Influence of volume fraction on the dynamics of granular impact

Variation of the volume fraction $\phi$ of non-cohesive granular media causes disproportionate changes in the forces exerted on impacting objects and, consequently, the impact kinematics. In our experiments, a computer controlled air fluidized granular bed is used to vary $\phi$ from 0.58 (low) to 0.62 (high) for 0.3~mm diameter glass spheres and \~1~mm poppy seeds. An accelerometer attached to a 4.0~cm diameter steel sphere measures collision forces for initial impact velocities ranging from 0.5 to 3.5~m/s. As an example of the dramatic changes produced by varying $\phi$, time series of the force during impact with poppy seeds at an impact velocity of 1~m/s change from monotonically increasing with slope 100~N/s at $\phi=0.59$ to monotonically decreasing with slope -100~N/s at $\phi=0.62$; glass beads show similar behavior. Increasing $\phi$ from low to high at fixed collision velocity causes the penetration depth to decrease monotonically by approximately 50\%. However, for the same parameters, the collision duration changes little, decreasing by $\approx 10$\% as $\phi$ is increased from 0.58 to $\approx 0.6$ and then increasing by about 3\% as $\phi$ is increased to 0.63. Our impact simulations exhibit the same collision dynamics vs.\ $\phi$ and reveal qualitative differences in grain velocity fields and local volume fraction changes between low and high $\phi$ states. Support by the Burroughs Wellcome Fund and the Army Research Lab MAST CTA.