## 3 Numerical Modeling  
The numerical simulations were performed using the Autodyn-3D finite element program, which has a good function for simulating high-strain-rate phenomena, such as impact and explosion [14]. The 3D modeling was performed using smooth particle-fluid dynamics (SPH) coding and Lagrange coding. SPH is a meshless modeling technology, and the debris cloud phenomenon generated by high-speed impact can be effectively simulated by using SPH coding. Lagrange coding is suitable for large deformations caused by tension or shear loadings and internal material fracture problems [15]. The relatively low-strain-rate deformation parts (rear plate) of the model were solved by the Lagrange coding, and the high-strain-rate deformation parts (projectile and bumpers) were solved by the SPH coding, which made the simulation accurate and efficient. In this study, the Johnson-Cook material model (JC model) was used for the Al 7075-T651 projectile and shields. In this model, the stress equation is expressed as  
\[\sigma=(A+B\varepsilon_{p}^{n})\Big{(}1+C\ln(\dot{\varepsilon}_{p}/\dot{ \varepsilon}_{p0})\Big{)}\Bigg{(}1-\Bigg{(}\frac{T-T_{0}}{T_{m}-T_{0}}\Bigg{)} ^{m}\Bigg{)} \tag{1}\]  
where \(\varepsilon_{p}\) and \(\dot{\varepsilon}_{p}\) is the plastic strain and plastic strain rate, respectively. \(A,B,C,m,n,\dot{\varepsilon}_{p0},T_{0}\) and \(T_{m}\) are the constants determined by the experiment and \(T\) is the absolute temperature. A detailed description of the JC model can be found in Ref. [16]. The JC model parameters are given in Table 2[17]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Values** \\ \hline Density (g/cm\({}^{3}\)) & \(\rho_{0z}\) & 2.804 \\ Shear modulus (GPa) & \(G\) & 29 \\ Static yield strength (GPa) & \(A\) & 527 \\ Strain-hardening coefficient (GPa) & \(B\) & 575 \\ Strain-hardening exponent & \(n\) & 0.72 \\ Strain rate coefficient & \(C\) & 0.017 \\ Reference strain rate (s\({}^{-1}\)) & \(\dot{\varepsilon}_{0}\) & 1.0 \\ Thermal softening exponent & \(m\) & 1.61 \\ Reference temperature (K) & \(t_{0}\) & 298 \\ Melting temperature & \(t_{m}\) & 900 \\ Damage constant & \(D_{1}\) & 0.11 \\ Damage constant & \(D_{2}\) & 0.572 \\ Damage constant & \(D_{3}\) & \(-\)3.446 \\ Damage constant & \(D_{4}\) & 0.016 \\ Damage constant & \(D_{5}\) & 1.099 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The material parameters for Al 7075-T651 [17]. Figure 4: A diagrammatic sketch of the experimental apparatus. The Johnson-Holmquist material model (JH-2 model) was used for modeling the B4C layer of Configuration II. The actual equivalent stress is given as  
\[\sigma=(1-D)\sigma_{i}(p,\dot{\epsilon})+D\sigma_{f}(p,\dot{\epsilon}) \tag{2}\]  
where \(D\in[0,1]\) is the damage parameter. \(\sigma_{i}\) and \(\sigma_{f}\) are the actual equivalent intact stress and the fractured stress, which are the functions of pressure \(p\) and strain rate \(\dot{\epsilon}\). \[\sigma_{i}(p,\dot{\epsilon})=A\sigma_{HEL}\bigg{(}\frac{\sigma_{hyd}+p}{p_{ HEL}}\bigg{)}^{N}\big{(}1+C\ln(\dot{\epsilon}/\dot{\epsilon}_{0})\big{)} \tag{3}\]  
\[\sigma_{f}(p,\dot{\epsilon})=B\sigma_{HEL}(p/p_{ HEL})^{M}\big{(}1+C\ln\big{(}\dot{\epsilon}/\dot{\epsilon}_{0}\big{)}\big{)} \leq S_{f\text{max}}\sigma_{HEL} \tag{4}\]  
where \(A,N,C,B,M,S_{f\text{max}}\) are the dimensionless parameters, \(\sigma_{hyd}\) is the maximum tensile hydrostatic stress, \(\dot{\epsilon}_{0}\) is strain rate, \(\sigma_{HEL}\) and \(p_{HEL}\) are the equivalent stress and pressure at the Hugoniot elastic limit (HEL). A detailed description of the JH-2 model can be found in Reference [18] and the model parameters are given in Table 3 [19]. The non-linear orthotropic material model (Ortho model) developed in [20; 21; 22; 23] is used for modeling the UHMW-PE composite. The material model includes orthotropic coupling of the material volumetric and deviatoric response proposed by [PERSON] et al. [24], the non-linear equation of state and orthotropic hardening proposed by [PERSON] et al.