Stefanos Papanikolaou, Corey S. O'Hern, Mark D. Shattuck
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 filling fraction, contact number, mobility distribution, and vibrational density of states using the GA model to those generated using the Cundall- Strack (CS) approach, where static friction is modeled by a tangential linear spring when two disks form a contact that is allowed to slide when their relative tangential displacement exceeds the Coulomb threshold. 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 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 structural and mechanical properties of granular packings.
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http://arxiv.org/abs/1207.6010
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