Parking spheres stochastically to model realistic granular packings

The packing geometry of granular solids and other amorphous materials is important to understand their macroscopic behaviors. However, their particle-scale assembly mechanism and the underlying statistical mechanical laws remain unclear. In this work, we develop a model to generate the local packing structures of granular spheres by parking them sequentially and stochastically, and connect the fluctuating structures to the thermodynamic equations of state. The influences of entropy, friction, and mechanical action on local configurations are decomposed with the aid of an effective interparticle interaction, a parking sequence of neighboring particles, and an external potential. Quasiuniversal laws of granular sphere packings observed in previous experiments are replicated by our model and their empirical dependences on particle friction and packing protocol are rationalized. This model provides a general statistical mechanical approach to understanding the nonequilibrium assembly mechanism of amorphous particle packing systems.