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Contact force measurements and stress-induced anisotropy in granular materials

Nature volume 435, pages 1079–1082 (2005)Cite this article

Abstract

Interparticle forces in granular media form an inhomogeneous distribution of filamentary force chains. Understanding such forces and their spatial correlations, specifically in response to forces at the system boundaries1,2, represents a fundamental goal of granular mechanics. The problem is of relevance to civil engineering, geophysics and physics3,4,5, being important for the understanding of jamming, shear-induced yielding and mechanical response. Here we report measurements of the normal and tangential grain-scale forces inside a two-dimensional system of photoelastic disks that are subject to pure shear and isotropic compression. Various statistical measures show the underlying differences between these two stress states. These differences appear in the distributions of normal forces (which are more rounded for compression than shear), although not in the distributions of tangential forces (which are exponential in both cases). Sheared systems show anisotropy in the distributions of both the contact network and the contact forces. Anisotropy also occurs in the spatial correlations of forces, which provide a quantitative replacement for the idea of force chains. Sheared systems have long-range correlations in the direction of force chains, whereas isotropically compressed systems have short-range correlations regardless of the direction.

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Figure 1: Experimental set-up and representative data.
Figure 2: Comparison of experimental images (a, c) and computed images (b, d).
Figure 3: Probability distributions of the normal forces, the tangential forces, and the mobilized friction, for the sheared and the isotropically compressed systems.
Figure 4: Contact orientation, variation of the mean force and spatial correlations for the sheared and the isotropically compressed systems.

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References

  1. Geng, J. et al. Footprints in sand: The response of a granular material to local perturbations. Phys. Rev. Lett. 87, 035506 (2001)

    Article  ADS  CAS  Google Scholar 

  2. Reydellet, G. & Clément, E. Green's function probe of a static granular piling. Phys. Rev. Lett. 86, 3308–3311 (2001)

    Article  ADS  CAS  Google Scholar 

  3. Behringer, R. P. & Jenkins, J. T. (eds) Powders and Grains 97 (Balkema, Rotterdam, 1997)

  4. Nedderman, R. M. Statics and Kinematics of Granular Materials (Cambridge Univ. Press, Cambridge, UK, 1992)

    Book  Google Scholar 

  5. Jaeger, H. M., Nagel, S. R. & Behringer, R. P. Granular solids, liquids, and gases. Rev. Mod. Phys. 68, 1259–1273 (1996)

    Article  ADS  Google Scholar 

  6. Meuth, D. M., Jaeger, H. M. & Nagel, S. R. Force distribution in a granular medium. Phys. Rev. E 57, 3164–3169 (1998)

    Article  ADS  Google Scholar 

  7. Løvoll, G., Måløy, K. J. & Flekkøy, E. G. Force measurements on static granular materials. Phys. Rev. E 60, 5872–5878 (1999)

    Article  ADS  Google Scholar 

  8. Tsoungui, O., Vallet, D. & Charmet, J. Use of contact area trace to study the force distributions inside 2D granular systems. Granular Matter 1, 65–69 (1998)

    Article  Google Scholar 

  9. Goldenberg, C. & Goldhirsch, I. Small and large scale granular statics. Granular Matter 6, 87–97 (2003)

    Article  Google Scholar 

  10. Snoeijer, J. H., van Hecke, M., Somfai, E. & van Saarloos, W. Force and weight distributions in granular media: Effects of contact geometry. Phys. Rev. E 67, 030302(R) (2004)

    Article  Google Scholar 

  11. Radjai, F., Wolf, D. E., Jean, M., Roux, S. & Moreau, J. in Powders & Grains 97 (eds Behringer, R. P. & Jenkins, J. T.) 211–214 (Balkema, Rotterdam, 1997)

    Google Scholar 

  12. Frocht, M. M. Photoelasticity Vol. 1 (Wiley & Sons, New York, 1941)

    Google Scholar 

  13. Frocht, M. M. Photoelasticity Vol. 2 (Wiley & Sons, New York, 1948)

    Google Scholar 

  14. Drescher, A. & De-Josselin-de-Jong, G. Photoelastic verification of a mechanical model for the flow of a granular material. J. Mech. Phys. Solids 20, 337–351 (1972)

    Article  ADS  Google Scholar 

  15. Durelli, A. J. & Wu, D. Use of coefficients of influence to solve some inverse problems in plane elasticity. J. Appl. Mech. 50, 288–296 (1983)

    Article  ADS  Google Scholar 

  16. Shukla, A. & Nigam, H. A numerical-experimental analysis of the contact stress problem. J. Strain Anal. 20, 241–245 (1985)

    Article  Google Scholar 

  17. Paikowsky, S. G., DiRocco, K. J. & Xi, F. in 2nd Int. Conf. on Discrete Element Methods (DEM) (eds Williams, J. R. & Mustoe, G. W.) 449–461 (IESL Publications, MIT, Boston, 1993)

    Google Scholar 

  18. Landau, L. Theory of Elasticity (Pergamon, New York, 1959)

    Google Scholar 

  19. Press, W. H., Teukolsky, H. A., Vetterling, W. T. & Flannery, B. P. Numerical Recipes in C: The Art of Scientific Computing (Cambridge Univ. Press, Cambridge, UK, 1992)

    MATH  Google Scholar 

  20. Landry, J. W., Grest, G. S., Silbert, L. E. & Plimpton, S. J. Confined granular packings: Structure, stress, and forces. Phys. Rev. E 67, 041303 (2003)

    Article  ADS  Google Scholar 

  21. Silbert, L. E., Grest, G. S. & Landry, J. W. Statistics of the contact network in frictional and frictionless granular packings. Phys. Rev. E 66, 061303 (2002)

    Article  ADS  Google Scholar 

  22. Cambou, B., Dubujet, Ph. & Nouguier-Lehon, C. Anisotropy in granular materials at different scales. Mech. Mater. 36, 1185–1194 (2004)

    Article  Google Scholar 

  23. Snoeijer, J. H., Vlugt, T. J. H., van Hecke, M. & van Saarloos, W. Force network ensemble: A new approach to static granular matter. Phys. Rev. Lett. 92, 054302 (2004)

    Article  ADS  Google Scholar 

  24. Tighe, B. P., Socolar, J. E. S., Schaeffer, D. G., Mitchener, W. G. & Huber, M. L. Force distributions in a triangular lattice of rigid bars. Preprint at http://arxiv.org/cond-mat/0505003 (2005).

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Acknowledgements

This work was supported by NSF DMR, NSF DMS, and NASA. We thank J. Snoeijer and collaborators, J. Socolar and B. Tighe for providing their data and for discussions. We thank H. Phatnani for critical reading of the manuscript.

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  1. Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina, 27708-0305, USA

    T. S. Majmudar & R. P. Behringer

  2. Center for Nonlinear and Complex Systems, Duke University,

    T. S. Majmudar & R. P. Behringer

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Correspondence to R. P. Behringer.

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Majmudar, T., Behringer, R. Contact force measurements and stress-induced anisotropy in granular materials. Nature 435, 1079–1082 (2005). https://doi.org/10.1038/nature03805

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