Numerical Evaluation of Dynamic Constitutive Models and Modified Analytical Modeling for High-Velocity Penetration of Ultra-High-Performance Concrete (UHPC)

Abstract

Abstract This study evaluates and improves models for predicting the high-velocity penetration response of ultra-high-performance concrete (UHPC) used in protective structures. The research scope involves systematically comparing three common concrete constitutive models: Holmquist–Johnson–Cook (HJC), Riedel–Hiermaier–Thoma (RHT), and Karagozian & Case (K&C). First, the models' theoretical differences regarding strain-rate effects and tension-compression asymmetry were analyzed. Next, their material parameters were calibrated using fundamental mechanical tests and literature data. An LS-DYNA finite element model was then established and validated against ballistic experiments (633-959 m/s) by evaluating penetration depth, surface crater morphology, and internal damage evolution. The results indicate that the HJC model is the optimal choice for high-velocity penetration simulations. It yielded the lowest average depth error (-11.89%), and its localized damage pattern best matched UHPC's high-strength and high-toughness traits. In contrast, the RHT model caused premature matrix softening under high hydrostatic pressure, leading to a -21.76% error. The K&C model overpredicted surface funnel-shaped crater damage, with its penetration depth error increasing to -26.34% at high velocities. Furthermore, extended simulations at 800–1500 m/s revealed that the traditional Forrestal analytical model deviates significantly in the ultra-high-velocity regime. To solve this, a modified analytical model tailored for UHPC was developed. By accounting for dynamic yield and high-pressure shear rheological softening mechanisms, the new model introduces a dynamic strengthening coefficient and a rheological softening factor. Ballistic validation demonstrates that, within the validated range, the theoretical predictions of this modified model match the experimental data well, with a maximum relative error of 14.54%. Overall, this research provides reliable numerical model selection and theoretical support for designing and evaluating UHPC protective structures against kinetic energy projectile impacts.