## 3 Results and Discussion
### Low-Speed Impact Analysis of Designed Energy-Absorbing Box
#### 3.2.2 Energy Absorption Evaluation Indexes Comparison  
The automobile energy-absorbing boxes are a passive protection mechanism in a low-speed car collision, and their peak load (\(F_{max}\)) and mean load (\(F_{m}\)) directly determine the degree of damage to the inner parts of the vehicle and the occupants. The load-displacement curve of the energy-absorbing box under low-speed impact is analyzed and processed, and the obtained energy-absorbing indexes are shown in Figure 15.  
Figure 14: The post-processing results of low-speed impact experiments. (**a**) The load–displacement curves drawn based on finite element simulation results (the spherical point: the first breakage judgment point of different energy-absorbing boxes). (**b**) The multi-component waterfall diagram obtained from three sets of low-speed impact tests and finite element simulation results. As shown in Figure 15, the peak load of the traditional thin-walled crash box is twice the average load, up to 133.47 kN. Although the average load of the traditional thin-walled energy-absorbing box is low and the effective compression stroke is better than the energy-absorbing box filled with the porous TPMS structures, it can be seen from the displacement-force curve under low-speed collision in Figure 14 that the curve of the platform stage fluctuates violently. The peak load of the traditional thin-walled crash box is higher than the energy-absorbing box filled with porous TPMS structures, which significantly reduces the protection performance of the vehicle in the event of a collision. According to the simulation calculation, in the effective compression stroke of each type of crash box, the Primitive-filled crash box absorbs 11.68 kJ of energy, the Gyroid-filled crash box absorbs 13.78 kJ of energy, and the traditional thin-walled crash box absorbs 6.62 kJ of energy. Under the same displacement, the energy-absorbing box filled with porous TPMS structures can absorb collision energy more efficiently through structural compression. Moreover, the Gyroid-filled energy-absorbing box has a higher specific energy absorption value than the traditional thin-walled energy-absorbing box, indicating that it has a better energy absorption capacity per unit mass. After the comprehensive analysis of the mechanical response, deformation mechanism, and various energy absorbing indexes of the energy absorbing boxes filled with porous TPMS structures when subjected to low-speed impact at 4.4 m/s, the following conclusions can be drawn: In automotive anti-shock applications, the smooth load fluctuations of the energy absorbing boxes filled with porous TPMS structure can reduce injuries to accident personnel. The stable layer-by-layer collapse mechanism and shear failure deformation solve the problem of excessive peak load of the traditional square tube energy absorbing box. The excellent \(SEA\) value of the Gyroid-filled energy absorbing box can provide assistance for the lightweight of the energy absorbing structure of the vehicle. The results of this work were compared with the novelty energy absorbing boxes designed by scientific researchers in Figure 16.  
Figure 15: Comparison of energy-absorbing indexes of energy-absorbing boxes. Structures BHTS 1-2 [45], BHTS-3 [46], FS\({}_{3}\)[47], BHTNS [48], Q. H, and O-BMCT [49] are biomimetic multi-cell tubes based on aluminum alloys, whereas NPR structure [50] is a novel three-dimensional double-arrow structure with negative Poisson's ratio. The SEA values of the aluminum alloy tubes fluctuate around 30 J/g, which is clearly lower than that of CFRP [51] honeycomb boxes (53.9 J/g) and TC [52] triple-cell boxes (58.0 J/g). The _SEA_ of energy absorbing boxes with porous, filled TPMS structures is 36.5% and 50.2% higher than that of the aluminum alloy energy absorbing boxes, approximately. The energy absorption capacity of an energy absorbing box filled with Primitive or Gyroid is comparable to composite structures of integrated biomimetic design or even slightly higher than them.