## 3 Results
### Helmet Evaluation and Optimization Based on YEAHM Response  
Although the helmet with a 40 mm thick liner presented a better response regarding the acceleration curves plotted in Figure 8, an additional analysis was performed with YEAHM. This analysis is considered important to assess the helmet from a biomechanical point of view. This evaluation consists in determining the risk of head injuries for each helmet thickness. Thus, it is possible to compare the helmets to determine which thickness makes it safer. Figure 10: Maximum deformation of a liner with a thickness of 40 mm: (**a**) First impact. (**b**) Second impact. Figure 9: Maximum deformation of a liner with a thickness of 35 mm: (**a**) First impact. (**b**) Second impact. To perform such analysis, the acceleration-time histories given in Figure 8 were used to drive YEAHM, by inducing them to YEAHM's skull. The criteria and respective thresholds previously reviewed in [56] are used together with YEAHM to perform an injury risk analysis. Table 7 summarizes the maximum values computed for each criterion. The results presented in Table 7 show a better performance by the thicker helmet. In the analysis with YEAHM, the lowest values given in Table 7 were computed with the 40 mm thick liner. The difference between the results computed for this helmet is significant. Nevertheless, these results were expected since the impacts were linear, and the significant lower accelerations were computed for the 40 mm thick helmet. In general, the results given in Table 7 correspond to very localized regions. In other words, the maximum values for each criterion were experienced by very small volumes of the brain, which may explain why some maximum pressure values are not linear with the peak accelerations, as other parameters are. The rest of the brain usually experiences much lower values for each criterion. However, this difference is not so significant for brain pressure. A considerable volume of the frontal lobes is under pressure values of almost the level of its maximum value. This was verified in all the impacts with these four helmets and in the ones performed with the certified helmet. Additionally, by comparing the results in Table 7 with the thresholds presented in the literature, injuries are predicted with all the helmets. The only one that did to exceed all the limits was obviously the one with a 40 mm thick liner. For some injury criteria, it has values in the range of given thresholds, between the lowest and the highest ones. However, this was only verified for strain and CSF pressure. The levels of brain pressure and von Mises stress in the brain were much higher than the proposed thresholds in the literature. These high predicted values cannot be justified with just the helmet response. Contrary to most of strain thresholds experimentally measured and proposed in the literature, the pressure and von Mises stress thresholds were proposed based on predictions of FEHMs. This means that these values are inherent to the respective models. Additionally, the pressure response is usually validated by comparing their predictions with [PERSON] et al. [70] experiments, as it was performed for YEAHM [36]. However, the results used to validate these models in the literature seem to be taken directly from the brain model, which does not correspond to what was done in [PERSON]'s experiment. In this, the surfaces of the pressure transducers were placed aligned with the inner surface of the skull, without rupturing the dura mater. Thus, in the experiments, the pressure was measured directly at the outer surface of the dura mater and not in the brain. The same was done when validating YEAHM for [PERSON]'s experiment. This fact may explain the higher values computed with YEAHM when compared with others proposed in the literature. Therefore, accident reconstructions must be carried in the future to develop the YEAHM's own criteria.