A e Specific constant in explosive material A h Material constant in Johnson-Holmquist material model a Volumetric modification coefficient B Material constant in Johnson-Cook material model B e Specific constant in explosive material B h Material constant in Johnson-Holmquist material model C Material constant in Johnson-Cook material model C h Material constant in Johnson-Holmquist material model C v Volumetric speed of sound or the intercept of the U S − U P curve D Damage parameter D 1 , D 2 Damage constant in Johnson-Holmquist model d 1 , d 2 , d 3 , d 4 , d 5 Material constants in Johnson-Cook material model E Internal energy f c Unconfined compressive strength of concrete F Fraction burn parameter K 1 , K 2 , K 3 Pressure constant in Johnson-Holmquist material model M Material constant in Johnson-Cook material model N Material constant in Johnson-Cook material model N h Material constant in Johnson-Holmquist material model P Applied pressure P eos Pressure of the equation of state P * Normalized pressure

Tandem projectile is one approach of the development of anti-structure concrete projectile, which is made of the forward shape charge and the follow-through projectile. In this paper, in order to study the performance of anti-structure tandem projectiles, experimental and numerical analyses of the penetration process were performed for forward shape charge with conical copper liner hitting into the concrete targets. Having a well agreement, numerical and empirical results indicate that a forward shape charge with a conical copper liner will make appropriate tunnel diameter through the concrete targets. Following the validation of the applied numerical method, numerical simulations were conducted for the penetration of the follow-through projectile, by three different concrete targets: undamaged concrete, pre-drilled concrete, and damaged pre-drilled concrete. The parametric results show that the damaged pre-drilled concrete affects the penetration depth and residual velocity of the follow-through projectile significantly.

The main objective of this research is to evaluate a proposed semi‐analytical model for penetration process of rigid projectile in concrete and concrete/metal targets using experimental and numerical methods. In theoretical analysis of this study, the dynamics cavity expansion theory and the wave reflection time in the form of tensile in concrete slab are used. The effect of the friction coefficient is also investigated during the penetration process. The equations are then generalized for two‐layered targets made out of concrete and steel. A series of penetration tests and numerical simulations in LS‐DYNA software are conducted to evaluate the proposed model. The main obtained parameters are residual velocity, penetration depth, and ballistic limit velocity. The analytical results are compared with experimental and numerical data. These results are in agreement with each other.