Analytical model of penetration depth and energy dissipation considering impact position

In the research of projectile penetration into reinforced concrete, the discreteness of penetration depth widely exists in the experiments and empirical formulas, and different impact positions are one of the main reasons for this discreteness. However, the existing theoretical models considering impact position require self-programming methods to solve, and analytical solutions for penetration depth have not been provided. Moreover, existing penetration depth formulas have not dealt with the influence of impact position on penetration depth. To incorporate the influence of the impact position in the penetration depth formulas, this study has investigated different impact positions of the projectile penetration. Herein, the Young formula is used as an example, the projectile penetration process is regarded as a uniformly variable motion based on the constant resistance assumption, two methods are used to obtain the penetration constant resistance, and the energy dissipation of the steel bar at three typical impact positions is theoretically modeled. Finally, analytical solutions for the penetration depth at the three positions are proposed and the mechanism of differences at the three typical impact positions is revealed. In addition, finite element models are established for the three impact positions based on published penetration tests. The penetration depth and steel bar energy consumption of the three impact positions are compared and analyzed, and the analytical model is verified. The results suggest that different impact positions can cause different energy consumption of the steel bar, ultimately leading to varying penetration depth. This analytical model, which fully considers the impact positions of the projectile and the arrangement of the steel bars, can be generalized to any penetration resistance theoretical model or penetration depth calculation formula. It can play an important role in further improving and developing the penetration depth calculation formula, and guiding the design of reinforced concrete protection engineering.