# A Sensitivity Analysis of the Damage Behavior of a Leading-Edge Subject to Bird Strike
## 4 Sensitivity Analysis
For each curve, only one parameter varies, while the other ones are set to their starting values. The performance of each configuration was evaluated in terms of both mass and crashworthiness; the latter deduced from the central point displacement and from the energy dissipated in the form of plastic deformation. Hereafter, for the sake of brevity, the comparison is reported considering only three configurations: the starting, the best and the worst one. Table 4 reports the design parameters for each of them, while Figures 9 and 10 show a comparison with respect to global displacement and plastic deformation state (ductile criteria) at several time steps. As reported in Table 4, the improved solution leads to an increase in structural mass since the core thickness is increased. However, compared to archived performance improvement, discussed below, this small weight increment (+4.7%) can be considered acceptable. Figures 9 and 10 highlight the effect of changing the skin parameters in terms of the thickness of the main components. The best configuration has an improved capability to dissipate the impact energy, and in particular, it is able to better redistribute the impact energy. In fact, the structure is able to store a greater amount of elastic deformation energy, which can generate the total rebound of the projectile and a greater deformation recovery. Therefore, the structure, when the impact is over, exhibits a smaller deformation state. The increase in global stiffness can be appreciated by comparing the deformation shape at the same time step. In fact, between 9 and 12 ms, the best solution has already rejected the bird, while in the starting configuration, this phenomenon occurs well beyond 12 ms. The worst configuration, on the other hand, presents a rapid and sudden catastrophic failure in the area close to the impact point. The skin tears itself completely and allows bird penetration. The bullet then finishes its run on the rear beam, totally destroying itself. Therefore, the remaining part of the structure is not able neither to absorb and convert energy nor to deform itself permanently. In fact, the distance between the ribs of this configuration is among the largest of the analyzed models. \begin{table}
\begin{tabular}{l c c c} \hline  & **Starting Configuration** & **Worst Configuration** & **Best Configuration** \\ \hline Inner thickness [mm] & 0.4 & 0.4 & 0.4 \\ Outer thickness [mm] & 1.4 & 0.4 & 1.4 \\ Core thickness [mm] & 6.35 & 6.35 & 12.7 \\ Total L.E. mass [kg] & 2.53 & 1.4 & 2.65 \\ \hline \end{tabular}
\end{table} 
Table 4: Design parameters of the starting, the best and the worst configuration. Figure 8: Sensitivity analysis results. (**A**) Apex displacement vs. thickness; (**B**) Apex displacement vs. mass. According to Figures 9 and 10, the starting and the best configurations are both able to absorb the kinetic energy of the bird not experiencing any critical damages. Indeed, in these cases, no bird penetration occurred, and the damages are localized on a wide area of the skin. Compared to the starting configuration, however, the plastic zones are concentrated around the impact area; on the other hand, the skin regions close to the ribs are subject to a smaller plasticization level, and so they are able to recover the deformation state. All that allows for a greater spring-back effect when the main impact event is over. In fact, from the previous images, it is possible to note that in the starting configuration, the plasticization reaches the regions close to the L-beams. On the other side, the worst configuration experienced penetration, and the damage is characterized by more localized and critical damages, as confirmed by the presence of fully damage elements, which are removed during the analysis, allowing the bird to pass through the structure. The associated plastic state, at the end of the simulation, is more localized with respect to previous cases. Figure 9: Von Mises stress for starting, best and worst configuration at different time steps.