Fluctuations,
Correlation and Representative Elementary Volume (REV) in Granular Materials
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. Mean stress s applied to a plane surface of size L² is calculated and its
fluctuation amplitude ds is found when local
forces are not correlated; it is found that ds/s µ 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