High-speed penetration modeling and shape optimization of the projectile penetrating into concrete shields

We generalize the existing engineering approaches to modeling of high-speed penetration of projectiles into semi-infinite concrete shields and suggest a modified semi-empirical two-stage model that is applicable for bodies of revolution with a flat bluntness. At the first stage of penetration (cratering), the resistance force is described as a linear function of the instantaneous distance between the nose of the impactor and the front surface of the shield, while at the second stage (tunneling), the resistance force is quadratic in the instantaneous velocity of the impactor. Using the developed model we determine the shape of the impactor, which penetrates at the maximum depth. It is found that the depth of penetration of the optimal impactors with the truncated-cone nose is close to the depth of penetration of the absolute optimal impactors. The suggested model can be generalized to three-dimensional impactors.