## 3 Results  
The double impact simulations were performed using the Abaqus Explicit solver. Four simulations were performed, one for each thickness of 25, 30, 35, and 40 mm. Figure 8 shows the measured \begin{table}
\begin{tabular}{c c c c} \hline \hline \(\rho\) [kg/m\({}^{3}\)] & \(C_{10}\) [MPa] & \(C_{01}\) [MPa] & \(D_{1}\) [MPa \({}^{-1}\)] \\ \hline
1000 & 0.9 & 1 & 0.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: CSF material properties. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Part** & **Number of Elements** & **Number of Nodes** \\ \hline Skull & 57257 & 14443 \\ CSF & 98032 & 27499 \\ Brain & 836328 & 153749 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: YEAHM’s mesh info. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\rho\) [kg/m\({}^{3}\)] & \(\mu\) [MPa] & \(\alpha_{1}\) & \(D_{1}\) [MPa\({}^{-1}\)] & \(g_{1}\) & \(g_{2}\) & \(\tau_{1}\) [s] & \(\tau_{2}\) [s] \\ \hline
1040 & 0.012 & 5.0507 & 0.04 & 0.5837 & 0.2387 & 0.02571 & 0.02570 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Brain material properties. \begin{table}
\begin{tabular}{c c c} \hline \hline \(\rho\) [kg/m\({}^{3}\)] & \(C_{10}\) [MPa] & \(C_{01}\) [MPa] & \(D_{1}\) [MPa \({}^{-1}\)] \\ \hline
1000 & 0.9 & 1 & 0.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Skull material properties. accelerations at the headform's COG (Center of Gravity). These were obtained for liners with different thicknesses and made of AC216 agglomerate. The results from the simulations of the double impacts show a better response in terms of maximum acceleration by the helmet with a 40 mm thick liner. This one performed slightly better than the one with 35 mm for the first impact, and in the second one, it was clearly better. In Figure 8, the difference between peak accelerations seems to differ for the first and the second impacts. Table 6 gives precisely the peak accelerations measured for each impact. In the first impact, by decreasing the thickness, the variation of the peak accelerations increases. On the other hand, in the second impact, the opposite is observed. Lowering the thickness leads to a peak acceleration limit, since similar results were computed for liners with thicknesses of 35, 30, and 25 mm. This is explained by the amount of deformation imposed to the material, reaching the densification regime. The time between impacts is so small that the material does not recover in time from the previous impact, starting the second impact with stored deformations higher than 10%. This explains the similar results for the second impacts with thicknesses lower than 40 mm. Figures 9 and 10 show the maximum deformation in both impacts with liner thicknesses of 35 and 40 mm, respectively. In Figure 9, although the densification regime is not reached during the first impact (maximum deformation of 50.2%), due to the stored strain energy that was not released in time for the next impact, this regime is reached by exceeding a strain of 60%. On the other hand, the maximum deformation of the liner with a thickness of 40 mm was lower than 50% for both impacts. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Impact** & **25 mm** & **30 mm** & **35 mm** & **40 mm** \\ \hline First & 405.5 & 361.5 & 324.7 & 314.1 \\ Second & 499.9 & 482.2 & 470.6 & 377.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Peak accelerations measured for each impact [g]. Figure 8: Acceleration-time history of double impacts performed with helmets composed of agglomerated cork liners with thicknesses ranging between 25 and 40 mm. These results emphasis the applicability of AC in multi-impact applications. The imposed impact conditions are severe, by performing two impacts of 7.5 m/s separated by an approximately 5 ms interval. The helmet standards of more demanding applications, such as motorcycle standards, usually demand one impact at the same velocity used in these simulations, or two impacts but with lower impact velocities (and low energies).