Simple models for granular force networks

A remarkable feature of static granular matter is the distribution of force along intricate networks. Even regular inter-particle contact networks produce wildly inhomogeneous force networks where certain “chains” of particles carry forces far larger than the mean. Although the full information of each inter-particle contact requires analysis of the stress tensor, potentially including friction and elasticity, there is a rich tradition of approximating these interactions with simple, scalar models that focus on the geometry of the system. In this paper, we briefly review past theoretical approaches to understanding the geometry of force networks. We then investigate the structure of experimentally derived granular force networks using a simple algorithm to obtain corresponding graphs. We compare our observations with the results of geometric models, including random bond percolation, which show similar spatial distributions without enforcing vector force balance. Our findings suggest that some aspects of the mean geometry of granular force networks may be captured by these simple descriptions.