title: 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 into a graph in which particles are represented by nodes and forces between particles are represented by weighted edges. Recent work 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 geometric and topological 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 the mesoscale structure of force chains in two-dimensional (2D) packings, including a 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.
authors.affiliation: Warren Center for Network and Data Science, University of Pennsylvania, Philadelphia, Pennsylvania, USA.
authors.forename: Chad
authors.initials: C
authors.lastname: Giusti
authors.affiliation: Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania, USA.
authors.forename: Lia
authors.initials: L
authors.lastname: Papadopoulos
authors.affiliation: Department of Physics, Presbyterian College, Clinton, South Carolina, USA.
authors.forename: Eli T
authors.initials: ET
authors.lastname: Owens
authors.affiliation: Department of Physics, North Carolina State University, Raleigh, North Carolina, USA.
authors.forename: Karen E
authors.initials: KE
authors.lastname: Daniels
authors.affiliation: Departments of Bioengineering and Electrical & Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania, USA.
authors.forename: Danielle S
authors.initials: DS
authors.lastname: Bassett