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Jamming by shear


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.


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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).

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