Fluctuations, Correlation and Representative Elementary Volume (REV) in Granular Materials

TL;DR

This paper investigates how fluctuations and correlations in granular materials affect the concept of the Representative Elementary Volume (REV), analyzing stress fluctuations and their dependence on sampling size, with theoretical and experimental insights.

Contribution

It provides a detailed analysis of stress fluctuations, correlation effects, and the conditions under which REV can be defined in granular materials.

Findings

Stress fluctuation amplitude scales as 1/L with sampling size L.

Large-scale stress fluctuations can be viewed as inhomogeneous stress fields.

Static equilibrium influences mean stress without altering contact force distribution.

Abstract

In general, the mechanics of granular matter is described using continuum mechanics approach; this requires to introduce the concepts of stress and strain, which are averaged quantities, so that this needs also to introduce the notion of representative elementary volume (REV) above which averaged quantities have some physical meaning. As local quantities fluctuate spatially in granular matter; a local measure of stress and strain shall exhibit fluctuations too, whose typical amplitude depends on the sampling size L. This paper discusses this problem and the causes for large scale correlation. The mean stress s applied to a plane surface of size L*L is calculated and its fluctuation amplitude Ds is found when local forces are not correlated; it is found that Ds/s scales as 1/L . It is shown also that large scale fluctuations of stress can always be interpreted as an inhomogeneous stress field and that static equilibrium modifies the mean stress applied to a rod (in 2d), even if it does not perturb the contact force distribution. This last result is compared to experiment, which indicates that the number N of contacts per rod (in 2d) is 2<N<3 . Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn