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Entropy 2018, 20(11), 862; https://doi.org/10.3390/e20110862

Emergence of Shear Bands in Confined Granular Systems: Singularity of the q-Statistics

1
Univ. Grenoble Alpes, CNRS, Grenoble-INP, Institute of Engineering Univ. Grenoble Alpes, 3SR, F-38000 Grenoble, France
2
Departamento de Física and National Institute of Science and Technology for Complex Systems, CEFET-MG, Belo Horizonte CEP 30510-000, Brazil
*
Author to whom correspondence should be addressed.
Received: 8 October 2018 / Revised: 31 October 2018 / Accepted: 1 November 2018 / Published: 9 November 2018
(This article belongs to the Special Issue Nonadditive Entropies and Complex Systems)
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Abstract

The statistics of grain displacements probability distribution function (pdf) 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 pdf of grain displacements has clear nonextensive (q-Gaussian) features at small scales, but approaches to Gaussian characteristics at large shear window scales—the granulence 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 pdf of grain displacements and the dependency of the q-statistics with the shear increment. This analysis has shown a singular behavior of q 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 q-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. View Full-Text
Keywords: granular materials; displacement fluctuations; q-Gaussian; strain localization granular materials; displacement fluctuations; q-Gaussian; strain localization
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Viallon-Galinier, L.; Combe, G.; Richefeu, V.; Picardi Faria Atman, A. Emergence of Shear Bands in Confined Granular Systems: Singularity of the q-Statistics. Entropy 2018, 20, 862.

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