Two dimensional mesoscale simulations of projectile instability during penetration in dry sand

To gain insight into the instability and trajectory change in projectiles penetrating dry sand at high velocities, two dimensional plane strain mesoscale simulations were carried out using representative models of a particulate system and of a small projectile. A program, ISP-SAND, was developed and used to generate the representative particulate system with mean grain sizes of 60 and $120μm$ as well as $±30%$ uniform size distribution from the mean. Target porosities ranged from 30% to 40%. The penetration of ogive nose steel projectiles with caliber radius head of 3.5 and length-to-diameter $(l/d)$ ratio of 3.85 was simulated using the updated Lagrangian explicit parallel finite element code ISP-TROTP. Deformation of the projectile and individual sand grains was analyzed using a nonlinear elastic-inelastic model for these materials. Grain-grain and grain-projectile interactions were analyzed using a contact algorithm with and without friction. Projectile instability was quantified and compared using the lateral displacement of the center of mass, lateral force acting on the projectile, and its rotational momentum about the center of mass. The main source of projectile instability and the ensuing trajectory change in the penetration simulations was found to be the inhomogeneous loading of the projectile due to the heterogeneities and randomness inherent in a particulate media like sand. The granularity of the media has not been considered explicitly in previous work. Projectile instability increased with impact velocity, as expected. However, it also increased for the case of elastic impactor that preserved the nose shape, with an increase in grain size, and for uniform grain sizes. Moreover, friction, inherently present in geologic materials, was found to be a major contributor to instability. Conclusions derived from one projectile depth simulations were confirmed by two deeper penetration simulations considering up to three full lengths of penetration (requiring a larger sand target). The deep penetration simulation predicted considerable instability with a trajectory change of approximately $45°$ when friction was considered in the dry sand medium. An overall conclusion of this work is that projectile penetration studies in geologic materials need to explicitly consider the heterogeneous or particulate nature of these materials.