## 3 Numerical Simulation Analysis  
### Simulation Model Setup  
The projectile used in this paper was a solid projectile. The diameter of the projectile was 30 mm, the length was 205 mm, the curvature-diameter ratio \(\varphi\) was 4 and the head of the projectile had a 2 mm fillet. The mesh size of the projectile was 2 mm. The target had a 600 mm \(\times\) 600 mm square area and the target thickness was 1 m. To reduce the computation period, the target was processed in two steps. First, because forward penetration was studied in this paper, 1/4 of the models were used for modeling. Second, grid densification was carried out within the range of 150 mm \(\times\) 150 mm (in the red box in Figure 6) centered on the impact point of the projectile to improve the contact accuracy of the projectile target. The mesh size of the encrypted area was 2 mm. The remaining part adopted the grid processing method of the grid's gradual change (the direction indicated by the red arrow in Figure 6), and the gradual change rate was 1.03 to ensure correct stress wave propagation and crack propagation in the target. The 3D modeling of the target and the projectile is shown in Figure 6.  
In the model, the projectile consisted of 30 CrMnSiNi2A, of which the material parameters are shown in Table 5. The targets were red sandstone and limestone. Since the projectile velocity studied in this paper was 600-1200 m/s, which belongs to the medium and low speed ranges, and the penetration process had little impact on the projectile shape and quality, the projectile was regarded as a rigid body for numerical simulation and the projectile adopted the \"MAT_RIGID material model, as shown in Table 5. Limestone adopted the \"MAT_RHT material model. The projectile-target contact used \"CONTACT_ERODING_SURFACE_TO_SURFACE to describe the interaction between the projectile and target.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Material** & **Density/ (g cm\({}^{-3}\))** & **Young’s Modulus/GPa** & **Poisson’s Ratio** \\ \hline Projectile & 30 CrMnSiNi2A & 7.85 & 211 & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Main parameters of projectile materials.  
Figure 6: Establishment of 3D model: (**a**) projectile model; (**b**) sectional view of target 1/4 model; (**c**) target impact surface 1/4 model.  
The Riedel-Hiermaier-Thoma (RHT) constitutive model, proposed by [PERSON], [PERSON], [PERSON] and [PERSON] in 1999, comprehensively considers various damage factors of concrete, such as compression damage, cracking and softening [42; 43]. The RHT model integrates the characteristics of various constitutive models describing concrete materials, considers various phenomena, such as compression damage, strain hardening, strain softening and cracking softening after failure, and is suitable for calculating the deep penetration process of rock and concrete materials [44; 45].  
According to the results of the quasistatic test, dynamic mechanical test and Brazilian disc splitting test, key parameters such as the uniaxial compressive strength and tensile strength were fitted, and then other parameters were obtained by reference to previous tests [46]. Finally, the different rock material model parameters are shown in Table 6.