Structures and heterogeneity in deforming, densely packed granular materials

Predictions of the mechanical properties of a densely packed granular material so far have been quite inaccurate. Many of the phenomena observed by such a material leave a lot of unanswered questions. For example the stiffness of a sample under a strain path is poorly predicted by the most recent theoretical work. Part of the difficulty of a granular material is the interplay between discrete and continuous measures. For any sample of a practical scale, the size and numbers of grains involved makes consideration of each individual grain a near impossible process. So on the whole, continuum measures and theories have been used to try to describe the material behaviour without acknowledgement of the particulate constituents. However, that the mechanics of the material as a whole is dependent on the inter-particle forces is undeniable. These inter- particle forces work at the level of the individual particle where discrete measures such as force and displacements should be used. So how can practical, continuum measures be constructed from discrete constituents? This thesis provides the theoretical means to traverse from the discrete constituents to continuum measures. A key feature is the formalisation of a mesodomain, which is the unit of a granular material where the continuum and discrete regimes meet. Use is made of the formulation of a heterogeneous material to describe this mesodomain and it is shown how material properties can be scaled up from the mesoscale to the size of a sample of granular material. Work external to this project provides a method for describing the mechanics within the mesodomain. This is used to calculate the values of important tensors that represent the fabric of the mesodomain.