Rigid clusters versus rigid regions in frictional granular packings and their role in packing mechanics

Force-chains are a well-established signature of granular packings and yet their role in packing mechanics remains elusive. We explore two new complementary mechanical signatures, namely that of rigid clusters and that of rigid regions. To determine rigid clusters, we implement a frictional version of a (3,3) pebble game on experimental packings of photoelastic disks undergoing a jamming transition. To determine rigid regions, we compute the dynamical matrix in the presence of friction and use a threshold-based criterion to determine which regions are rigid. While the rigid cluster decomposition depends on the topology of the contact network, the latter approach depends both on the topology and forces of the contact network. We find that the rigid clusters correlate well with the rigid regions, particularly near the jamming transition. We also observe "partial rigidity" with both signatures containing holes of floppiness involving groups of disks in the contact network and we look for correlations between rigid clusters/regions and force chains. In some cases we find that spanning force chains can dictate the boundary of a rigid cluster/region, while in other cases there is little correlation, hinting at the complexity of the problem.