Based on the three-stage perforation model, a semi-theoretical analysis is conducted for the ballistic per- formances of a rigid kinetic projectile impacting on concrete plates. By introducing the projectile resistance coefficients, dimensionless formulae are proposed for depth of penetra- tion （DOP）, perforation limit thickness, ballistic limit veloc- ity, residual velocity and perforation ratio, with the projec- tile nosed geometries and projectile-target interfacial fric- tion taken into account. Based on the proposed formula for DOP and lots of penetration tests data of normal and high strength concrete targets, a new expression is obtained for target strength parameter. By comparisons between the re- sults of the proposed formulae and existing empirical formu- lae and large amount of projectile penetration or perforation tests data for monolithic and segmented concrete targets, the validations of the proposed formulae are verified. It is found that the projectile-target interfacial friction can be neglected in the predictions of characteristic ballistic parameters. The dimensionless DOP for low-to-mid speed impacts of non-flat nosed projectiles increases almost linearly with the impact factor by a coefficient of 2/（nS）. The anti-perforation ability of the multilayered concrete plates is dependent on both the target plate thickness and the projectile impact velocity. The variation range of the perforation ratio is 1-3.5 for concrete targets.
With a target treated as the incompressible Tresca and Mohr-Coulomb material, by assuming that cavity expansion produces plastic-elastic and plastic-cracked-elastic response region, the decay function for the free-surface effect is constructed for metal and geological tar- gets, respectively. The forcing function for oblique penetration and perforation is obtained by multiplying the forcing function derived on the basis of infinite target assumption with the de- cay function. Then the projectile is modeled with an explicit transient dynamic finite element code and the target is represented by the forcing function as the pressure boundary condition. This methodology eliminates discretizing the target as well as the need for a complex contact algorithm and is implemented in ABAQUS explicit solver via the user subroutine VDLOAD. It is found that the free-surface effect must be considered in terms of the projectile deformation, residual velocity, projectile trajectory, ricochet limits and critical reverse velocity. The numerical predictions are in good agreement with the available experimental data if the free-surface effect is taken into account.
