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Force chains form heterogeneous physical structures that can constrain themechanical stability and acoustic transmission of granular media. However,despite their relevance for predicting bulk properties of materials, there isno agreement on a quantitative description of force chains. Consequently, it isdifficult to compare the force-chain structures in different materials orexperimental conditions. To address this challenge, we treat granular materialsas spatially-embedded networks in which the nodes (particles) are connected byweighted edges that represent contact forces. We use techniques from communitydetection, which is a type of clustering, to find sets of closely connectedparticles. By using a geographical null model that is constrained by theparticles' contact network, we extract chain-like structures that arereminiscent of force chains. We propose three diagnostics to measure thesechain-like structures, and we demonstrate the utility of these diagnostics foridentifying and characterizing classes of force-chain network architectures invarious materials. To illustrate our methods, we describe how force-chainarchitecture depends on pressure for two very different types of packings: (1)ones derived from laboratory experiments and (2) ones derived from idealized,numerically-generated frictionless packings. By resolving individual forcechains, we quantify statistical properties of force-chain shape and strength,which are potentially crucial diagnostics of bulk properties (includingmaterial stability). These methods facilitate quantitative comparisons betweendifferent particulate systems, regardless of whether they are measuredexperimentally or numerically.

Extraction of Force-Chain Network Architecture in Granular Materials Using Community Detection