Rheology of Granular Materials with a Discrete Element Method
Résumé
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.
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