Elasticity from the force network ensemble in granular media

Transmission of forces in static granular materials is studied within the framework of the force network ensemble, by numerically evaluating the mechanical response of hexagonal packings of frictionless grains and rectangular packings of frictional grains. In both cases, close to the point of application of the overload, the response is nonlinear and displays two peaks, while at larger length scales, it is linear and elasticlike. The crossover between these two behaviors occurs at a depth that increases with the magnitude of the overload and decreases with increasing friction.