How do large-force networks, or force chains, arise in granular materials?*

Stress transmission in static and slowly deforming granular materials is characterized by the emergence of an inhomogeneous distribution of quasi-linear large force-carrying network of particles, called force chains. Despite many studies, there is little understanding of how such a correlated network of force-bearing chains arises from an essentially disordered assembly of grains, and what the relevance of these force chains to the macroscopic mechanics of the granular assembly is. Here we show from a classification of a subset of the contact network based on a simple definition of its linearity, there emerges a sharp transition from an essentially disordered network to an ordered, quasi-linear network of grains. This transition is remarkably similar to that of a continuous phase transition in thermodynamic systems.  The sub-network of particles at the critical value of linearity are the force chains, and explain many of the observed statistical features of granular force networks.  More significantly, it explains several interesting mechanical features observed in granular materials confined in various geometries.