(372a) Emergence of Force Chains in Granular Materials

An important but unresolved question on the mechanics of granular materials is the relation between the stress and the microstructure. Several experiments on two dimensional disks have reported the presence of anisotropic quasi-linear structures, called "force chains", which have been shown to carry a large fraction of the stress. Several studies have tried to quantify these structures using conventional mechanical definitions and network theory-based measures, but the problem largely remains unsolved. We report here the results of our computational studies on static and sheared collections of grains. Our main advance is the definition of an order parameter Qâ? which measures long-range correlations based on the linearity of contacts. The value of Q is limited to the range [0, 1], the upper limit representing particles aligned in a straight line, and the lower limit representing a self-avoiding walk that cannot take turns greater than 90 degrees. The size (number of particles) of the clusters N(Q) shows a sharp transition at a critical value of Q_c of the order parameter, similar to phenomena observed in phase transitionâ??s. The average inter-particle normal force of clusters corresponding to a particular value of Q shows a sharp peak exactly at Q_c, which is reminiscent of the divergence of certain quantities in phase transitions as a critical point is approached. We hypothesize that the force chains observed experimentally and numerically are the linear-most set of percolating clusters, as corroborated by the percolation probabilities of these clusters. All our observations hold even for randomly generated particle configurations, where Q_c shows strong dependence on the coordination number. Thus, it appears that self-organization is not necessary for the emergence of force chains, rather these chain-like structures are a generic property of random geometric networks. Finally, we show that the cluster size distribution does not depend on the number of particles in the system, indicating that the long-range correlations are not system-size dependent.