Estimation of perforation thickness for concrete shield against high-speed impact

We extended the existing engineering two-stage models for high-speed penetration of projectiles into concrete shields and suggested a semi-empirical model that is applicable for truncated bodies of revolution penetrating into shields having a finite thickness. In this model at the first stage of penetration (cratering), the resistance force is a linear function of the distance between the nose of the impactor and the front surface of the shield, while at the second stage (tunneling), the resistance force is proportional to a squared instantaneous velocity of the impactor and the linear term vanishes. The proposed model allows determining the minimal thickness of the plate which prevents from the perforation. The obtained theoretical predictions are compared with available experimental data.