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.National Natural Science Foundation of China (No.
42107155), the Royal Society, Sino-British Fellowship Trust
International Exchanges Award (No. IES\R2\202023), the
Fundamental Research Funds for the Central Universities
(No. 2682021CX061), the National Key R&D Program of
China (No. 2017YFC1502500
