Nonlinear Force Propagation during Granular Impact

Abstract: We experimentally study nonlinear force propagation into granular material during impact from an intruder, and we explain our observations in terms of the nonlinear grain-scale force relation. Using high-speed video and photoelastic particles, we determine the speed and spatial structure of the force response just after impact. We show that these quantities depend on a dimensionless parameter, $M'=t_c v_0/d$, where $v_0$ is the intruder speed at impact, $d$ is the particle diameter, and $t_c$ is the collision time for a pair of grains impacting at relative speed $v_0$. The experiments access a large range of $M'$ by using particles of three different materials. When $M' \ll 1$, force propagation is chain-like with a speed, $v_f$, satisfying $v_f \propto d/t_c$. For larger $M'$, the force response becomes spatially dense and the force propagation speed departs from $v_f\propto d/t_c$, corresponding to collective stiffening of a strongly compressed packing of grains.