Isostaticity and mechanical response of two-dimensional granular piles

We numerically study the static structure and the mechanical response of two-dimensional granular piles. The piles consist of polydisperse disks with and without friction. Special attention is paid to the rigid grain limit by examining the systems with various disk elasticities. It is shown that the static pile structure of frictionless disks becomes isostatic in the rigid limit, while the isostaticity of the frictional pile depends on the pile forming procedure, but in the case where the infinite friction is effective, the structure becomes very close to isostatic in the rigid limit. The mechanical response of the piles is studied by infinitesimally displacing one of the disks at the bottom. It is shown that the total amount of displacement in the pile caused by the perturbation diverges in the case of the frictionless pile as it becomes isostatic, while the response remains finite for the frictional pile. In the frictionless isostatic pile, the displacement response in each sample behaves in a rather complicated way, but its average shows wavelike propagation.