  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 framework 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.
