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

Abstract

Abstract. In this paper, the dynamics of a spherical projectile obliquely impacting into a two-dimensional granular bed is numerically investigated using the discrete element method. The influences of projectile's initial velocities and impacting angles are mainly considered. Numerical results show that the relationship between the final penetration depth and the initial impact velocity is very similar to that in the verticalimpact case. However, the dependence of the stopping time on the impact velocity of the projectile exhibits critical characteristics at different impact angles: the stopping time approximately increases linearly with the impact velocity for small impact angles but decreases in an exponential form for larger impact angles, which demonstrates the existence of two different regimes at low and high impact angles. When the impact angle is regarded as a parametric variable, a phenomenological force model at large impact angles is eventually proposed based on the simulation results, which can accurately describe the nature of the resistance force exerted on the projectile by the granular medium at different impact angels during the whole oblique-impact process. The degenerate model agrees well with the existing experimental results in the vertical-impact cases.

Influence of particle rotation on the oblique penetration in granular media

“…The size distribution of particles is very similar to that used in an existing physical experiment [6], in order to directly validate our simulation method. It has been confirmed that the scaling of penetration depth is almost independent of the choice of system parameters if the variation of packing fraction induced by size distribution is small [33]. The method of generating targets has significant influence on the final material [36], which is mainly for cohesive aggregation, but also for some noncohesive cases.…”

“…We establish a simulating model substantially similar to the previously proposed model [33], and its effectiveness has been evaluated carefully. Since the positions and forces of individual particles are conveniently traced in a DEM simulation, the influences of particle rotation on the entire dynamical process can be quantitatively examined by analyzing the evolution of velocity field and the trajectories of projectiles for oblique impact.…”

“…See, e.g., Fig. 2 Therefore, in addition to the impact angle [33], the rotational angular velocity also plays a very important role in the dynamics process of a projectile obliquely impacting into a granular bed. From Fig.…”

“…Such oblique impact phenomena are commonly found in the particle-bed collision for the formation of sand dunes and ripples [26][27][28], secondary impacts on the Moon or Mars [29][30][31], etc. The variation of impact angles may significantly affect the trajectories of projectiles [32], the morphology and scaling of impact craters [15], and the basic dynamic processes [33]. However, research on the dynamics of projectiles and formation of craters under oblique impacting conditions is still very limited.…”

Granular matter: A special buffer for impact load

“…The formation of impact craters due to the penetration of projectile into granular media has been studied comprehensively [4,[11][12][13][14][15]. The influence of confinement on the penetration depth was studied experimentally [16][17].…”