Topological evolution in dense granular materials: A complex networks perspective

One of the great challenges in the science of complex materials – materials capable of emergent behavior such as self-organized pattern formation – is deciphering their “inherent” structural design principles as they deform in response to external loads. We have been exploring the efficacy of techniques from complex networks to the study of dense granular materials as a means to: (i) uncover such design principles and (ii) identify suitable metrics that quantify the evolution of structure during deformation. Herein, we characterize the developing network structure and loss of connectivity in a quasistatically deforming granular medium from the perspective of complex networks. Attention is paid to the evolution of the contact and contact force networks at the local or mesoscopic level, i.e., a particle and its immediate neighbors, as well as the macroscopic level. We explore network motifs and other topological properties at these multiple length scales, in an attempt to find that which best correlates with the constitutive properties of nonaffine deformation and dissipation, spatially and with respect to strain. Key processes or rearrangement events that cause loss of connectivity within the material domain, e.g. microbanding and force chain buckling, are investigated. Network statistics of these processes, previously shown to be major sources of energy dissipation and nonaffine deformation, are then tied to corresponding trends observed in the evolving macroscopic network. It is shown that consideration of the unweighted contact network alone is insufficient to tie dissipation to loss of material connectivity.