Nontrivial power-law scaling of impact forces into granular materials

When an intruder strikes a granular material, the grains exert a force which decelerates and stops the intruder. Existing ballistic models can successfully describe much of the intruder-material interaction using a macroscopic force law, but these models often fail near the moment of impact. Here, we show results from experiments and numerical simulations, focusing on microscopic intruder-grain interactions during the early stages of impact. We record high-speed videos of intruders (of varying size and density) impacting assemblies of photoelastic disks, and we quantify both the intruder dynamics and the forces in the material. We show nontrivial power law scaling of peak forces during the initial transient phase of the impact into granular materials. Experiments and simulations indicate that this scaling is insensitive to many system details, such as friction, grain stiffness, and whether grain-grain interactions are linear (Hookean) or nonlinear (Hertzian). We also find important similarities to impact forces in dense suspensions, suggesting that our results may be generic for impacts into many kinds of soft, deformable materials.