## 3 Application of Full-Process Analyzing Method
### Numerical Simulations of Low-Velocity Impact Behavior
#### 3.1.2 Numerical Simulation Results  
Table 4 shows the numerical simulation results and the errors of the damage projection areas between experiments [18] and simulation results after the impact energies of 11.0 J, 16.8 J, 23.4 J. As seen from Table 4, the maximum error is 17.8%. Figure 5 shows the progressive damage process of the laminate and the projection diagrams of experimental and simulation damage after the impact of 16.8 J. As can be seen from it, at 0.1 ms, the punch contacted the laminate, but the laminate was not damaged; at 0.2 ms, the upper layers of the laminate were damaged by the mode of the delamination failure (DF); at 0.4 ms, the fiber compression failure (FCF) was found on the center of the laminate; at 0.6 ms, the fiber tension failure (FTF) was found at lower layers of the laminate for the first time; at 0.8 ms, the FTF and FCF were extended, but the DF was not extended; at 1.1 ms, the damage inside the laminate no longer expanded with the time increase, and the damage area reached the maximum. The damage modes from the center to the outside are orderly FTF, FCF, and DF. The images that were obtained by the experiment are similar to the impact damage results that were obtained by the simulation. Therefore, the simulation results are consistent with the experimental results, which prove the rationality of the full-process analyzing method that was developed in this paper.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Impact Energy (J)** & **Experiment [18] (mm2)** & **Simulation (mm2)** & **Error (\%)** \\ \hline
11.0 & 522 & 477.8 & 8.5 \\
16.8 & 770 & 633.5 & 17.8 \\
23.4 & 1415 & 1241.7 & 12.3 \\ \hline \end{tabular}
\end{table}
Table 4: Comparison between experiment and simulation for the damage projection area.  
Figure 4: Finite element model of the stitched laminate.  
Throughout the process of impact, Figure 6 shows the final failure of each layer. When the punch impacts the laminate, the laminate undergoes concave deformation, which results in the compressive phenomenon in the upper layers and the tensile phenomenon in the lower layers. Therefore, on the upper layers of the laminate, the damage modes are mainly the FCF and MCF, but on the lower layers of the laminate, the damage modes are mainly the FTF and matrix tension failure (MTF). Figure 7 shows the final failure of each interface. The DF is found in every interface of the laminate. From the view of the damage area of the DF, the distribution of the area shows the shape of a Pyramid, namely, from the upper layers of the laminate to the lower layers, the damage areas of the DF are changed from small to large, which means that the effect of compressive stress is greater than that of tensile stress. Moreover, the SBF cannot be found in the whole process of the impact.  
Figure 5: Progressive damage process of the laminate and the damage projection diagrams obtained by experiment [18] and simulation after the impact of 16.8 J. Note: (1) DF: delamination failure; (2) FTF: fiber tensile failure; (3) FCF: fiber compressive failure; (4) MTF: matrix tensile failure; (5) MCF: matrix compressive failure; (6) FMSF: fiber-matrix shear failure; and, (7) SBF: suture breakage failure.  
Figure 6: Final failure of each layer after the impact of 16.8 J.