Sphere penetration by impact in a granular medium: A collisional process

Abstract

The penetration by a gravity driven impact of a solid sphere into a granular medium is studied by two-dimensional simulations. The scaling laws observed experimentally for both the final penetration depth and the stopping time with the relevant physical parameters are here recovered numerically without the consideration of any microscopic solid friction but with dissipative collisions only. Dissipative collisional processes are thus found as essential in catching the penetration dynamics in granular matter whereas microscopic frictional processes can only be considered as secondary effects.

The scaling and dynamics of a projectile obliquely impacting a granular medium

“…And it is suggested that the final stages of the excavation of the crater under these two impact conditions may have some analogies, particularly the crater morphology and corresponding dynamical behaviors [5,8]. Therefore, a large number of experiments [4][5][6][7][8][9][10][11][12][13][14][15][16], numerical simulations [17,18] and theoretical models [12][13][14][15]17] on lowvelocity impacts have been performed to explore the formation of the impact crater in granular media and attempt to propose some universal scaling describing the dimensions of the impact crater.…”

“…Despite the fact that recent progresses have been made on the penetration process of a rigid sphere into a granular material and various scaling laws about the penetration depth have been proposed under different system parameters, dimensions, impact conditions, etc. [4,6,9,[12][13][14][15][16][17][18], such impact dynamics is still difficult to be understood well as it involves both complex friction and collision processes. So far, the scaling law of the penetration depth with the impact velocity is still a controversial issue.…”

“…The stopping time of a projectile perpendicularly impacting into a granular medium displays a unique feature [12,15,16,18]: for a low impact velocity, the stopping time decreases with the impact velocity, while for a velocity larger than a characteristic velocity (the characteristic velocity is defined as the velocity when the stopping time reaches an asymptotic plateau value), it is almost independent of the impact velocity. Although some existing experimental results have presented various characteristic times (the asymptotic plateau time) and characteristic velocities, the relationship between stopping time and impact velocity seems to exhibit a similar scaling law.…”

Granular Impact

“…Of course, a response to an intruder is expected to be more complicated since it leads to a large scale rearrangement of granular particles, which is not expected in a response to a localized (small) point force. Indeed, it has been suggested that friction is not necessarily crucial in understanding this response [17].…”

“…Related phenomena occur in industrial settings, for instance in mixers or other machinery, where a blade can impact a material. There is a large relevant literature, of which we note a number of references, including the references which they cite [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] During an impact, a number of coupled processes are at work, and most of these are only partially understood. At the largest scale, the granular material exerts a force on the intruder, bringing it to rest.…”