Studying projectile penetration in sand beds is of great significance for solving practical problems in the fields of weapon damage, consolidation of foundations, and mine explosions. In this study, a coupled model using the elastic-viscoplastic-kinetic constitutive relation and discrete particle dynamics was established to describe the multiple phases of sand-like materials, namely, the solid-like, liquid-like, gas-like, and inertial discrete phases. A linear elastic model was used to describe the solid-like phase; however, after the plastic yield point was reached, a viscoplastic constitutive model based on rheology was used to describe this liquid-like phase. When the volume fraction of the particles reduced to a certain value, the gas-like phase was described using the kinetic theory of granular flow; however, when the assumption of binary collisions was no longer satisfied, discrete particle dynamics was used to describe this inertial discrete phase. Smoothed discrete particle hydrodynamics coupled with the discrete element method was used to discretize our model based on established multiphase models of sand-like materials. Our new theoretical model and numerical method were used to simulate the high-speed penetration of spherical and slender projectiles in dry sand accumulation. A comparison with the results from experiments and other numerical methods shows that the new numerical method is suitable for describing the different motion states of sand-like materials owing to different projectile penetration velocities. Finally, the ricochet phenomenon of a conical projectile penetrating a sand bed was captured, which further verifies the applicability of our model for solving engineering problems.

研究弹丸在沙层中的穿透性，对于解决武器破坏、地基加固、地雷爆炸等领域的实际问题具有重要意义。本研究建立了一种利用弹-粘塑性-动力学本构关系和离散粒子动力学的耦合模型来描述类砂材料的多相，即类固体、类液体、类气体和惯性相。离散相。线弹性模型用于描述类固相；然而，在达到塑性屈服点后，基于流变学的粘塑性本构模型用于描述这种类似液体的相。当颗粒的体积分数降低到一定值时，用颗粒流动力学理论描述类气体相；然而，当不再满足二元碰撞的假设时，离散粒子动力学被用来描述这种惯性离散相。光滑的离散粒子流体动力学与离散元方法相结合，用于基于已建立的类砂材料多相模型来离散我们的模型。我们新的理论模型和数值方法用于模拟球形和细长弹丸在干砂堆积中的高速穿透。与实验结果和其他数值方法的比较表明，新的数值方法适用于描述不同弹丸穿透速度的砂状材料的不同运动状态。最后，捕捉到圆锥形弹丸穿透沙床的跳弹现象，