Force distribution in static granular matter in two dimensions

Granular matter is a large assemblage of individual solids, which is fundamentally different from any other type of matters, such as solid and liquid. The intrinsic nature of granular matter is of multi-scale, inclusive of microscale of particle size, mesoscale of force chain and macroscale of the bulk of granular matter. The mesoscale of force chain bridges single particle and granular matter, and leads to unique properties and behaviours of granular matters, and thus acts as the key issue in the study of granular matter. In this work, we firstly propose a multiscale methodology for granular matter dynamics, and point out that the characteristics of force chain is the key to the granular dynamics. We then propose a discrete element model based on rigorous Hertzian contact law and Mindlin-Deresiewicz contact theory for normal and tangential contact forces, respectively. The static packing of 12000 sand grains under the action of gravity in two dimensions is simultaed, and the force chain pattern and stress distribution are obtained. The force distribution, force chain length distribution and the angle distribution are calculated and analyzed. Friction coefficient of particle is found to be a very sensitive factor affecting properties of granular matter, and thus its influence on the above parameters is studied as well.