  Force chains form heterogeneous physical structures that can constrain the
mechanical stability and acoustic transmission of granular media. However,
despite their relevance for predicting bulk properties of materials, there is
no agreement on a quantitative description of force chains. Consequently, it is
difficult to compare the force-chain structures in different materials or
experimental conditions. To address this challenge, we treat granular materials
as spatially-embedded networks in which the nodes (particles) are connected by
weighted edges that represent contact forces. We use techniques from community
detection, which is a type of clustering, to find sets of closely connected
particles. By using a geographical null model that is constrained by the
particles' contact network, we extract chain-like structures that are
reminiscent of force chains. We propose three diagnostics to measure these
chain-like structures, and we demonstrate the utility of these diagnostics for
identifying and characterizing classes of force-chain network architectures in
various materials. To illustrate our methods, we describe how force-chain
architecture 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 force
chains, we quantify statistical properties of force-chain shape and strength,
which are potentially crucial diagnostics of bulk properties (including
material stability). These methods facilitate quantitative comparisons between
different particulate systems, regardless of whether they are measured
experimentally or numerically.
