Critical-like features of a granular intruder

Abstract

We study the mechanical behavior of a particulate system in response to a dynamical intruder using computer simulations of a model granular material in two dimensions. We generated mechanically stable disordered packings of frictionless, bidisperse disks, at different distances above the jamming transition, which is located at a critical packing fraction φc, below which the entire packing loses mechanical stability. We then observe the critical force Fc, required to induce motion of a probe particle that we attempt to drag, at constant force, through the system. Below this critical force, the probe particle exhibits large velocity fluctuations before ultimately coming to rest. Just above the threshold force, the velocity of the probe particle is strongly intermittent as it moves through the system. At larger forces still, the probe moves with a well-defined average velocity. We find that the critical force scales as a power-law with distance from the jamming transition, Fc ∼ (φ – φc)β, where β ≈ 0.5, with a crossover to an independent regime very far from jamming. To further investigate the nature of the transition we analyze correlation in the stress fluctuations in an effort to extract a correlation length that characterizes the response of the system.