manual (2006) Solutions, CorrelatedGoogle Scholar
  30. 30.
    Bornert M, Brémand F, Doumalin P, Dupré J-C, Fazzini M, Grédiac M, Hild F, Mistou S, Molimard J, Orteu J-J et al (2009) Assessment of digital image correlation measurement errors: methodology and results. Exp Mech 49(3):353–370CrossRefGoogle Scholar
  31. 31.
    MATLAB (2013) version 8.1.0 (R2013a). The MathWorks Inc., Natick, MassachusettsGoogle Scholar
  32. 32.
    Davies ER (2004) Machine vision: theory, algorithms, practicalities. ElsevierGoogle Scholar
  33. 33.
    Atherton TJ, Kerbyson DJ (1999) Size invariant circle detection. Image Vis Comput 17(11):795–803CrossRefGoogle Scholar
  34. 34.
    Grant M, Boyd S (2008) CVX: Matlab software for disciplined convex programming (web page and software).
  35. 35.
    Hall SA, Wright J (2014) Characterisation of 3d force transmission in real granular media. Presented at the International Conference on Experimental MechanicsGoogle Scholar
  36. 36.
    Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29(1):47–65CrossRefGoogle Scholar
  37. 37.
    Dwivedi SK, Teeter RD, Felice CW, Gupta YM (2008) Two dimensional mesoscale simulations of projectile instability during penetration in dry sand. J Appl Phys 104(8):083502CrossRefGoogle Scholar
  38. 38.
    Tsimring LS, Volfson D (2005) Modeling of impact cratering in granular media. In: Garca-Rojo R, Herrmann HJ, McNamara S (eds) Powders and Grains 2005, vol 2. A. A. Balkema, Rotterdam, pp 1215–1223Google Scholar

Copyright information

© Society for Experimental Mechanics 2015

Authors and Affiliations

  • R.C. Hurley
    • 1
  • K.W. Lim
    • 1
  • G. Ravichandran
    • 1
  • J.E. Andrade
    • 1
  1. 1.Division of Engineering & Applied ScienceCalifornia Institute of TechnologyPasadenaUSA

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