## 4 Results and Discussion  
### Comparisons with Available Test Data  
Figure 4 presents a comparative analysis of numerical predictions and experimental data for 5.73 mm thick fiber-metal laminates (FMLs), which are constructed from polypropylene (PP) fiber and PP matrix composites. These laminates were subjected to a transverse impact by a hemispherical impactor weighing 46.7 g with a diameter of 12.7 mm, delivering an impact energy of 300 J with a corresponding impact velocity of 113 m/s [7]. The material parameters utilized in the numerical simulations are detailed in Tables 1 and 2. The numerical predicted results obtained by [PERSON] et al. [14], who employed the elastoplastic model for both metal and PP/PP materials, are also presented in the figure, alongside \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} Basic \\ parameters \\ \end{tabular} } & \(\rho\)(kg/m\({}^{3}\)) & \(E\)(GPa) & \(\
u\) & \(T_{m}\)(K) & \(T_{a}\)(K) & \(\chi\) & \(C_{p}\)(J/kgK) \\ \cline{2-8}  & 2700 & 72 & 0.3300 & 775 & 293 & 0.9000 & 875 \\ \hline \multirow{2}{*}{\begin{tabular}{c} Equation of \\ state \\ \end{tabular} } & \(C_{0}\)(m/s) & \(S_{1}\) & \(\Gamma_{0}\) & & & & \\ \cline{2-8}  & 5328 & 1.3380 & 2 & & & & \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Strength \\ model \\ \end{tabular} } & \(A_{t}\)(MPa) & \(B_{t}\)(MPa) & \(n_{t}\) & \(A_{s}\)(MPa) & \(B_{s}\)(MPa) & \(n_{s}\) & \(C\) \\ \cline{2-8}  & 369 & 684 & 0.7300 & 369 & 684 & 0.7300 & 0.0083 \\ \cline{2-8}  & \(\dot{\varepsilon}_{qs}\) (s\({}^{-1}\)) & \(m\) & & & & & \\ \cline{2-8}  & \(3.3\times 10^{-4}\) & 1.7 & & & & & \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Failure \\ criterion \\ \end{tabular} } & \(C_{1}\) & \(C_{2}\) & \(C_{3}\) & \(C_{4}\) & & & & \\ \cline{2-8}  & 1.466 & 2.394 & 0.210 & 0.005 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of various parameters for 2024-T3 aluminum alloy in JC(+BW) model [7,24]. Figure 3: The relationship between \(\sigma^{T}/\sigma^{RM}\) and \(T^{*}\) at a plastic strain of 0.14.  
the numerical results derived by the authors using the JC + BW model for 2024-T3 aluminum. It is evident that the failure patterns of FMLs predicted by the current model exhibit strong concordance with the test results. It also reveals that the failure pattern on the rear face predicted by the present model aligns more closely with the experimentally observed failure patterns than those predicted by the Guan model and the JC + BW model. Although the JC constitutive model effectively predicts the hole-opening on the impact face and cross-sectional deformation, it fails to provide an accurate forecast of the initial crack propagation. Prior to penetration by the projectile, the aluminum alloy can fully deform independently and absorb energy due to the superior plastic properties of PP/PP between aluminum alloy layers. As damage to the metal accumulates to a critical threshold, initial cracks develop, ultimately resulting in tearing failure on the rear surface. Figure 4: Comparison between the numerical predicted results and experimental observations at an impact energy of 300 J (The color represents the degree of damage). The stress triaxiality-time history at the central point on the rear surface is illustrated in Figure 5. Prior to the removal of the element, the value of stress triaxiality remained consistently stable at approximately 0.65. Under impact loading, the rear surface will experience tensile deformation, whilst compressive deformation will occur in the thickness direction due to the contact between the projectile and target. As a result, this element is subjected to in-plane tensile stress and compressive stress in the thickness direction, which is different from the stress state of uniaxial tension (i.e., \(\eta=1/3\)), thereby leading to distinct fracture characteristics, as shown in Figure 4.  
Figure 6 shows energy-time histories at an impact energy of 300 J.