Multiscale resolution of networks of granular media network evolution – a network of networks

The experimental technique of Digital Image Correlation is used to measure the displacement of clusters of glass beads in an assembly across strain intervals
throughout a plane strain compression test. For each strain interval a complex network is constructed whose connectivity captures similarity of kinematical response of the observed clusters. We propose a method of obtaining a network
of networks which collates the temporal activity of these kinematical networks through loading. This is done by considering convex combinations of network adjacency matrices with coefficients determined using a distance kernel
function. The use of a distance kernel allows the introduction of a network interaction score which enables the deformation history to be partitioned into temporal sequences of different kinematical behaviour. A network of networks in each of these temporal ranges helps identify areas within the material responsible for onset of failure, the localized failure zone and shear band activity