Impact, drag, and the granular critical state

The response of dense ensembles of non-cohesive granular media (GM) subject to the motion of an intruder is important in many industrial and biological [1] settings. Previous studies of impact [2] and drag [3, 4, 5] have identified general features of force and flow response, however the role of the initial volume fraction, ϕ, has not been studied in detail. Here we investigate the response of GM perturbed by the motion of single intruders as a function of ϕ in experiment and in soft sphere discrete particle simulation [6, 7, 1]. Comparing the response for experiments with different intruder shape, trajectory, and driving reveals the importance of the critical volume fraction, ϕc, the packing density at which grains neither dilate nor consolidate when sheared. Experiments examining impact dynamics of ballistic spheres with GM reveal a pronounced dependence on ϕ. Post-impact crater morphology identifies the critical packing state ϕc, and indicates an associated change in spatial response. Existing phenomenological models fail to capture the observed impact force for most ϕ; only near ϕc is force separable into additive terms linear in depth and quadratic in velocity. At fixed depth the quadratic drag coefficient decreases (increases) with depth for ϕ < ϕc (ϕ> ϕc). At fixed low velocity