Stopping of porous projectiles in granular targets

Abstract

Using granular mechanics, we determine the stopping force acting on spherical granular projectiles impinging on a flat granular bed. We find that the stopping force is proportional to the impact energy, as in Poncelet's law. For fixed velocity, it is proportional to the projectile cross-sectional area rather than to its volume. These dependences only hold in the early stages of stopping, before the projectile has been strongly fragmented. Analogies to the stopping of atomic clusters in compact matter are pointed out.