Contact orientation distributions for visualisation of granular fabric

Contact orientation distributions are widely used to describe the fabric of granular assemblies and its evolution under load. Different types of visualisations, mainly histograms, are used in the literature to plot these distributions. While there are different ways to create such histograms, however, there is generally no discussion of how the chosen way affects the visualisation of the distribution and its interpretation. We develop in this paper a novel, rigorous framework for discussing contact orientations and their visualisation through histograms. This allows presenting, for the first time, in a unified way several existing visualisations and explaining how they are computed. We identify first some issues in how existing visualisations represent the main features of the contact distribution. We then exploit the framework to introduce new histogram types that avoid these issues and provide a better insight into the granular fabric.