Granular impact and the critical packing state

Impact dynamics during collisions of spheres with granular media reveal a pronounced and nontrivial dependence on volume fraction φ Postimpact crater morphology identifies the critical packing state φcps, where sheared grains neither dilate nor consolidate, and indicates an associated change in spatial response. Current phenomenological models fail to capture the observed impact force for most φ only near φcps 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< φcps (φ> φcps). At fixed low velocity, depth dependence of force shows a Janssen-type exponential response with a length scale that decreases with increasing φ and is nearly constant for φ> φcps.