Friction and pressure-dependence of force chain communities in granular materials
- 341 Downloads
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.
KeywordsForce chains Network community structure Numerical simulations Friction Pressure
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.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
- 2.Dantu, P.: Contribution l’étude méchanique et géométrique des milieux pulvérulents. In: Proceedings of the Fourth International Conference on Soil Mechanics and Foundation Engineering, London, pp 144–148 (1957)Google Scholar
- 11.Zhang, L., Wu, J.-Q., Zhang, J.: Force-chain identification in quasi-2D granular systems. In: AIP Conference Proceedings, Powders and Grains, pp. 397–400 (2013)Google Scholar
- 17.Navakas, R., Džiugys, A., Peters, B.: Application of graph community detection algorithms for identification of force clusters in squeezed granular packs. Modern Build. Mater. Struct. Tech. 1–4 (2010)Google Scholar
- 24.LAMMPS. http://lammps.sandia.gov
- 26.Chen, Y., Best, A., Butt, H.-J., Boehler, R., Haschke, T., Wiechert, W.: Pressure distribution in a mechanical microcontact. Appl. Phys. Lett. 88, 20–23 (2006)Google Scholar
- 30.Jutla, I.S., Jeub, L.G.S., Mucha, P.J.: A generalized Louvain method for community detection implemented in MATLAB. http://netwiki.amath.unc.edu/GenLouvain
- 35.Newman, M., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004)Google Scholar
- 36.Janssen, H.A.: Versuche über Getreidedruck in Silozellen. Zeitschr. d. Vereines deutscher Ingenieure 39, 1045–1049 (1895)Google Scholar