Socolar, JES, *Discrete models of force chain networks*,
Discrete and Continuous Dynamical Systems Series B, vol. 3 no. 4
(2003),
pp. 601-618 [0212162] .
**Abstract:**

*A fundamental property of any material is its response to a localized stress applied at a boundary. For granular materials consisting of hard, cohesionless particles, not even the general form of the stress response is known. Directed force chain networks (DFCNs) provide a theoretical frame-work for addressing this issue, and analysis of simplified DFCN models reveal both rich mathematical structure and surprising properties. We review some basic elements of DFCN models and present a class of homogeneous solutions for cases in which force chains are restricted to lie on a discrete set of directions.*