Granular Dynamics During Impact

We study the impact of a projectile onto a bed of 3 mm grains immersed in an index-matched fluid. We vary the amount of prestrain on the sample, strengthening the force chains within the system. We find this affects only the prefactor of the linear depth-dependent term in the stopping force. We propose a simple model to account for the strain dependence of this term, owing to increased pressure in the pile. Interestingly, we find that the presence of the fluid does not affect the impact dynamics, suggesting that dynamic friction is not a factor. Using a laser sheet scanning technique to visualize internal grain motion, we measure the trajectory of each grain throughout an impact. Microscopically, our results indicate that weaker initial force chains result in more irreversible, plastic rearrangements, suggesting static friction between grains does play a substantial role in the energy dissipation.

Figure 1

A schematic of the experimental setup. The beads are in an index-matched fluid (dimethyl sulfoxide) with a fluorescent dye, allowing illumination of the sample in the impact plane. The sample is strained via displacement of the back wall.

Figure 2

Depth vs total height for many different sample preparations. The fits shown are to simple power laws. Each point corresponds to five experimental runs. The dry and wet unstrained samples show the same exponent $\approx 0.4$, and differ in prefactor by about 15%.

Figure 3

(a) Three sample trajectories for a fixed drop height with differing amounts of prestrain. From the trajectories, we are able to find a value of (b) $d_1$ for each strain value and (c) $k$ for each strain. The dashed and dotted lines show the values of $d_1$ and $k$ for the unstrained wet impact, scaling out fluid mass.

Figure 4

Particle tracks of the grains during impact. The tracks go from red (early) to blue (late). Grains below the intruder move down, and grains to the side of the intruder move out and up. The frame-to-frame motion is not always smooth, due to the frustrated nature of the packing.

Figure 5

(a) Spatial map of $D_{\min }^2$ for three different strains. The drop height is the same in each case, and $D_{\min }^2$ is measured in the $z=0$ limit. (b) For three drop heights and five strains, the average $D_{\min }^2$ value is normalized by the energy of the intruder just before impact.