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.
Highlights
Packed granular materials exhibit a rich internal network of physical interactions [1,2,3,4,5,6], which have come to be referred to as force chains (Fig. 1)
A necessary first step toward understanding the physical properties of packed granular materials is the development of statistics that provide insight into the structure of models
We have extended the data-driven, network-theoretic approach to the study of force chains initiated in Ref. [11], extracting putative chains using techniques from community detection
Summary
Packed granular materials exhibit a rich internal network of physical interactions [1,2,3,4,5,6], which have come to be referred to as force chains (Fig. 1). We perform analyses on two common systems [twodimensional (2D) experimental packings and numerical simulations done under similar conditions] and observe qualitatively comparable features that suggest broad similarities in the mesoscale structure of their force networks In both cases, we find that the gap factor and hull ratio are better able to extract force-chain structure at each pressure than the purely topological statistic. The three statistics together provide a broad picture of the mesoscale structure of the packing, and our findings suggest that both physical and topological information is useful to consider when studying granular systems. We discuss three such measures and assess their ability to (i) identify force-chain structure in packings of granular particles, and (ii) detect variations in force-chain architecture as a function of the applied pressure.
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