A continuum theory for a random array of identical, elastic, frictional disks

We derive a stress–strain relation for static deformations of a random array of identical disks that interact through elastic, frictional contacts. In doing this, we take into account force and moment equilibrium of pairs of disks in the aggregate and average over pairs that have the same orientation. However, we defer consideration of the influence of deviations from the average packing on the stress–strain relation. We apply the result to biaxial straining at constant pressure and obtain explicit expressions for the shear stress, area strain, and the amount of contact deletion.