Rheology of Granular Materials with a Discrete Element Method

Serge Dumont (1, 2) , Jérôme Fortin (3) , Youssef Ouafik (4)

1 UNIMES - Université de Nîmes
2 IMAG - Institut Montpelliérain Alexander Grothendieck
3 LTI - Laboratoire des technologies innovantes - UR UPJV 3899
4 MEPS - Laboratoire de Mathématiques et Physique des Systèmes

To study the rheology of granular materials various strategies coexist: either continuous, or discrete. The most common in the continuous models is the Soil mechanics model which stipulates a relation between the stresses and the deformations. But it proves that they are not able to provide a simple explanation to the complex behaviors of this kind of material. Other continuous theories like the model of Janssen or model OSL introduce relations between the components of the stress tensors without considering deformations. The first is a shell model which works on a mean stress while the relation between stresses proposed by OSL is local. The Discrete Element Method (DEM) developed in this paper consider the granular material as a set of rigid particules which are subjected to their own weight and with the contact forces exerted by the particules in the neighbourhood. The knowledge of these local forces makes it possible to identify a stress homogenized for a sample test. To deduce from it the behavior of the whole studied material, one meshes space in basic cells which behave each one like the studied sample. The DEM are limited by the CPU time. The extrapolation of results for macro assemblies remains delicate. One proposes here, starting from a DEM approach, to establish the link between the discrete approach and the continuous one by simulating a set of particle and by validating the various phenomenologic models. Initially, the DEM will enable us to identify the importance of some local parameters and in the second time, to propose a new approach for the continuous model to the rheology of granular materials.

Mots clés: Granular materials; Discrete elements method; Homogenization

Domaines: Mécanique des structures [physics.class-ph]; Analyse numérique [math.NA]

Serge Dumont, Jérôme Fortin, Youssef Ouafik. Rheology of Granular Materials with a Discrete Element Method. 9th US National Congress on Computational Mechanics, Jul 2007, San Francisco, CA, United States. ⟨hal-01818081⟩