Semi-analytical model for rigid and erosive long rods penetration into sand with consideration of compressibility

Abstract Sand is a granular, porous material with high compressibility, which influences the penetration process. According to the sand responses at different penetration velocities, the P-alpha equation of state and Mohr-Coulomb Tresca-limit yield criterion are used to describe the constitutive behavior. In the plastic region, the spherical cavity-expansion model is applied, and in the fluid-like region the hydrodynamic model with compressibility considered is applied based on the Alekseevskii-Tate model. Comparison with experimental results shows that the model is suitable for calculating sand penetration depths for rigid and erosive projectiles. Initial sand density affects penetration dissimilarly for different striking velocities, and a critical striking velocity exists. The compressibility should be considered with P-alpha equation of state below this critical striking velocity, and otherwise the fully compacted density can directly be used to calculate the penetration depth. Projectile dynamic yield strength influences penetration strongly. For an erosive projectile, the penetration depth and change in residual projectile length vary with the projectile dynamic yield strength.