Similarities in the penetration depth of concrete impacted by rigid projectiles

Similarity can reflect common laws in the mechanism of rigid-body penetration. In this paper, the similarities in rigid-body penetration depth are demonstrated by three non-dimensional but physically meaningful quantities, i.e., ρ_kinetic , I_ln^* and N^'_1 . These three quantities represent the non-dimensional areal density of projectile kinetic energy, the effect of nose geometry, and the friction at the interactive cross section between projectile and target respectively. It is shown that experimental data of rigid projectile penetration, from shallow to deep penetration, can be uniquely unified by these three similarity quantities and their relationships. Furthermore, for ogival nose projectiles, their penetration capacities are dominated by ρ_kinetic , which is consisted by non-dimensional effective length L_eff and non-dimensional quantity D_n^p = ρ_p v_0^2/AY which has the same form as Johnson’s damage number. On the sacrifice of minor theoretical accuracy, the non-dimensional penetration depth P/d can be understood as directly controlled by D_n^p , enhanced by projectile effective length L_eff under a multiplication relation, and optimized by projectile nose geometry in the formation of I_ln^* . Graphic abstract