Viallon-Galinier Léo, Combe Gaël, Richefeu Vincent, Picardi Faria Atman Allbens
Univ. Grenoble Alpes, CNRS, Grenoble-INP, Institute of Engineering Univ. Grenoble Alpes, 3SR, F-38000 Grenoble, France.
Departamento de Física and National Institute of Science and Technology for Complex Systems, CEFET-MG, Belo Horizonte CEP 30510-000, Brazil.
Entropy (Basel). 2018 Nov 9;20(11):862. doi: 10.3390/e20110862.
The statistics of grain displacements probability distribution function () during the shear of a granular medium displays an unusual dependence with the shear increment upscaling as recently evinced (see "experimental validation of a nonextensive scaling law in confined granular media"). Basically, the of grain displacements has clear nonextensive (-Gaussian) features at small scales, but approaches to Gaussian characteristics at large shear window scales-the ranulence effect. Here, we extend this analysis studying a larger system (more grains considered in the experimental setup), which exhibits a severe shear band fault during the macroscopic straining. We calculate the of grain displacements and the dependency of the -statistics with the shear increment. This analysis has shown a singular behavior of at large scales, displaying a non-monotonic dependence with the shear increment. By means of an independent image analysis, we demonstrate that this singular non-monotonicity could be associated with the emergence of a shear band within the confined system. We show that the exact point where the -value inverts its tendency coincides with the emergence of a giant percolation cluster along the system, caused by the shear band. We believe that this original approach using Statistical Mechanics tools to identify shear bands can be a very useful piece to solve the complex puzzle of the rheology of dense granular systems.
颗粒介质剪切过程中颗粒位移概率分布函数（）的统计显示出与剪切增量放大的异常依赖关系，这一点最近已得到证实（见“受限颗粒介质中非广延标度律的实验验证”）。基本上，颗粒位移的在小尺度上具有明显的非广延（非高斯）特征，但在大剪切窗口尺度上接近高斯特征——即湍流效应。在这里，我们扩展了这一分析，研究了一个更大的系统（实验装置中考虑了更多颗粒），该系统在宏观应变过程中出现了严重的剪切带断层。我们计算了颗粒位移的以及 - 统计量与剪切增量的依赖性。该分析表明在大尺度上具有奇异行为，显示出与剪切增量的非单调依赖性。通过独立的图像分析，我们证明这种奇异的非单调性可能与受限系统内剪切带的出现有关。我们表明值反转其趋势的精确点与由剪切带引起的沿着系统出现的巨大渗流团簇相吻合。我们相信，这种使用统计力学工具识别剪切带的原始方法可能是解决致密颗粒系统流变学复杂难题的非常有用的一部分。
