Analysis of grain-scale measurements of sand using kinematical complex networks

Abstract

Plastic deformation in a plane strain compression test of a dense sand specimen is studied using functional networks. Kinematical information for the deforming material is obtained using digital image correlation (DIC) and summarized by two types of complex network with different connectivity rules establishing links between the network nodes which represent the DIC observation sites. In the first, nodes are connected to a minimum fixed number of neighbors with similar kinematics such that the resulting network forms one connected component. In the second, nodes are connected to other nodes whose kinematical behavior lies within a fixed distance of each other in an observation space. The fixed radius is determined using optimization with a stopping criterion again with the resulting network forming one connected component. We find different network properties of each network provide useful information about plastic deformation and nonaffine kinematical processes emerging within the material. In particular, persistent shear bands and mesoscale structures within them (e.g. vortices) appear to be closely related to values of network properties including closeness centrality, clustering coefficients, k-cores and the boundaries of community structures determined using local modularity.