Multiphase theory of granular media and particle simulation method for projectile penetration in sand beds

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.