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Logarithmic rate dependence of force networks in sheared granular materials

Nature volume 421, pages 928–931 (2003)Cite this article

Abstract

Many models of slow, dense granular flows1,2,3,4,5 assume that the internal stresses are independent of the shearing rate. In contrast, logarithmic rate dependence is found in solid-on-solid friction6,7,8, geological settings9,10,11 and elsewhere12,13,14,15. Here we investigate the rate dependence of stress in a slowly sheared two-dimensional system of photoelastic disks, in which we are able to determine forces on the granular scale. We find that the mean (time-averaged) stress displays a logarithmic dependence on the shear rate for plastic (irreversible) deformations. However, there is no perceivable dependence on the driving rate for elastic (reversible) deformations, such as those that occur under moderate repetitive compression. Increasing the shearing rate leads to an increase in the strength of the force network and stress fluctuations. Qualitatively, this behaviour resembles the changes associated with an increase in density. Increases in the shearing rate also lead to qualitative changes in the distributions of stress build-up and relaxation events. If shearing is suddenly stopped, stress relaxations occur with a logarithmic functional form over long timescales. This slow collective relaxation of the stress network provides a mechanism for rate-dependent strengthening.

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Figure 2: Mean stress versus shearing rate, Ω, for a range of densities for pentagonal particles.
Figure 1: Time series for stress (normalized by σ0 ≈ 4.11 N m-1) for a range of shearing rates Ω that span the experimental range.
Figure 3: Stress relaxation in sheared and compressed systems.
Figure 4: Stress “avalanches” in sheared granular materials.
Figure 5: Mean stress versus oscillation rate, ω, for several densities for oscillatory compression.

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Acknowledgements

We thank S. Coppersmith for discussion. This work was supported by NSF Division of Materials Research, NSF Division of Mathematical Sciences and by NASA.

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Authors and Affiliations

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

    R. R. Hartley & R. P. Behringer

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

    R. R. Hartley & R. P. Behringer

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Correspondence to R. P. Behringer.

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Hartley, R., Behringer, R. Logarithmic rate dependence of force networks in sheared granular materials. Nature 421, 928–931 (2003). https://doi.org/10.1038/nature01394

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