Nonlinear force propagation during granular impact.

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^{'}≪1, force propagation is chainlike with a speed, v_{f}, satisfying v_{f}∝d/t_{c}. For larger M^{'}, the force response becomes spatially dense and the force propagation speed departs from v_{f}∝d/t_{c}, corresponding to collective stiffening of a strongly compressed packing of grains.