Granular materials represent the most abundant form of matter on earth and are most simply
described as a collection of a large numbers of interacting solid particulates (often referred to
as grains or simply particles). Such materials are represented in the construction industry
(e.g. concrete powder), as powders in the pharmaceutical industry and make up a large
proportion of agricultural processing. Beyond industrial motivations, countless natural phenomena are manifested as granular materials/flows, such as avalanches, volcanic eruptions
and landslides. Evidently, the ubiquity of granular materials means that being able to predict
their rheological properties is essential for both optimising industrial processes and understanding important natural phenomena. In this thesis, the canonical micro-to-macro transition
is followed, primarily, in the context of non-spherical particles using the Multi-Sphere Discrete
Element Method (MS-DEM).
A brief overview of the motivations of this thesis, as well as a cursory introduction to some
of the most important concepts explored is provided in Chapter 1. In Chapter 2, the validity
of contact models used for the MS-DEM is investigated. Five sources of critical error are
identified, three errors are found to be algorithmic in nature, with two shown to occur due to
erroneous fundamental physics. Interestingly, the foundational source of error is independent
of the contact model, making the findings in Chapter 2 applicable to a wide range of problems.
All of the errors are shown to be rectified with the proposals put forward in Chapter 2 and
should substantially improve the quality of not only MS-DEM simulations, but related methods
for simulating non-spherical particles.
In Chapter 3, Lees-Edwards boundary conditions are implemented for the MS-DEM. It is
shown that a traditional approach to implementing Lees-Edwards conditions will result in
significant microstructural and macroscopic errors when using the MS-DEM. By proposing
a new algorithm, Lees-Edwards conditions are successfully implemented for the MS-DEM,
allowing one to perform accurate simulations of large strain simple shear flows to study the
rheology of non-spherical particulate systems.
In Chapters 4 to 6, a new kinetic energy based dimensionless number is proposed, which is
shown to form a power-law relationship with the inertial number. Extensive volume-controlled
discrete element method simulations show that this power law scaling successfully collapses
simple shear flow data, spanning from dilute systems to beyond the jamming point. The
constitutive equations derived from this scaling are valid across a broad range of inter-particle
friction coefficients and are insensitive to finite stiffness effects. Additionally, the constitutive
equations remain valid for highly dilute systems, a wide range of restitution coefficient as well
as for elongated particles. Moreover, it is also shown that the traditional µ(I) rheology can
be recovered from the proposed framework. An extensive analysis of the differences between
the granular kinetic energy and temperature is then performed to understand the utility of the
kinetic energy for constitutive modelling. Finally, a brief summary of the findings in this thesis
and suggestions for future work are provided in Chapter 7
