GIDE: Graphic Interface for Discrete Element - Visual Computing: Scientific Visualization and Imaging Systems - page 61

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3.1 Introduction

Traditionally, when carrying out a numeric investigation of the mechanical
behaviour of a deformable body undergoing several stresses, use is made of the
Finite Element Method (FEM), which is an important tool in the analysis of
structures and more generally in engineering science [ 1 ]. It is based on the
mechanics of continuous media; however, the bodies are not continuous, but
the assumption of continuity affords a simplification making it possible to solve the
problems of classical mechanics. However, the assumption of continuity appears
difficult to accept for systems composed of several rigid or deformable parts,
interconnected by links. We then refer to multi-body systems. Currently, numerous
applications involve the study of such systems. In the field of sport, we study the
movements of athletes. In civil engineering, the modelling of granular materials by
a multi-body system enables understanding of the origin of mechanical behaviour,
whether it is microscopic, macroscopic, etc. In the field of the automobile and
transport, we seek continually to improve the performance, comfort, and safety of
cars, lorries, and trains. In granular mechanics, geomaterials or masonry, numer-
ical simulations based on the individual behaviour of grains or blocks are qualified
as DEM or Distinct Element Method [ 2 ], in contrast to the FEM strategy used
when a homogenised behaviour law has been chosen, assimilating the granulate or
masonry to a continuous medium.
For the moment in granulate mechanics, because of limitations in memory size
and calculation time, discrete numerical simulations are limited to samples of a
few thousand, or even a few tens of thousands of grains. For comparison, 1 cm 3 of
sand with 0.1 mm diameter grains contains about 10 6 grains. Thus, another sub-
stantial problem in modelling granular media is to be able to define the average
magnitudes (average stresses, average strains, etc.), taking into account the overall
behaviour of a granular medium considered as a continuous medium, and repre-
sentative of the physics at the scale of the grain (contact efforts, volume efforts,
local rotations and speeds, etc.). The final aim is to obtain homogenised behaviour
laws. This is the object of the micro-mechanical approaches that can be enriched
with the results obtained by discrete numerical simulations of granular media,
some quantities such as intergranular forces being difficult to measure

experimentally.