Macroscopic Continuous Approach versus Discrete Approach, Fluctuations, criticality and SOC. A state of the question based on articles in Powders & Grains 2001

TL;DR

This paper reviews recent research comparing macroscopic continuous models and microscopic discrete models of granular media, concluding that macroscopic approaches remain valid despite force fluctuations, with a small representative volume.

Contribution

It synthesizes recent microscopic studies to clarify the validity of macroscopic continuum models in granular media, highlighting the typical size of the representative elementary volume.

Findings

Macroscopic models are validated despite force fluctuations.

The representative elementary volume is usually a few grains.

Fluctuations do not invalidate continuum assumptions.

Abstract

The macroscopic continuous approach of the mechanics of granular media assumes that the whole system of discrete variables (contact locations, contact forces,...) can be replaced by continuous field equations relating stress and strain on macroscopic scale. On the contrary, recent approaches contest this validity on the basis that microscopic studies show the existence of large fluctuations of forces, of chains of forces,... This paper tries and establishes the state of this question using recent works reported at Powders & Grains 2001 which have studied the microscopic variables, their fluctuations and their evolution. This paper shows that these results validate the macroscopic approach despite the existence of these fluctuations. It concludes that the representative elementary volume is of few grains most of the time, except in some peculiar cases. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn