Topological and geometric measurements of force chain structure

Abstract: Developing quantitative methods for characterizing structural properties of force chains in densely packed granular media is an important step toward understanding or predicting large-scale physical properties of a packing. A promising framework in which to develop such methods is network science, which can be used to translate particle locations and force contacts to a graph in which particles are represented by nodes and forces between particles are represented by weighted edges. Applying network-based community-detection techniques to extract force chains opens the door to developing statistics of force chain structure, with the goal of identifying shape differences across packings, and providing a foundation on which to build predictions of bulk material properties from mesoscale network features. Here, we discuss a trio of related but fundamentally distinct measurements of mesoscale structure of force chains in arbitrary 2D packings, including a novel statistic derived using tools from algebraic topology, which together provide a tool set for the analysis of force chain architecture. We demonstrate the utility of this tool set by detecting variations in force chain architecture with pressure. Collectively, these techniques can be generalized to 3D packings, and to the assessment of continuous deformations of packings under stress or strain.