## 5 Conclusions  
This study showed an experimental investigation into and finite element predictions of axial crushing behavior and crashworthiness characteristics of carbon fiber reinforced hat-shaped tubes. Different velocities were conducted. The impact speed and force-displacement curves were explored for closed top-hat profiles fabricated by the vacuum bagging process. Explicit FE code ABAQUS were used to develop the crash energy absorption of composite materials. Experimental failure modes and load-displacement curves of the top-hat section were validated. Numerical and experimental results were compared to determine the predictive capability of the finite element modelling of the top-hat composite sections. The maximum difference was found to be 13% between the experimental and FEA results. This is within the acceptable range for finite element analysis [44; 45]. To add to this, the comparison was made between the average values of the experimental results against the FEA result. Besides this, for complex and non-linear problems such as the crushing of composite structures, errors below 20% are acceptable because the composite material failure models used in modelling are not an exact model. Active research is still ongoing in this aspect [45; 46]. Below are some of the conclusions that can be derived from this study: \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Approximate** & \multirow{2}{*}{**Parameter**} & **Average** & **Numerical** & **Error \%** \\ \cline{2-5}
**Impact Energy** & & & **Experimental** & **Numerical** & **Error \%** \\ \hline \multirow{3}{*}{\(\sim\)2.1 kJ (_sample ID: 2 k_)} & Mean load (kN) & 66.9 & 58.2 & 13 \\ \cline{2-5}  & Energy (J) & 2047 & 1850 & 10 \\ \cline{2-5}  & Crushing length (mm) & 34 & 33.8 & 1 \\ \cline{2-5}  & Mean load (kN) & 66.6 & 62.3 & 6 \\ \cline{2-5}  & Energy (J) & 3179 & 2755 & 13 \\ \cline{2-5}  & Crushing length (mm) & 50 & 48.8 & 2 \\ \hline \multirow{3}{*}{\(\sim\)6.6 kJ (_sample ID: 6 kJ_)} & Mean load (kN) & 63 & 65.5 & 4 \\ \cline{2-5}  & Energy (J) & 6580 & 5756 & 13 \\ \cline{2-5}  & Crushing length (mm) & 97 & 90 & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Predicted and experimental results for composite material reinforced closed top-hat. Figure 12: (**a**) Force-displacement curves of dynamic and quasi-static axial crush (**b**) Energy-displacement curve of dynamic and quasi-static axial crush. * Increases in impact speed led to increases in energy absorption and the energy absorption increases linearly with the impact speed
* The predicted force-displacement and energy-displacement results for different speeds have shown good agreement with the experimental results. Therefore, it can be concluded that the numerical model was able to predict the failure and behavior of the closed top-hat. * The average peak loads of the dynamic test 2 kJ, 3 kJ and 6 kJ were 107, 108 and 112 kN, respectively, with a reduction of 35% to 45% compared with the quasi-static test. In addition, the average energy absorption of the dynamic test with 2, 3 and 6 kJ were 2050, 3180 and 6500 J, respectively, with a reduction from 28% to 77% compared with the quasi-static test. Now that the finite element model has been validated, the next step is to use this model in a full vehicle finite element model to evaluate the crash performance followed by optimizing the top-hat structure to enhance energy absorption. The following are available online at [[https://www.mdpi.com/article/10](https://www.mdpi.com/article/10)]([https://www.mdpi.com/article/10](https://www.mdpi.com/article/10)) 3390/app11114792/s1, Video S1: Dynamic crushing of hat structures. [PERSON] conceptualized the aims and objectives of the paper followed with the experimental work and data analysis. [PERSON] worked on the writing--original draft preparation, writing--review and editing the manuscript. Both authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.