Force mobilization and generalized isostaticity in jammed packings of frictional grains

We show that in slowly generated two-dimensional packings of frictional spheres, a significant fraction of the friction forces lie at the Coulomb threshold-for small pressure p and friction coefficient mu , about half of the contacts. Interpreting these contacts as constrained leads to a generalized concept of isostaticity, which relates the maximal fraction of fully mobilized contacts and contact number. For p-->0 , our frictional packings approximately satisfy this relation over the full range of mu . This is in agreement with a previous conjecture that gently built packings should be marginal solids at jamming. In addition, the contact numbers and packing densities scale with both p and mu .