Penetration of Rigid Rods, Flexible Rods, and Granular Jets into Low-Density Granular Media

Abstract

The penetration of projectiles into granular materials has been mainly studied using spherical intruders. Here we explore the dynamics of rods penetrating vertically in a two-dimensional granular bed composed of expanded polystyrene spheres. The experiments were performed using rigid rods, flexible rods and vertical arrays of non-cohesive particles, and the dynamics for the three cases was compared. In contrast to the vertical penetration observed for a single spherical projectile, high speed videos reveal that a rod rapidly deviates from its initial vertical direction due to inhomogeneities of the bed packing fraction. Then, the rod rotates due to the torque induced by the resistance force and follows a curved trajectory until be aligned horizontally at a final depth. A short rod tends to deviate faster than a longer rod due to the smaller moment of inertia. Moreover, long flexible rods always lose their vertical alignment and experience buckling, whereas rigid rods of the same size penetrate deeper before being deviated. On the other hand, experiments and molecular dynamics simulations show that a initially vertical array of grains also loses its verticality and stops adopting a final horizontal configuration. The granular array penetrates considerably less than the rods of equivalent mass, and the stopping mechanism is based on vertical-to-horizontal momentum transfer during a collisional process of the constituting particles.

Figures (6)

• Figure 1: Experimental setup. A Hele-Shaw cell of 1m$^2$ and 5 mm thick was filled with a monolayer of expanded polystyrene spheres. Then, different arrays were released from the top and the dynamics was filmed with a high-speed camera at 1000 fps.
• Figure 2: Comparison of the penetration of a-b) rigid and c-d) flexible rods ($l= 7. 1$ cm, $m=7.2$ g) falling vertically into the 2D granular bed. The intruder path and material fluidization is visualized. Scale bar=10cm.
• Figure 3: Individual paths of a-c) rigid and b-d) flexible rods depending on the length $l$ (N spheres). Insets show enlarged (rescaled) views of the paths for the three indicated coloured dots used to track the rotation of the rods. (x,y) represent coordinates.
• Figure 4: Granular jet of $25\times5$ steel spheres falling vertically into the granular bed stop in horizontal configuration.
• Figure 5: $y_F$ vs $N$ for rigid rods, flexible rods and granular jets of the same length. For clarity, $y_F$ vs $N$ is also shown in the inset for the granular jet. Solid symbols represent the mean value and the standard deviation of five measurements, and lines the fits of the form: $y_F=A(1-e^{-N/N^*})$.