## 3 Perforation Model Validation
### Numerical Results, Validation and Discussion  
In this work, five penetration simulations with different striking velocities (\(V_{s}\)), were carried out to validate the numerical model. After simulation, numerical predictions of projectile residual velocities (\(V_{r,n}\)) were compared against test data (\(V_{r,e}\)) as shown in Figure 7a. As listed in Table 4, the numerical predictions agreed well with the test data. It is also suggested that with a 436 m/s striking velocity, the projectile perforated the SC wall with quite a small residual velocity which was overestimated by the numerical model. Figure 7b shows the projectile velocity history during perforation, implying that it takes less time to perforate the SC wall at higher striking velocity.  
Figure 8 compares the post-test target and numerical results from different views. Figure 8a shows the constraints of the target, which was fixed in the steel frame. The actual destructive forms of the rear target are also shown. A three-stage perforation model [16; 40] consisting of front impact crater, ballistic tunnel, and a nearly frustum-of-cone shaped rear crater is shown in Figure 8b. In Figure 8c, the steel plate deformation is shown and it was notable that the neighboring area of the plate around the projectile suffers severe deformation. From a cross-section view of the SC walls, Figure 8d illustrates the damage mode of the target in which the foregoing three-stage thick plate model was numerically verified. From the validation results in terms of damage mode and residual velocity, the numerical predictions match well with SC wall perforation tests.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**RO** & **G** & **\(A\)** & **B** & **C** & **\(N\)** & **FC** & **T** & **EPSO** & **EFMIN** \\
2.24 & 0.1486 & 0.79 & 1.6 & 0.007 & 0.61 & \(4.1\times 10^{-4}\) & \(4.1\times 10^{-5}\) & \(1\times 10^{-6}\) & 0.01 \\ \hline
**SFMAX** & **PC** & **UC** & **PL** & **UL** & **D1** & **D2** & **K1** & **K2** & **K3** \\
7.0 & \(1.6\times 10^{-4}\) & 0.001 & 0.008 & 0.1 & 0.04 & 1.0 & 0.85 & \(-1.71\) & 2.08 \\ \hline \end{tabular}
\end{table}
Table 1: Material parameters of concrete (units: cm-g-\(\upmu\)s).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**RO** & **G** & **\(A\)** & **B** & **N** & **C** & **M** & **TM** & **TR** & **EPSO** \\
7.896 & 0.818 & \(35\times 10^{-3}\) & \(2.75\times 10^{-3}\) & 0.36 & 0.022 & 1 & 1793 & 293 & \(1\times 10^{-6}\) \\ \hline
**CP** & **PC** & **SPALL** & **IT** & **\(D_{\bf 1}\)** & **\(D_{\bf 2}\)** & **\(D_{\bf 3}\)** & **\(D_{\bf 4}\)** & **\(D_{\bf 5}\)** & **C2/P** \\
0.452\(\times 10^{-5}\) & 0 & 2 & 0 & \(-0.8\) & 2.1 & \(-0.5\) & 0.0002 & 0.61 & 1 \\ \hline \end{tabular}
\end{table}
Table 2: Material parameters of steel plate (units: cm-g-\(\upmu\)s).  
Figure 6: Finite element model. (**a**) Projectile; (**b**) concrete slab; (**c**) reinforcement mesh; (**d**) rear steel plate (**e**) projectile impact SC walls.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Part** & **Projectile** & **Concrete Slab** & **Steel Mesh** & **Steel Plate** \\ \hline Number of elements & 800 & 1,822,500 & 8712 & 18,496 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Element numbers for each component of the SC wall perforation model.  
Figure 7: Numerical results of projectile perforation on SC walls. (**a**) Residual velocity comparison; (**b**) projectile velocity evolutions.