The scientific problems related to granular matter are ubiquitous. It is currently an
active area of research for physicists and earth scientists, with a wide range of applications
within the industrial community. Simple analogue experiments exhibit behaviour that is
neither predicted nor described by any current theory. The work presented here consists
of modelling granular media using a two-dimensional combined Finite-Discrete Element
Method (FEM-DEM). While computationally expensive, as well as modelling accurately
the dynamic interactions between independent and arbitrarily shaped grains, this method
allows for a complete description of the stress state within individual grains during their
transient motion.
After a detailed description of FEM-DEM principles, this computational approach is
used to investigate the packing of elliptical particles. The work is aimed at understanding
the influence of the particle shape (the ellipse aspect ratio) on the emergent properties of
the granular matrix such as the particle coordination number and the packing density. The
diff erences in microstructure of the resultant packing are analysed using pair correlation
functions, particle orientations and pore size distributions. A comparison between frictional
and frictionless systems is carried out. It shows great diff erences not only in the calculated
porosity and coordination number, but also in terms of structural arrangement and stress
distribution. The results suggest that the particle's shape a ffects the structural order of the
particle assemblage, which itself controls the stress distribution between the pseudo-static
grains.
The study then focuses on describing the stress patterns or \force chains" naturally
generated in a frictional system. An algorithm based on the analysis of the contact
force network is proposed and applied to various packs in order to identify the force
chains. A statistical analysis of the force chains looking at their orientation, length and
proportion of the particles that support the loads is then performed. It is observed
that force chains propagate less efficiently and more heterogeneously through granular
systems made of elliptical particles than through systems of discs and it is proposed
that structural diff erences due to the particle shape lead to a signifi cant reduction in the length of the stress path that propagates across connected particles. Finally, the e ffect
of compression on the granular packing, the emergent properties and the contact force
distribution is examined. Results show that the force network evolves towards a more
randomly distributed system (from an exponential to a Gaussian distribution), and it
confi rms the observations made from simulations using discs.
To conclude, the combined finite-discrete element method applied to the study of
granular systems provides an attractive modelling strategy to improve the knowledge of
granular matter. This is due to the wide range of static and dynamic problems that can be
treated with a rigorous physical basis. The applicability of the method was demonstrated
through to a variety of problems that involve di fferent physical processes modelled with
the FEM-DEM (internal deformations, fracture, and complex geometry). With the rapid
extension of the practical limits of computational models, this work emphasizes the
opportunity to move towards a modern generation of computer software to understand
the complexity of the phenomena associated with discontinua.