Amorphous packings of frictionless, spherical particles are isostatic at
jamming onset, with the number of constraints (contacts) equal to the number of
degrees of freedom. Their structural and mechanical properties are controlled
by the interparticle contact network. In contrast, amorphous packings of
frictional particles are typically hyperstatic at jamming onset. We perform
extensive numerical simulations in two dimensions of the geometrical asperity
(GA) model for static friction, to further investigate the role of
isostaticity. In the GA model, interparticle forces are obtained by summing up
purely repulsive central forces between periodically spaced circular asperities
on contacting grains. We compare the packing fraction, contact number,
mobilization distribution, and vibrational density of states using the GA model
to those generated using the Cundall-Strack (CS) approach. We find that static
packings of frictional disks obtained from the GA model are mechanically stable
and isostatic when we consider interactions between asperities on contacting
particles. The crossover in the structural and mechanical properties of static
packings from frictionless to frictional behavior as a function of the static
friction coefficient coincides with a change in the type of interparticle
contacts and the disappearance of a peak in the density of vibrational modes
for the GA model. These results emphasize that mesoscale features of the model
for static friction play an important role in determining the properties of
granular packings.Comment: 4.5 pages, 5 figures, http://prl.aps.org/covers/110/1