## 4 Component Modelling and Interaction Analysis
### Energy Assessment  
The energy dissipation per unit volume for each material was also retrieved from the simulations. For that, the energy dissipation per unit volume was calculated for both materials for each of the samples by obtaining the energy dissipated by each material and its volume. The sum of these values was divided by the number of samples, obtaining the average value for the sampling. This was compared to the values that would have been obtained if the tubes and the reinforcements were crushed separately. In the case of foam-filled extrusions, the difference in plateau stress depending on the foam density was taken into account for the calculations. The results are presented in Table 6. Both the tubes and cores showed higher values of energy dissipation per unit volume as a consequence of being crushed together, although this increase varied depending on the component. The highest gains were found for the foam-filled square extrusion, with over 55% more energy dissipation per unit volume for both parts.  
The effect of the thickness and outer dimensions of the tubes on the increase in energy dissipation per unit volume for the extrusions was also studied. The surfaces in Figure 10 were adjusted to the data from the foam-filled circular tube, showing that a higher percentage of energy dissipation per unit volume is gained with thinner tube walls. Moreover, Figure 10 illustrates how the main contribution to this increase stemmed from the aluminium extrusion, although friction also provided a small increase in energy dissipation by the component. The contribution from friction to the energy dissipation was found to increase slightly with higher-density foams.  
The interaction in circular tubes with cork cores was affected by thickness as with foam cores, although the overall gain in energy dissipation was smaller. Moreover, Figure 11 shows that thinner walls also led to a larger increase in energy dissipation per unit volume when the diameter was  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & & \multicolumn{2}{c}{**Tube**} & \multicolumn{2}{c}{**Filling**} \\
**Cross-Section** & **Core** & **Original** & **Simulation** & **Original** & **Simulation** \\ \hline Circular & Cork & 50.134 & 55.971 (+11.62\%) & 1.633 & 1.844 (+12.92\%) \\  & Foam & 50.747 & 54.986 (+8.35\%) & 1.749 & 2.331 (+33.28\%) \\ Square & Cork & 39.347 & 50.957 (+29.51\%) & 1.491 & 1.703 (+14.22\%) \\  & Foam & 38.774 & 60.230 (+55.33\%) & 1.793 & 2.788 (+55.49\%) \\ \hline \end{tabular}
\end{table}
Table 6: Average energy dissipation per unit volume for the aluminium extrusions and filling materials. All values in J/cm\({}^{3}\).  
Figure 9: Sampling data points, fitted Hanssen interaction formula, and Hanssen interaction term for the foam-filled circular tube with a foam density of 80 kg/m\({}^{3}\) and 200 kg/m\({}^{3}\).  
reduced. The contribution from friction to the energy dissipation was found to increase as wall thickness was reduced.  
A similar study on energy dissipation and its relation with side length, wall thickness, and foam density was performed for the square tube. Figure 12 showed that the thickness had the strongest effect on the increase in energy dissipation of the full component. It can also be hinted that the use of higher-density foams provided a slight improvement in energy dissipation in specimens with thick tube walls due to a higher contribution from friction. Moreover, Figure 13 shows that energy dissipation of the components also increased as side length was reduced, rooted in the higher contribution from friction and the aluminium extrusion.  
Figure 11: Increase of energy dissipation of the full component versus thickness and diameter, and contribution from the aluminium extrusion and friction for the cork-filled circular tube. Sampling data and interpolated surfaces.  
Figure 10: Increase of energy dissipation of the full component versus thickness and diameter, and contribution from the aluminium extrusion and friction for the foam-filled circular tube. Sampling data and interpolated surfaces.