## 4 Numerical Results and Discussion
### Out-of-Plane Simulation
#### 4.1.2 Damage Kinetics  
Figure 37 shows the failing process of the \(8\times 8\times 8\) specimen simulation under 1.0 MPa loading. Before 75 us, the input bar moved rapidly toward the output bar. Then, they moved forward together at relatively the same velocity until 135 us. After this moment, some sub-laminates were squeezed out and torn, becoming many fragments, as shown at 200 us in Figure 37a-c. During this period, the output bar became still, and the input bar again moved rapidly toward the output bar. Moreover, with the input bar moving, more and more sub-laminates were squeezed out and torn, becoming fragments, as shown in Figure 37b,c. Finally, the fragments separated from the specimen, while the main body of the specimen was divided into several big blocks, as shown in Figure 37d. By comparing Figure 37 with Figure 38, it can be seen that the two features of the simulation result were similar to those of the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter: Value** & **Parameter: Value** \\ \hline Density, \(\rho\) (kg/m\({}^{3}\)) [4]: 0.97 & AOPT, MACF [4]: 3.0, 1.0 \\ Young’s modulus, E\({}_{\text{a}}\), E\({}_{\text{b}}\), E\({}_{\text{c}}\) (GPa): 70, 70, 8 & Tensile strengths, \(X_{\text{T}}\), Y\({}_{\text{T}}\), Z\({}_{\text{T}}\) (GPa) [4]: 3, 3, 3 \\ [PERSON]’s ratio, \(\gamma_{\text{b}a}\), \(\gamma_{\text{c}a}\), \(\gamma_{\text{c}b}\) [4]: 0.006, 0.06, 0.06 & Compressive strengths, \(X_{\text{C}}\), \(Y_{\text{C}}\), \(Z_{\text{C}}\) (GPa) [4]: 2, 2, 2 \\ Shear modulus, C\({}_{\text{ab}}\), C\({}_{\text{bc}}\), C\({}_{\text{ca}}\) (GPa) [4]: 4.6, 5, 5 & Shear strengths, \(S_{\text{ba}}\), \(S_{\text{ca}}\), \(S_{\text{cb}}\) (MPa): 600, 600, 600 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Material model properties of UHMWPE composite used in the out-of-plane direction [4]. Figure 36: The experimental and simulated initial waves under out-of-plane loading: (**a**) non-damaged situation under 0.6 MPa loading; (**b**) damaged situation under 1.0 MPa loading. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter: Value** & **Parameter: Value** \\ \hline Normal strength, T, (MPa) [14]: 1.0 & Shear strength, S (MPa) [24]: 1.6 \\ Normal stiffness, E\({}_{\text{N}}\) (MPa/mm): 400.0 & Shear stiffness, E\({}_{\text{T}}\) (MPa/mm) [24]: 689.0 \\ Energy release rate for mode I, G\({}_{\text{C}L}\), (MPa-mm): 0.05 & Energy release rate for mode II, G\({}_{\text{iL}}\), (MPa-mm) [24]: 0.1016 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Material model properties of cohesive element used in the out-of-plane direction [14,24]. experimental result; the layers were squeezed out and torn to fragments, while the main body of the specimen was divided into several relatively big blocks. The contours of the simulation specimen at a certain moment are shown in Figure 39. As shown for the simulation specimen in Figure 39a, the effective stress distribution across the sub-laminates at the two end faces was relatively higher than the effective stress distribution at the center. As the sub-laminates at the end faces failed, some elements were deleted while some elements remained. At the edge of the remaining elements, the effective stress became lower. Correspondingly, the elements at the edge had a higher effective strain than the other elements, as shown in Figure 39b. As shown in Figure 39c, a greater misalignment between two adjacent sub-laminates resulted in a greater effective strain of the cohesive elements in the corresponding region. At this moment, the misalignment of the two adjacent sub-laminates at the end faces was greater than the misalignment at the center. Thus, the effective strain of cohesive elements near the end faces was higher. With regard to the end face at the front, the misalignment was higher at the lower left corner; thus, the effective strain of cohesive elements in this region was higher. The cohesive element was deleted when the damage degree reached \(1.0\).