## 4 Numerical Results and Discussion
### Out-of-Plane Simulation  
#### 4.1.1 Numerical Model  
The FE model of the bars and specimen is shown in Figure 34. The size of the specimen was \(8\times 8\)\(\times 4\) mm. The loading direction and out-of-plane direction were both parallel to the \(z\)-axis direction. The out-of-plane direction was the \(x\)-axis direction. The specimen was discretized into 20 sub-laminates to form multiple layers through the thickness [4; 23]. Each sub-laminate contained two layers of elements, as shown in detail in Figure 34, which represents one [0\({}^{\circ}\)/90\({}^{\circ}\)/0\({}^{\circ}\)/90\({}^{\circ}\)] stack. A layer of cohesive element between sub-laminates was applied [52]. Figure 33: Traction–separation law of a cohesive element. In addition, according to Reference [23], a small gap between two neighbor sub-laminates could solve the over-penetration of elements to some extent. Therefore, a small thickness was defined for the cohesive element. As shown in Figure 35, the influence of different gap thicknesses under 0.4 MPa loading was determined. A larger gap thickness resulted in the slope of the non-linear period of the simulation result being closer to the experimental result. The slope of the linear period and the maximum stress did not vary with the gap thickness. Therefore, a gap thickness of \(1.0\times 10^{-2}\) mm was applied. Thus, the sum of all gaps was 0.19 mm, which is small (\(<\)5%) compared to the total thickness of the specimen; it could then be considered to have a negligible effect on the ballistic performance [23]. This result also indicates that the non-linear period was mainly caused by the gap between sub-laminates. The element size of the sub-laminate was 0.2/0.2/0.1 mm. The total element amount of the specimen was 94,000, in which the element amount of sub-laminates was 64,000 and the element amount of cohesive element was 30,400. The sub-laminate was studied using the *MAT_COMPOSITE_FAILURE_SOLID_MODEL. Since the composite plate used here and the plate used in Reference [4] were taken from the same factory, the material parameters shown in Table 6 were derived from Reference [4]. The AOPT is Material axes option and the MACF is Material axes change flag for brick elements. The cohesive material parameters mostly derived from Reference [24] are shown in Table 7, in which T was cited from Reference [14]. G\({}_{\text{IC}}\) and G\({}_{\text{IIC}}\) are equal to T*E\({}_{\text{N}}\)/2 and S*E\({}_{\text{T}}\)/2, respectively, as shown in Figure 33. According to the current slope of the linear period of the dynamic stress-strain curve, E\({}_{\text{a}}\)/E\({}_{\text{b}}\) and Ec were estimated as ranging from 93 GPa and 11.5 GPa to 70 GPa and 8 GPa [25]. Because the shear failure happened during loading, S\({}_{\text{ba}}\), S\({}_{\text{ca}}\), and S\({}_{\text{cb}}\) were estimated as ranging from 500 MPa in Reference [4] to 600 MPa, thereby better fitting the current maximum stress and its increasing trend. E\({}_{\text{N}}\) and E\({}_{\text{T}}\) were estimated  
Figure 34: The simulated model of specimen under out-of-plane loading. Figure 35: The simulation results of different gap values between sub-laminates: (**a**) stress–strain curves; (**b**) first derivative of stress–strain curves. according to the notion that, if they are higher, the slopes of the non-linear and linear periods would also be higher. The dynamic tests could allow obtaining more suitable material parameters for the current specimen applied in the numerical model. The material properties and failure criterion of the numerical model have a comprehensive relationship with both sub-laminates and cohesive elements. Therefore, in future work, it will be essential to separately study the dynamic properties of the fiber and dynamic cohesive properties of the matrix, and then study the integrated criterion. In order to compare the results with the initial wave obtained by the strain gauges in the experiments, two elements in the middle of the input and output bars were chosen to use their strain evolution as initial waves.