EVENT: Applied Mathematics Seminar

Dense assemblies of granular materials subject to deformation exhibit complex, self-organized and emergent behaviour. Force chains, quasi-linear arrangements of particles bearing above average load, form and align in the direction of principal stress. Collective buckling of force chains is one mechanism towards the emergence of persistent shear bands and material failure. The methods of complex systems, in particular properties of networks representing the topology of particle contacts, are useful for extracting key particle structures and rearrangements responsible for force chain failure and shear banding in compression and shear tests. The functional role of small subgraphs of the contact network, e.g., cycles of three or more contacting particles, with respect to mechanical performance is described. The evolution of a particles local cycle topology through deformation can be used as a proxy for fluctuating kinetic energy and dissipation. The preferred structural ordering of four-node subgraphs in the contact network exhibits superfamily behaviour and suggests a classification of the material into pre-failure and failure regimes. The transition dynamics of subgraphs representing a particle and its contacting neighbours can be used to extract preferred structural conformations and preferred structural rearrangements, useful as a starting point for continuum modelling frameworks. The above features of contact network evolution will be introduced and described with respect to data from computer simulations and laboratory experiments of compression and shear.