Granular materials transmit stress via a network of force chains. Despite the importance of these chains in characterizing the stress state and dynamics of the system, there is no common framework for quantifying their properties. Recently, attention has turned to the tools of network science as a promising route to such a description. In this paper, we apply a common network-science technique, community detection, to the force network of numerically-generated packings of spheres over a range of interparticle friction coefficients and confining pressures. In order to extract chain-like features, we use a modularity maximization with a recently-developed geographical null model (Bassett et al. in Soft Matter 11:2731–2744, 2015), and optimize the technique to detect sparse structures by minimizing the normalized convex hull ratio of the detected communities. We characterize the force chain communities by their size (number of particles), network force (interparticle forces), and normalized convex hull ratio (sparseness). We find that the first two are highly correlated and are therefore largely redundant. For both pressure P and interparticle friction \(\mu \), we observe two distinct transitions in behavior. One, for \(\mu \lesssim 0.1\) the packings exhibit more distinguishability to pressure than at higher \(\mu \). Two, we identify a transition pressure \(P^*\) at which the frictional dependence switches behaviors. Below \(P^*\) there are more large/strong communities at low \(\mu \), while above \(P^*\) there are more large/strong communities at high \(\mu \). We explain these phenomena by comparison to the spatial distribution of communities along the vertical axis of the system. These results provide new tools for considering the mesoscale structure of a granular system and pave the way for reduced descriptions based on the force chain structure.
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We are grateful for support from the National Science Foundation (DMR-1206808) and the James S. McDonnell Foundation. The simulations were performed at the NC State High Performance Computing Center. We are grateful to Leo Silbert, Danielle Bassett, and Mason Porter for valuable conversations.
Conflict of interest
The authors declare that they have no conflict of interest.
This research has been supported by the James S. McDonnell Foundation and the National Science Foundation (DMR-1206808).
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Huang, Y., Daniels, K.E. Friction and pressure-dependence of force chain communities in granular materials. Granular Matter 18, 85 (2016). https://doi.org/10.1007/s10035-016-0681-6
- Force chains
- Network community structure
- Numerical simulations