## 3 Results and Discussions  
### Impact Dynamics  
The contact force and absorbed energy are two important parameters in low-velocity impact analysis process. Therefore, the contact force histories and absorbed energy histories from the experiments and simulations are clearly presented in this section. The typical force-time (_f-t_) history curve consists of an ascending section of loading until reaching a peak force, and a descending section of unloading. In the _f-t_ curve, the oscillations demonstrate the possibility of failures in the material caused by the reduced stiffness of the material, and no sudden force drop implies that the material have higher resistance under low-velocity impact. The peak force on the _f-t_ curve is an important index to evaluate the load capacity of composite laminates after impact. Before reaching the peak force value, the smooth trend on the f-t curve represents the elastic response of composite laminates, and the first sudden force drop reveals the development of a crack on the impacted side of composite laminates or the occurrence of delamination. After reaching the peak force value, a sudden drop in the magnitude of force indicates the occurrence of perforation on the impacted side of composite laminates. Figure 6 shows the typical force-time history curves for different laminates from experimental and numerical results for the case of 32 J of impact energy, and (a)-(d) indicate the laminate types of I, II, III and IV, respectively. As seen from Figure 6, the _f-t_ curve obtained by numerical simulations matches well with the _f-t_ curve obtained by experiments, except for that of the laminate of \([0/90]_{8}\). It is remarkable that the numerical simulation can predict the peak force values well in all specimens, and the level of peak force values obtained from numerical calculations is almost identical to the level of peak force values obtained from experimental tests. Moreover, in terms of peak force, the laminate-stitched SMAs have a larger load capacity than the laminate-unstitched SMAs. In terms of the trend of the _f-t_ curve, the laminate-stitched SMAs have smaller damages than the laminate-unstitched SMAs. Figure 4: Finite element model of composite laminate under impact loading. Figure 5: Schematic diagram of different types of laminates under different impact energies. The absorbed energy of composite laminates is relevant to the area under the force-time history curve, which can be calculated by the following equation:  
\[E_{a}=V_{0}\int_{0}^{t}F_{t}dt-\frac{1}{2}m(V_{0}-V_{t})^{2} \tag{14}\]  
where \(E_{a}\) is the absorbed energy of composite laminates subjected to low-velocity impact, \(V_{0}\) and \(m\) are the impactor's initial velocity and mass, respectively, and \(F_{t}\) and \(V_{t}\) are the impact force and impact velocity at time \(t\), respectively. Figure 7 show the absorbed energy-time (_e-t_) history curves for different laminates from experimental and numerical results for the case of 32 J of impact energy, and (a)-(d) indicate the laminate types of I, II, III and IV, respectively. As seen from Figure 7, the _e-t_ curve obtained by numerical simulations does not match very well with the _e-t_ curve obtained by experiments. It is also found that the maximum absorbed energy values are predicted well in all of the test specimens, and the level of the maximum absorbed energy values obtained from the numerical calculations is almost identical to the level of the maximum absorbed energy values obtained from experimental tests. However, the absorbed energy in the final state is not well-predicted. It is remarkable that the numerical simulation can predict the maximum absorbed energy values, but it does not predict the ultimate energy absorption capacity of composite laminates specimens well in the no-perforation condition of the 32-J case.