# Crushing Analysis and Optimization of Adjacent Variable Thickness Hexagonal Tubes
## 3 Results and Discussion  
### FE Model Validation  
The model validation was based on the axial compression of four types of specimen tubes. It focused on three aspects: deformation, crushing force and energy absorbing curves, and crashworthiness indices. We prepared two specimen tubes and performed two quasi-static compressive tests, Experiment-1 and Experiment-2, for each type of AVTHT.  
All the deformation processes between the two tests are basically the same; thus, the comparison here only shows the process of Experiment 1 in Figure 6. Note that all the AVTHTs deform with progressive folding mode, and most of the AVTHTs have no material tearing or failure. All the deformation modes and sequences maintained the same results in the simulations and the experiments, except for the sequence difference and slight tearing of specimen S1426 in the experiments. Material failure is not considered in the FE model since it is not the concern of the present work, and it is hard to predict its occurrence accurately [16]. In the literature [7], two distinct folding mechanisms were observed and distinguished: propagating hinge line (Mode I) and stationary hinge line (Mode II). The main features of the former are the hinge line moving and extension is limited to the neighborhood of the hinge line, and then extension occurs over an entire flange, which will be called Mode II. S2020 in simulations and experiments produces folds of Mode II and exhibits an extensional deformation mode, which is consistent with the conclusion in the literature [41]. The remaining three types of AVTHTs produce folds of Mode I and are exhibited in the nextensional deformation mode.  
For energy absorbing curves, it was found that force-displacement and energy-displacement curves between simulations and experiments agreed well (Figure 7). All force-displacement curves basically show four local peaks, which is due to the generation of four sets of folds for each tube. However, as the difference in wall plate thickness increases, the displacement it takes to produce four sets of folds is increased, which indicates that the wavelength for folds is increased.  
In addition, the details of the crashworthiness indices are shown in Table 4. For the experimental results, the maximum standard deviation values of F\({}_{\text{max}}\), SEA, and CFE are 0.820, 0.119, and 0.009, respectively; the maximum coefficient of variation values of F\({}_{\text{max}}\), SEA, and CFE are 1.831%, 1.035%, and 1.992%, respectively. This indicates that the consistency and accuracy of the experimental data are very good. Compared with the two corresponding experimental results, the maximum average error of the simulation results is \(-\)8.879%, which occurs in the CFE value of specimen S1426.  
Figure 6: The results of the deformation process for simulations and experiments: (**a**) S2020; (**b**) S1822; (**c**) S1624; (**d**) S1426.  
Figure 7: Energy absorbing curves for simulations and experiments: (**a**) S2020; (**b**) S1822; (**c**) S1624; (**d**) S1426.  
Above all, the FE model has good accuracy to predict the crushing performance of the AVTHTs and can be used in following research.