Local Anisotropy in Globally Isotropic Granular Packings
K Karimi and CE Maloney, PHYSICAL REVIEW LETTERS, 107, 268001 (2011).
We report on two-dimensional computer simulations of frictionless granular packings at various area fractions phi above the jamming point phi(c). We measure the anisotropy in coarse-grained stress epsilon(s) and shear modulus epsilon(m) as functions of coarse-graining scale, R. epsilon(s) can be collapsed onto a master curve after rescaling R by a characteristic length scale xi and epsilon(s) by an anisotropy magnitude A. Both A and xi accelerate as phi -> phi(c) from above, consistent with a divergence at phi(c). epsilon(m) shows no characteristic length scale and has a nontrivial power-law form, epsilon(m) similar to R(-0.62), over almost the entire range of R at all phi. These results suggest that the force chains present in the spatial structure of the quenched stress may be governed by different physics than the anomalous elastic response near jamming.
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