Scaling and dynamics of sphere and disk impact into granular media

Direct measurements of the acceleration of spheres and disks impacting granular media reveal simple power law scalings along with complex dynamics which bear the signatures of both fluid and solid behavior. The penetration depth scales linearly with impact velocity while the collision duration is constant for sufficiently large impact velocity. Both quantities exhibit power law dependence on sphere diameter and density, and gravitational acceleration. The acceleration during impact is characterized by two jumps: a rapid, velocity-dependent increase upon initial contact and a similarly sharp depth-dependent decrease as the impacting object comes to rest. Examination of the measured forces on the sphere in the vicinity of these features leads to an experimentally based granular force model for collision. We discuss our findings in the context of recently proposed phenomenological models that capture qualitative dynamical features of impact but fail both quantitatively and in their inability to capture significant acceleration fluctuations that occur during penetration and which depend on the impacted material.