Examining overlapping community structures within grain property networks

Granular materials (e.g, geological materials, powders and grains) when subjected to shear or compression deform through grain rearrangements. The structural topology of the grains, or fabric, can be usefully represented as a complex (contact) network whereby network nodes correspond to individual grains and network links correspond to grain contacts. Properties of each node (e.g, degree) can be calculated and throughout deformation this results in time series akin to sensor measurements for each grain in the assembly. These signals can be processed and collated into a particle property network with a corresponding community structure summarizing the relationship between each signal. Different properties give rise to different networks each with their own community structures, i.e, each network possesses the same set of nodes but a different link structure. The overlapping structure of these property network communities is of interest. We describe how the overlapping communities within networks constructed from properties related to grain behaviour with respect to multiscale cyclic structures is consistent with a power law description. Furthermore this behaviour is exhibited across a suite of computer simulations of compression tests which hints at possible universal features in the mechanical response of granular materials.