## 5 Discussion  
As shown by the statistical analysis, the simulation succeeded in reproducing the physical phenomenon of a low-velocity impact test. The correct estimate of the a-max and HIC values by the simulation leads us to assess the risk of an athlete suffering an injury following a head impact, or in other words allows for ensuring an adequate level of protection for the athlete. The two curves of accelerations (real and simulated) show a similar trend, with discrepancies only in the last part of the impact event, where the simulation curve goes to zero and the real acceleration assumes negative values. This observed difference is due to the oscillations of the piezoelectric accelerometer before returning to zero values. This means that the simulations were performed correctly.  
The values of the indexes \(RMSE\) and \(R^{2}\) in Table 1 confirmed the good correlation between the experimental results and the simulated ones, except for the 50 mm EVA foam, which at an impact velocity of 5.2 m/s showed a remarkable difference in the region where the material reached the peak of acceleration (see Figure 7 and Table 3).  
Regarding the data in Table 2, it is worth observing that the test fall height for the EVA 50 mm corresponding to the impact velocity of 5.2 m/s (equal to 1.709 m) appears to be very close to the CFH of the architecture (equal to 1858 m). Moreover, the simulation data show that the material reaches the densification stage during this test, while the behaviour of the material was modelled by the Du Bois model and not by the data obtained from the compression tests. Thus, the lack of knowledge about  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Acceleration** & \multirow{2}{*}{\(t_{i}\) (ms)} & \multirow{2}{*}{\(t_{f}\) (ms)} & **Sampling** & \multirow{2}{*}{**RMSE**} & \multirow{2}{*}{\(R^{2}\)} \\ \cline{5-6}
**Time-History Region** & & & & & \\ \hline \multirow{3}{*}{Initial region (I)} & \multirow{3}{*}{0} & \multirow{3}{*}{10} & 0.25 & 4.35 & 0.93 \\ \cline{5-6}  & & & 0.50 & 4.32 & 0.94 \\ \hline \multirow{3}{*}{Central region (II)} & \multirow{3}{*}{10} & \multirow{3}{*}{16} & 0.25 & 23.68 & 0.24 \\ \cline{5-6}  & & & 0.50 & 23.71 & 0.24 \\ \hline \multirow{3}{*}{Final region (III)} & \multirow{3}{*}{16} & \multirow{3}{*}{30} & 0.25 & 4.32 & 0.94 \\ \cline{5-6}  & & & 0.50 & 4.27 & 0.94 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical analysis of the missile acceleration curve for the EVA 50 mm at 5.2 m/s.  
Figure 7: Comparison between the acceleration curve predicted by the simulation and the experimental curve for the EVA 50 mm at 5.2 m/s.  
the real behaviour of the EVA foam in the densification zone is responsible for the poor correlation between the simulation and the test results observed in region II of Figure 7 and in Table 3.  
The numerical simulations allowed us to investigate the behaviour of EVA polymeric foams subjected to a low-velocity impact. The main strength of the model is that its accuracy is insensitive to the large strains suffered by the foam material, which instead are responsible of numerical instabilities with a typical FEM analysis [14; 21].  
Furthermore, the developed numerical model may be employed to analyse the passive safety properties of shields for sports equipment made of generic polymeric foam and can be used when basic characteristic parameters of the materials under examination are known, such as the density, the Young's modulus, the Poisson ratio or the compressive stress-strain curve. The main application concerns the characterization of a foam mat under impact conditions. The use of the simulation in replacing the current testing standard is not feasible, as the deterioration of the absorption properties of the material in consecutive impacts is not contemplated in the model.