This dissertation explores the use of packings of frictionless hard particles as models of the microstructure of particulate heterogeneous materials.
In the first part of this dissertation, we present the current mathematical framework used for understanding the properties of particle packings,
as well as the methods and algorithms we have developed to generate packings of frictionless hard particles with a computer.
We develop two algorithms to model hard-particle systems: a collision-driven molecular dynamics algorithm for the simulation of packings of spheres,
and a novel hybrid algorithm employing both molecular dynamics and Monte Carlo techniques for the simulation of packings of particles with general convex shapes,
such as spheres, cylinders, ellipsoids, polyhedra, etc.
We focus heavily on performance in order to enable the simulation of large systems containing 10⁶–10⁷ particles, previously too computationally expensive to simulate.
We use performance benchmarks to demonstrate that our implementations of these algorithms scale roughly linearly with the number N of particles in the system,
and show the impact that polydispersivity has on performance.
In the second part of this dissertation we explore the properties of disordered and ordered hard-particle packings.
We reproduce key results found in the literature for packings of spheres and polyhedra, and discuss some of their statistical properties.
We then follow the discussion with applications of particle packings as models of the microstructure of particulate materials obtained via computed tomography.
We find that the shape of the particles and their size distribution both play a crucial role in the determination of the statistical properties of heterogeneous materials
