Statistical mechanics framework for static granular matter

Silke Henkes*, Bulbul Chakraborty

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

93 Citations (Scopus)

Abstract

The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming diagram. This work focuses on the case of static granular matter, where we have constructed a statistical ensemble which mirrors equilibrium statistical mechanics. This ensemble, which is based on the conservation properties of the stress tensor, is distinct from the original Edwards ensemble and applies to packings of deformable grains. We combine it with a field theoretical analysis of the packings, where the field is the Airy stress function derived from the force and torque balance conditions. In this framework, Point J characterized by a diverging stiffness of the pressure fluctuations. Separately, we present a phenomenological mean-field theory of the jamming transition, which incorporates the mean contact number as a variable. We link both approaches in the context of the marginal rigidity picture proposed by Wyart and others.

Original languageEnglish
Article number061301
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume79
Issue number6
DOIs
Publication statusPublished - 3 Jun 2009

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Copyright 2009 Elsevier B.V., All rights reserved.

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