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Jamming by shear

Abstract

A broad class of disordered materials including foams, glassy molecular systems, colloids and granular materials can form jammed states. A jammed system can resist small stresses without deforming irreversibly, whereas unjammed systems flow under any applied stresses. The broad applicability of the Liu–Nagel jamming concept1,2 has attracted intensive theoretical and modelling interest but has prompted less experimental effort1,2,3,4,5,6. In the Liu–Nagel framework, jammed states of athermal systems exist only above a certain critical density. Although numerical simulations for particles that do not experience friction broadly support this idea7,8,9,10,11,12,13, the nature of the jamming transition for frictional grains is less clear14,15,16,17. Here we show that jamming of frictional, disk-shaped grains can be induced by the application of shear stress at densities lower than the critical value, at which isotropic (shear-free) jamming occurs. These jammed states have a much richer phenomenology than the isotropic jammed states: for small applied shear stresses, the states are fragile, with a strong force network that percolates only in one direction. A minimum shear stress is needed to create robust, shear-jammed states with a strong force network percolating in all directions. The transitions from unjammed to fragile states and from fragile to shear-jammed states are controlled by the fraction of force-bearing grains. The fractions at which these transitions occur are statistically independent of the density. Jammed states with densities lower than the critical value have an anisotropic fabric (contact network). The minimum anisotropy of shear-jammed states vanishes as the density approaches the critical value from below, in a manner reminiscent of an order–disorder transition.

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Figure 1: Jamming phase diagrams in the T = 0 plane.
Figure 2: Using percolation analysis of the strong force network to classify states.
Figure 3: Relationship between fabric and stress anisotropies and how they vanish at φJ.
Figure 4: Effective free energy for shear-jammed states.

References

  1. 1

    Liu, A. & Nagel, S. Jamming is not just cool any more. Nature 396, 21–22 (1998)

    ADS  CAS  Article  Google Scholar 

  2. 2

    Liu, A. J. & Nagel, S. R. Granular and jammed materials. Soft Matter 6, 2869–2870 (2010)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Trappe, V., Prasad, V., Cipelletti, L., Segre, P. N. & Weitz, D. A. Jamming phase diagram for attractive particles. Nature 411, 772–775 (2001)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Majmudar, T. S., Sperl, M., Luding, S. & Behringer, R. P. Jamming transition in granular systems. Phys. Rev. Lett. 98, 058001 (2007)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Lechenault, F. et al. Critical scaling and heterogeneous superdiffusion across the jamming/rigidity transition of a granular glass. Europhys. Lett. 83, 46003 (2008)

    ADS  Article  Google Scholar 

  6. 6

    Candelier, R. & Dauchot, O. Creep motion of an intruder within a granular glass close to jamming. Phys. Rev. Lett. 103, 128001 (2009)

    ADS  CAS  Article  Google Scholar 

  7. 7

    O’Hern, C. S., Silbert, L. E., Liu, A. J. & Nagel, S. R. Jamming at zero temperature and zero applied stress: the epitome of disorder. Phys. Rev. E 68, 011306 (2003)

    ADS  Article  Google Scholar 

  8. 8

    Silbert, L. E., Liu, A. J. & Nagel, S. R. Structural signatures of the unjamming transition at zero temperature. Phys. Rev. E 73, 041304 (2006)

    ADS  Article  Google Scholar 

  9. 9

    Silbert, L. E., Liu, A. J. & Nagel, S. R. Vibrations and diverging length scales near the unjamming transition. Phys. Rev. Lett. 95, 098301 (2005)

    ADS  Article  Google Scholar 

  10. 10

    Wyart, M. On the rigidity of amorphous solids. Ann. Phys. Fr. 30, 1–96 (2005)

    Article  Google Scholar 

  11. 11

    Heussinger, C. & Barrat, J.-L. Jamming transition as probed by quasistatic shear flow. Phys. Rev. Lett. 102, 218303 (2009)

    ADS  Article  Google Scholar 

  12. 12

    Olsson, P. & Teitel, S. Critical scaling of shear viscosity at the jamming transition. Phys. Rev. Lett. 99, 178001 (2007)

    ADS  Article  Google Scholar 

  13. 13

    Olsson, P. & Teitel, S. Glassiness, rigidity and jamming of frictionless soft core disks. Phys. Rev. E 83, 031307 (2011)

