Exploring the combined effect of particle shape and friction on cell structures in granular packings via LS-DEM modeling

Abstract

To comprehensively understand and predict the macroscopic behavior of a granular system, one must consider not only the properties of individual particles but also the local structures. In this study, we prepare mechanically stable granular packings of super disks using the two-dimensional level set discrete element method (LS-DEM). We identify the cells, the irreducible loops enclosed by contacting particles, in the prepared granular packings and then analyze the statistics of these structures. We find the following. (1) The packing fraction or mean coordination number of studied systems exhibits a non-trivial dependency on particle shapes and inter-particle frictions, making it challenging to establish a direct correlation between them. (2) Using the cell-based description as a bridge, we can measure the packing behavior without considering the influence of particle shape and inter-particle friction. Specifically, the mean coordination number can be explicitly represented as a function of the mean cell order according to Euler’s topological relation. Upon the assumption that all cells are regular polygons, we can also approximately estimate the rattlers-free packing fraction via the mean cell order. (3) We have observed a nearly linear relationship between the mean cell order and rattler fraction. This enables us to determine the packing fraction as well.