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

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Abstract

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.

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References

  1. Bathurst RJ, Rothenburg L (1990) Observations on stress-force-fabric relationships in idealized granular materials. Mech Mater 9(1):65–80

    Article  Google Scholar 

  2. Christoffersen J, Mehrabadi MM, Nemat-Nasser S (1981) A micromechanical description of granular material behavior. J Appl Mech 48(2):339–344

    Article  MATH  Google Scholar 

  3. Radjai F, Wolf DE, Jean M, Moreau JJ (1998) Bimodal character of stress transmission in granular packings. Phys Rev Lett 80(1):61–64

    Article  Google Scholar 

  4. Rothenburg L, Bathurst RJ (1989) Analytical study of induced anistropy in idealized granular materials. Géotechnique 39(4):601–614

    Article  Google Scholar 

  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 72:021301

    Article  Google Scholar 

  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):021309

    Article  Google Scholar 

  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):513–515

    Article  Google Scholar 

  8. Mueth DM, Jaeger HM, Nagel SR (1998) Force distribution in a granular medium. Phys Rev E 57 (3):3164

    Article  Google Scholar 

  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): 194301

    Article  Google Scholar 

  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):4673

    Article  Google Scholar 

  11. Clark AH, Petersen AJ, Behringer RP (2014) Collisional model for granular impact dynamics. Phys Rev E 89(1):012201

    Article  Google Scholar 

  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 20:337–340

    Article  Google Scholar 

  13. Howell D, Behringer RP, Veje C (1999) Stress fluctuations in a 2d granular couette experiment, A continuous transition. Phys Rev Lett 82:5241–5244

    Article  Google Scholar 

  14. Majmudar TS, Behringer RP (2005) Contact force measurements and stress-induced anisotropy in granular materials. Nature 435(1079):1079–1082

    Article  Google Scholar 

  15. Clark AH, Kondic L, Behringer RP (2012) Particle scale dynamics in granular impact. Phys Rev Lett 238302:109

    Google Scholar 

  16. Hurley R, Marteau E, Ravichandran G, Andrade JE (2014) Extracting inter-particle forces in opaque granular materials: beyond photoelasticity. J Mech Phys Solids 63:154–166

    Article  Google Scholar 

  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):8603–8607

    Article  Google Scholar 

  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):55–66

    Article  MATH  Google Scholar 

  19. Alshibli KA, Reed AH (2010) Applications of X-ray Microtomography to Geomaterials, 1st edn. Wiley-ISTE

  20. Desrues J, Viggiani G, Bésuelle P (eds) (2006) Advances in X-ray Tomography for Geomaterials. Wiley-ISTE

  21. Wang JY, Park L, Fu Y (2007) Representation of real particles for dem simulation using x-ray tomography. Constr Build Mater 21(2):338–346

    Article  Google Scholar 

  22. Sutton MA, Orteu JJ, Schreier H (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer

  23. Hall S, Wright J, Pirling T, Andò E, Hughes D, Viggiani G (2011) Can intergranular force transmission be identified in sand Granul Matter 13:251–254

    Article  Google Scholar 

  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):84–88

    Google Scholar 

  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):539–549

    Article  Google Scholar 

  26. Poulsen HF (2004) Three-dimensional X-ray diffraction microscopy: mapping polycrystals and their dynamics. Springer, New York

    Book  Google Scholar 

  27. Boyd S, Vandenberghe L (2004) Convex Optimization. Cambridge University Press, New York

    Book  MATH  Google Scholar 

  28. Dassault Systèmes Simulia (2011) Abaqus 6.11 Analysis User’s Manual

  29. Vic-2D Users’ Manual (2006) Solutions, Correlated

  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):353–370

    Article  Google Scholar 

  31. MATLAB (2013) version 8.1.0 (R2013a). The MathWorks Inc., Natick, Massachusetts

    Google Scholar 

  32. Davies ER (2004) Machine vision: theory, algorithms, practicalities. Elsevier

  33. Atherton TJ, Kerbyson DJ (1999) Size invariant circle detection. Image Vis Comput 17(11):795–803

    Article  Google Scholar 

  34. Grant M, Boyd S (2008) CVX: Matlab software for disciplined convex programming (web page and software). http://stanford.edu/boyd/cvx

  35. Hall SA, Wright J (2014) Characterisation of 3d force transmission in real granular media. Presented at the International Conference on Experimental Mechanics

  36. Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29(1):47–65

    Article  Google Scholar 

  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):083502

    Article  Google Scholar 

  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 1215–1223

    Google Scholar 

Download references

Acknowledgments

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.

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Authors and Affiliations

  1. Division of Engineering & Applied Science, California Institute of Technology, Pasadena, CA, 91125, USA

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

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  1. R.C. Hurley
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  2. K.W. Lim
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  3. G. Ravichandran
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  4. J.E. Andrade
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Correspondence to J.E. Andrade.

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Hurley, R., Lim, K., Ravichandran, G. et al. Dynamic Inter-Particle Force Inference in Granular Materials: Method and Application. Exp Mech 56, 217–229 (2016). https://doi.org/10.1007/s11340-015-0063-8

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  • DOI: https://doi.org/10.1007/s11340-015-0063-8

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