Abstract
This study investigates the dynamics of a spherical projectile impact onto a granular bed via numerical simulations by discrete element method (DEM). The granular bed is modeled as an assembly of polydisperse spherical particles and the projectile is represented by a rigid sphere. The DEM model is used to investigate the cratering process, including the dynamics of the projectile and energy transformation and dissipation. The cratering process is illustrated by tracking the motion of the projectile and granular particles in the bed. The numerical results show that the dynamics of the projectile follows the generalized Poncelet law that the final penetration depth is a power-law function of the falling height. The numerical results can match well the experimental data reported in the literature, demonstrating the reliability of the DEM model in analyzing the impact of a spherical projectile on a granular bed. Further analyses illustrate that the impact process consists of three main stages, namely the impact, penetration and collapse, as characterized by the evolution of projective velocity, strong force chains and crater shape. The initial kinetic and potential energy of the projectile is dissipated mainly by inter-particle friction which governs the projectile dynamics. The stopping time of projectile decreases as the initial impact velocity increases. The final penetration depth scales as one-third the power of total falling height and is inversely proportional to the macroscopic granular friction coefficient.
Highlights
The impact of projectiles on granular media are widespread phenomena in nature, such as asteroids colliding onto planetary surfaces (Senft and Stewart, 2009), raindrops falling into soil (Marston et al, 2010), people walking on sand beaches (Uehara et al, 2003) and rockfalls impacting onto soil buffering layers (Wang and Cavers, 2008; Calvetti and di Prisco, 2012; Su et al, 2018; Shen et al, 2019)
For a spherical projectile impacting onto granular media, it is well established that the crater diameter scales with the power of 1/4 the kinetic energy of the projectile and the final penetration depth scales with the power of 1/3 the falling height (Uehara et al, 2003)
For the tests with μb ≥ 0.4, the evolution of the projectile penetration depth is nearly identical and the projectiles almost stop at the same position. These results indicate that the interparticle friction has a significant influence on the projectile dynamics
Summary
The impact of projectiles on granular media are widespread phenomena in nature, such as asteroids colliding onto planetary surfaces (Senft and Stewart, 2009), raindrops falling into soil (Marston et al, 2010), people walking on sand beaches (Uehara et al, 2003) and rockfalls impacting onto soil buffering layers (Wang and Cavers, 2008; Calvetti and di Prisco, 2012; Su et al, 2018; Shen et al, 2019). The related research contributes to a better understanding of the formation of impact craters and the design of efficient shock absorbers Though it has been studied via experiments, numerical simulations and analytical theories (Newhall and Durian, 2003; Wada et al, 2006; Crassous et al, 2007; Katsuragi and Durian, 2007; Clark et al, 2015; Li et al, 2016; Ye et al, 2016; Horabik et al, 2018; Ye et al, 2018; Zhang et al, 2021) in the past several decades, the understanding of impact. A part of these factors have been systematically analyzed by a series of experimental tests (Newhall and Durian, 2003; Uehara et al, 2003; Katsuragi and Durian, 2013) The focus of these tests is on the ejection process, the crater morphology and the penetration dynamics, aiming to find a scaling law for crater size and penetration depth. The influence of inter-particle friction and damping on the dynamics of projectile has not been investigated (Clark et al, 2015)
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