This paper investigates the prediction of the depth of penetration (DOP) for concrete targets under high-speed projectile impact using multiple simulation algorithms in LS-DYNA. Three numerical methods, i.e., the traditional finite element method (FEM), a fixed-coupling FEM-SPH (Smooth Particle Hydrodynamics) model, and an adaptive coupling FEM-SPH model, are employed to simulate the penetration processes. The computational results are compared against established empirical formulas to evaluate their predictive accuracy and efficiency. The findings indicate a distinct trade-off between numerical precision and computational cost. The adaptive FEM-SPH algorithm achieves the highest accuracy, with a maximum error of less than 10% across considered velocity ranges, and effectively captures cavity expansion effects. The standard FEM algorithm offers the highest computational efficiency, requiring less than half the time of the other methods, albeit with a maximum error of up to 25%. The fixed-coupling FEM-SPH model provides an intermediate solution, showing improved accuracy at velocities above 400 m/s but lower efficiency. This comparative analysis offers a practical guideline for selecting appropriate simulation techniques in protective structure design, balancing the demands for rapid estimation, detailed physical insight, and final safety verification.
Li et al. (Sun,) studied this question.