Analytical engineering models for predicting high speed penetration of hard projectiles into concrete shields: A review

We describe virtually all known analytical models for predicting protective properties of concrete shields against normal high-speed impact by rigid projectiles. Presented formulas can be directly used in practical calculations. Particular emphasis is given to widely used one-stage and two-stage models which are systemized in a hierarchical classification system using a unified approach. One-stage models employ the same formula along the whole trajectory of a projectile for calculating a force exerted on a penetrating projectile by a shield. In the case of two-stage models, a resistance force at the first stage of penetration is a linear function of the instantaneous depth of penetration while at the second stage of penetration normal stresses at every location on projectile-shield contact surface are polynomial function of normal velocity component. Conditions of continuity of the resistance force and velocity of a projectile are invoked in the transition point between these two sub-models. A wide variety of models can be devised by using different sub-models at each stage of penetration.