ABSTRACT
Lagrange multiplier method is used to propose a simple modelling of the distribution of contact forces and of the voids; they use very basic argument of statistical physics and the recognition that mean stress and mean density are physical constrains. It is found that both obey a Poisson law; the analogue T σ & Tv of the temperature T of a gas is here the mean stress a and the mean void size vv. In a second step we couple the two statistics by generalising an approach proposed by Boutreux & de Gennes; we describe the contraction of a normally consolidated sample under isotropic compression σ. It is found that the void index e can vary as λ ln(σ), as it is found experimentally. The value of λ is determined.
Despite the fact that granular materials are discontinuous materials, their mechanical behaviour is described commonly by continuum-mechanics. Indeed, this is very often the case for classical systems with a large number of particles (liquid, gas,...). We recall why it is possible in these cases. In this paper, after having recall a classical approach of statistical mechanics (section 1), we transpose these arguments to find the distribution of contact forces (section 2) and of voids (section 3) in a granular assembly. Section 4 tries and extends a procedure proposed by Boutreux & de Gennes (1997) for the compaction of powders with a tap-tap. So, we couple the evolution of these two statistics when varying the pressure σ of a normally consolidated sample. We find the e-e0=−λ ln(σ/σ o) classical law.
