## 5 Discussion  
The results presented in Table 5 are related to the differences in the crushing modes observed for different cross-section geometries. In order to shed some light upon this, a closer look was taken at the different values obtained for \(\alpha\) and \(\beta\). The \(\alpha\) parameter reached values close to its upper bound for the circular tube showing that the increment in energy dissipation was favoured by higher foam densities and, consequently, a higher plateau stress of the foam. Stronger foams exerted a stiffer constraint on the tube's fold formation, which in turn led to more and shorter folds giving a higher energy dissipation per unit volume. This effect is illustrated in Figure 14, where the empty tube developed four folds in concertina mode and then transitioned to a diamond mode. However, with a reinforced specimen as that from Figure 14b, the core made the tube collapse solely in concertina mode, developing ten full concertina folds in the same crushing distance, thus dissipating more energy per unit volume. A different behaviour was found in the square extrusions, with \(\alpha\) and \(\beta\) being closer to their lower bounds. This suggested a stronger contribution from the extrusion material properties and wall thickness to the increase of the energy dissipation increase from the interaction term. Table 6 showed how the main energy gains within the Hanssen interaction term arose from the folding of the aluminium extrusions, responsible for over 29% of this improvement. This was caused by a significant decrease in fold length during the collapse process due to the constraining core, as shown in Figure 15a-c. Since a higher number of folds were produced, more energy was dissipated through bending of the aluminium walls as shown by the values of \(\Omega\approx 0.8\) in Table 7. As with the circular tube, wall thickness directly influenced the energy dissipation from the full \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cross-Section** & **Core** & **Integration Point Failure (\%)** & **Bending-to-Membrane Loading Ratio, \(\Omega\)** \\ \hline Circular & Cork & 5.270 \(\pm\) 1.840 & 0.794 \(\pm\) 0.035 \\  & Foam & 4.214 \(\pm\) 2.020 & 0.885 \(\pm\) 0.023 \\ Square & Cork & 8.215 \(\pm\) 2.338 & 0.777 \(\pm\) 0.027 \\  & Foam & 5.161 \(\pm\) 1.967 & 0.812 \(\pm\) 0.011 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Percentage of failed integration points and average element bending-to-membrane loading ratio. Average value and standard deviation. Figure 14: Deformation comparison between empty and foam-filled circular tubes (\(D=130\) mm, \(t=1.9\) mm, foam density = 135 kg/m\({}^{3}\)). effect was noticeably larger as shown in Figure 12. This behaviour might stem from the difference in constraining force required to shorten the length of the folds, a key contributor to higher energy dissipation. Fold formation in tubes with thinner walls was more constrained by the existence of a core than with thicker walls, as less force was required from the reinforcement to reduce the fold length. Regarding the difference in the interaction effect from using either reinforcing material, it was seen that foam-filled components obtained higher energy dissipation gains for the full component than those filled with cork. Moreover, Figure 15(a),b shows a cut view of the deformed square components filled with foam and cork, with a clear difference in the collapse mechanism between both configurations. This discrepancy was attributed to the hyperelastic behaviour of the cork, which makes the material much more prone to buckling than the plastic behaviour of the foam. Global buckling of the cork core was found in some components with large cross-sections and thin tube walls as that from Figure 15(b), which led to lower values of energy dissipation per unit volume of the cork than in uniaxial compression.