| Granular materials are a class of materials which are important both to industry and to the physics community. Their importance to the physics community stems from the fact that granular materials are a simple example of an out-of-equilibrium, dissipative system, for which energy is not conserved and the traditional approach of statistical mechanics fails.;The aim of this thesis is to construct and examine a statistical mechanics-like framework for granular materials, based on a conservation law other than energy. We restrict our attention to packings in mechanical equilibrium, also known as jammed packings, where we are able to show that the total force moment tensor of the system is a conserved quantity. We build an ensemble using the stress, and test it on simulated packings.;This allows us also to explore the solid to liquid transition which occurs as the density of the packing is reduced, which is also known as the jamming transition. We then use the basis laid out by the ensemble to, first to study the properties of the system at then transition, and then to develop a field theoretical model for jammed packings, which predicts a diverging stiffness at the jamming transition. Finally, we discuss an empirical mean-field theory derived from the analysis of simulated packings. |
