A community detection method for network structure analysis of force chains in granular medium in a rotating drum

We analyze the motion of granular matter in a partially filled drum rotating around the horizontal axis. The motion of granular medium is simulated using the discrete element model (DEM). As the drum rotates, the free surface sloping angle changes periodically as it attains the limit repose angle leading to an avalanche, after which its value is reduced to below the repose angle. Systems of this type are of interest from both theoretical and application viewpoints: similar setups are used in industry, such as rotary kilns and mixers; besides, dynamics of granular matter leads to macroscopic effects, such as segregation and emergence of patterns. Observable macroscopic effects depend largely on the underlying structure of force chains arising from pairwise mechanical contacts between the particles. Discrete element simulations produce the data for each individual particle: position, translational and rotational velocity, force vector between the interacting particle pairs. These data about the microscopic state must be processed to obtain the observable macroscopic states. Particle configurations at each time moment available from DEM simulations can be represented as graphs: each particle is represented as a graph vertex, the vertex pairs are connected by edges if the respective particle pairs are in contact, and the edge weights are proportional to the interaction force. After the graph for a particle state is created, the algorithms of the graph analysis can be applied to analyze the corresponding state of granular matter. Among such algorithms, we use the community detection algorithms to analyse the emergence of force groups among the particles, i.e., the groups of particles that have stronger mechanical forces among the particles in the group than the forces with particles that do not belong to the given group. Such groups are structures of larger scale than the usual force chains. Distribution of group sizes (number of particles belonging to the group) and their positions depend on the rotation velocities of the drum; in turn, they influence the variation of the repose angle and the process of the avalanches. We report the relations between the characteristics of the detected force groups and the observable effects in the granular matter obtained by DEM simulations.