Collisional Model of the Stopping Force of 3D Granular Impact

A dense granular packing can cause a free-falling intruding object to come to an abrupt stop as its momentum is dissipated to the grains. An empirical force law has been widely accepted to describe this process; it characterizes the stopping force as the sum of depth-dependent friction and velocity-dependent inertial drag.\footnote{H. Katsuragi et al, Nat. Phys. {\bf 3}, 6 (2007)} However, a complete interpretation of this force, incorporating grain-scale interactions during impact, remains unresolved. Here, the momentum transfer is proposed to occur through sporadic collisions with clusters of high force-carrying grains at the intruder's surface.\footnote{Y. Takehara et al EPL {\bf 92}, 44003 (2010), A. Clark et al, PRE {\bf 89}, 012201 (2014)} To test this model in 3D impact experiments, we determine the forces acting on an intruder decelerating through a dense granular medium using high-speed video of its trajectory. By attaching a rod to the intruder and observing its motion from perpendicular angles, we obtain all translational and rotational dynamics. We vary the shape of the impeding object to infer intruder-grain interactions from its consequent path. As a result, we connect the inertial drag to the effect of intruder shape and rotation based on the collisional model.