Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA.
Phys Rev Lett. 2011 Dec 23;107(26):268001. doi: 10.1103/PhysRevLett.107.268001.
We report on two-dimensional computer simulations of frictionless granular packings at various area fractions φ above the jamming point φ(c). We measure the anisotropy in coarse-grained stress ε(s) and shear modulus ε(m) as functions of coarse-graining scale, R. ε(s) can be collapsed onto a master curve after rescaling R by a characteristic length scale ξ and ε(s) by an anisotropy magnitude A. Both A and ξ accelerate as φ→φ(c) from above, consistent with a divergence at φ(c). ε(m) shows no characteristic length scale and has a nontrivial power-law form, ε(m)~R(-0.62), over almost the entire range of R at all φ. 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.
我们报告了在摩擦性颗粒填充体的二维计算机模拟，其中填充体的面积分数φ高于阻塞点φ(c)。我们测量了粗粒化应力ε(s)和剪切模量ε(m)的各向异性作为粗粒化尺度 R 的函数。在重新缩放 R 并将 ε(s)乘以特征长度尺度 ξ和各向异性幅度 A 之后，ε(s)可以折叠到主曲线上。A 和 ξ 都随着 φ→φ(c)从上方加速，与 φ(c)处的发散一致。ε(m)没有特征长度尺度，并且在几乎所有 φ 的整个 R 范围内具有非平凡的幂律形式，ε(m)~R(-0.62)。这些结果表明，在淬火应力的空间结构中存在的力链可能受到不同于在接近阻塞时的异常弹性响应的物理控制。
