## 4 Numerical Results and Discussion
### In-Plane Simulation  
#### 4.2.1 Numerical Model  
The FE model of bars and specimen is shown in Figure 44. The size of the specimen was \(8\times 8\times 8\) mm. The loading direction was parallel to the \(z\)-axis direction. The out-of-plane direction was parallel  
Figure 42: The experimental and simulated stress–strain curves of different specimens under the same impact velocity: (**a**) effect of thickness; (**b**) effect of diameter/area; (**c**) effect of cross-section shape. Figure 43: The experimental and simulated first-derivative curves of different specimens under the same impact velocity: (**a**) effect of thickness; (**b**) effect of diameter/area; (**c**) effect of cross-section shape. to the _x_-axis direction. The specimen was discretized into 96 sub-laminates to form the multiple layers through the thickness [4; 23]. Each sub-laminate contained one layer of elements, as shown in detail in Figure 44, which represents one [0\({}^{\circ}\)/90\({}^{\circ}\)] stack. A layer of cohesive element between sub-laminates was applied [52]. As mentioned above, a small thickness was defined for the cohesive element to solve the over-penetration of elements to some extent [23]. A gap thickness of 0.001 mm was applied. Thus, the sum of all gaps was 0.095 mm, which is small (\(<\)5%) compared to the total thickness of specimen. The element size of the sub-laminate was 0.0833/0.0833/0.1667 mm. The total element amount of specimen was 880,128, in which the element amount of sub-laminates was 442,368 and the element amount of cohesive element was 437,760. The sub-laminate was studied using the *MAT_COMPOSITE_FAILURE_SOLID_MODEL. The material parameters are shown in Table 9, and they were derived from Reference [4]. According to the current slope of the experimental stress-strain curves, E\({}_{\text{a}}\)/E\({}_{\text{b}}\) and Ec were estimated as 30 GPa and 4.7 GPa to get better agreement with the modulus [25]. The failure of layers during this loading direction was bending, and the bending strength was smaller than the punch-shear strength. The punch-shear strength of UHMWPE laminate is \(\sim\)160 MPa [4]; thus, the S\({}_{\text{ca}}\)/S\({}_{\text{cb}}\) applied here, which was 70 MPa and smaller than 160 MPa, could be considered acceptable. The cohesive material parameters, which were mostly derived from Reference [24], are shown in Table 10, in which T is cited from Reference [14]. G\({}_{\text{G}}\) and G\({}_{\text{IIC}}\) were equal to T*E\({}_{\text{N}}\)/2 and S*E\({}_{\text{T}}\)/2, respectively, as shown in Figure 33.  
In order to compare the results with the initial wave obtained by the strain gauges in the experiments, two elements on the middle of the input and output bars were chosen to use their strain as initial waves. As shown in Figure 45, under 0.2 MPa loading, the value, wave length, and trend of strain of the simulation results were similar to the features of experimental strain. \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, 3.0 \\ Young’s modulus, E\({}_{\text{a}}\), E\({}_{\text{b}}\), E\({}_{\text{c}}\) (GPa): 30, 30, 4.7 & Tensile strengths, X\({}_{\text{T}}\), Y\({}_{\text{T}}\), Z\({}_{\text{T}}\) (GPa) [4]: 3, 3, 3 \\ Poisson’s ratio, \(\
u_{\text{ba}}\), \(\
u_{\text{ca}}\), \(\
u_{\text{cb}}\) [4]: 0.06, 0.06, 0.006 & Compressive strengths, X\({}_{\text{C}}\), Y\({}_{\text{C}}\), Z\({}_{\text{C}}\) (GPa) [4]: 2, 2, 2 \\ Shear modulus, \(\text{C}_{\text{ab}}\), G\({}_{\text{bc}}\), \(\text{C}_{\text{ca}}\) (GPa) [4]: 4.6, 5, 5 & Shear strengths, \(\text{S}_{\text{ba}}\), \(\text{S}_{\text{ca}}\), \(\text{S}_{\text{cb}}\) (MPa): 600, 70, 70 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Material model properties of cohesive element used in out-of-plane direction [14; 24]. Figure 44: The simulated model of specimen under in-plane loading.