Model for estimation of critical packing density in polydisperse hard-disk packings

We introduce a geometric model for unjamming the polydisperse hard-disk packing. The unjamming corresponds to a critical packing density which is assumed to happen uniformly throughout the packing. However, this model can be used for prediction of local dilation in packings. Molecular dynamics (MD) simulations are also performed to create random packings of polydisperse hard disks. In MD simulations, a densification scheme is applied to the event-driven algorithm in which the size of particles increases with controlled rates. The packing densities upon the onset of the critical state are estimated in a series of bidisperse packings by feeding the textural information of the mixtures from MD simulations into the model. These results are relevant for studies of unjamming and shear banding phenomena in granular materials, colloids, metallic glasses and similar systems.