Macroscopic
Continuous Approach versus Discrete
Approach, Fluctuations, criticality and SOC.
A state of the question based on articles in Powders & Grains 2001
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 s and strain e 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
poudres & grains 12 (8), 122-150 ( Novembre 2001)