    ADS  Article  Google Scholar 

  14. 14

    Makse, H., Johnson, D. L. & Schwartz, L. M. Packing of compressible granular materials. Phys. Rev. Lett. 84, 4160–4163 (2000)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Silbert, L. E. Jamming of frictional spheres and random loose packing. Soft Matter 6, 2918–2924 (2010)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Otsuki, M. & Hayakawa, H. Critical scaling near jamming transition for frictional granular particles. Phys. Rev. E 83, 051301 (2011)

    ADS  Article  Google Scholar 

  17. 17

    Pastore, M., Ciamarra, M. P. & Coniglio, A. Flow and jam of frictional athermal systems under shear stress. Phil. Mag. 91, 2006–2013 (2011)

    ADS  CAS  Article  Google Scholar 

  18. 18

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

    Book  Google Scholar 

  19. 19

    Hatano, T. Scaling properties of granular rheology near the jamming transition. J. Phys. Soc. Jpn 77, 123002 (2008)

    ADS  Article  Google Scholar 

  20. 20

    Peyneau, P.-E. & Roux, J.-N. Frictionless bead packs have macroscopic friction, but no dilatancy. Phys. Rev. E 78, 011307 (2008)

    ADS  Article  Google Scholar 

  21. 21

    Ciamarra, M. P. Nicodemi, M. & Coniglio, A. Recent results on the jamming phase diagram. Soft Matter 6, 2871–2874 (2010)

    ADS  CAS  Article  Google Scholar 

  22. 22

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

    CAS  Article  Google Scholar 

  23. 23

    Henkes, S., van Hecke, M. & van Saarloos, W. Critical jamming of frictional grains in the generalized isostaticity picture. Europhys. Lett. 90, 14003 (2010)

    ADS  Article  Google Scholar 

  24. 24

    Radjai, F., Wolf, D. E., Jean, M. & Moreau, J.-J. Bimodal character of stress transmission in granular packings. Phys. Rev. Lett. 80, 61–64 (1998)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Walker, D. M. et al. Percolating contact subnetworks on the edge of isostaticity. Granul. Matter 13, 233–240 (2011)

    Article  Google Scholar 

  26. 26

    Göncü, F., Duran, O. & Luding, S. Constitutive relations for the isotropic deformation of frictionless packings of polydisperse spheres. C.R. Méc. 338, 570–586 (2010)

    ADS  Article  Google Scholar 

  27. 27

    Cates, M. E., Wittmer, J. P., Bouchaud, J.-P. & Claudin, P. Jamming, force chains, and fragile matter. Phys. Rev. Lett. 81, 1841–1844 (1998)

    ADS  CAS  Article  Google Scholar 

  28. 28

    Goddard, J. D. Continuum Modeling of Granular Assemblies 1–24 (Kluwer, 1998)

    Book  Google Scholar 

  29. 29

    Alonso-Marroquín, F., Luding, S., Herrmann, H. J. & Vardoulakis, I. Role of anisotropy in the elastoplastic response of a polygonal packing. Phys. Rev. E 71, 051304 (2005)

    ADS  Article  Google Scholar 

  30. 30

    Majmudar, T. S. & Behringer, R. P. Contact force measurements and stress-induced anisotropy in granular materials. Nature 435, 1079–1082 (2005)

    ADS  CAS  Article  Google Scholar 

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Acknowledgements

D.B. and B.C. acknowledge support from US NSF grant DMR-0905880. R.P.B. and J.Z. acknowledge support from US NSF grants DMR-0906908 and NSF-0835571, and from US ARO grant W911NF-07-1-1031. B.C. and R.P.B. acknowledge the hospitality of the Aspen Center for Physics and discussions with S. Teitel, H. Hayakawa and M. Otsuki. D.B. and B.C. acknowledge discussions with M. Mailman.

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All authors contributed in comparably equal ways. Specifically, R.P.B. and J.Z. designed the experimental project, including the force-inverse algorithm, and performed the experiments. B.C. and D.B. performed the theoretical analysis. D.B. and J.Z. carried out the data analysis. All authors contributed equally to writing the manuscript.

Corresponding author

Correspondence to R. P. Behringer.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

The file contains Supplementary Text and Supplementary Figures 1-9 with legends. (PDF 2596 kb)

Supplementary Movie 1

The movie shows the evolution of the strong force cluster and transition from unjammed to fragile and eventually to SJ. (MOV 6275 kb)

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Bi, D., Zhang, J., Chakraborty, B. et al. Jamming by shear. Nature 480, 355–358 (2011). https://doi.org/10.1038/nature10667

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