Rheology of granular materials: dynamics in a stress landscape

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
Dapeng Bi, B Chakraborty

Abstract

We present a framework for analysing the rheology of dense driven granular materials, based on a recent proposal of a stress-based ensemble. In this ensemble, fluctuations in a granular system near jamming are controlled by a temperature-like parameter, the angoricity, which is conjugate to the stress of the system. In this paper, we develop a model for slowly driven granular materials based on the stress ensemble and the idea of a landscape in stress space. The idea of an activated process driven by the angoricity has been shown by Behringer et al. (Behringer et al. 2008 Phys. Rev. Lett. 101, 268301) to describe the logarithmic strengthening of granular materials. Just as in the soft glassy rheology (SGR) picture, our model represents the evolution of a small patch of granular material (a mesoscopic region) in a stress-based trap landscape. The angoricity plays the role of the fluctuation temperature in the SGR. We determine (i) the constitutive equation, (ii) the yield stress, and (iii) the distribution of stress dissipated during granular shearing experiments, and compare these predictions with the experiments of Hartley & Behringer (Hartley & Behringer 2003 Nature 421, 928-931.).

References

Jan 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·O Pouliquen, R Gutfraind
Mar 23, 2002·Physical Review Letters·Robin C Ball, Raphael Blumenfeld
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Sep 28, 2004·Physical Review Letters·Raphael Blumenfeld
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Junfei Geng, R P Behringer
Apr 12, 2006·Physical Review Letters·Eric BertinMichel Droz
Aug 7, 2007·Physical Review Letters·Silke HenkesBulbul Chakraborty
Nov 13, 2007·Physical Review Letters·Peter Olsson, S Teitel
Mar 21, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Philip T Metzger
May 14, 2009·Physical Review Letters·R P BehringerR R Hartley
Aug 8, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Silke Henkes, Bulbul Chakraborty
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G LoisR P Behringer

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Citations

Jan 20, 2016·Soft Matter·Pierre LidonSébastien Manneville
Nov 26, 2009·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Michael E CatesPaul Bartlett

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