Friction and Pressure-Dependence of Force Chain Communities in Granular Materials

摘要

Granular materials transmit stress via a network of force chains. Despite theimportance of these chains to characterizing the stress state and dynamics ofthe system, there is no common framework for quantifying their theirproperties. Recently, attention has turned to the tools of network science as apromising route to such a description. In this paper, we apply communitydetection techniques to numerically-generated packings of spheres over a rangeof interparticle friction coefficients and confining pressures. In order toextract chain-like features, we use a modularity maximization with arecently-developed geographical null model \cite{Bassett2015}, and optimize thetechnique to detect branched structures by minimizing the normalized convexhull of the detected communities. We characterize the force chain communitiesby their size (number of particles), network strength (internal forces), andnormalized convex hull ratio (sparseness). We find the that the first twoexhibit an approximately linear correlation and are therefore largelyredundant. For both pressure $P$ and interparticle friction $\mu$, we observecrossovers in behavior. For $\mu \lesssim 0.1$, the packings exhibit moresensitivity to pressure. In addition, we identify a crossover pressure wherethe frictional dependence switches from having more large/strong communities atlow $\mu$ vs. high $\mu$. We explain these phenomena by comparison to thespatial distribution of communities along the vertical axis of the system.These results provide new tools for considering the mesoscale structure of agranular system and pave the way for reduced descriptions based on the forcechain structure.