## 6 Geometries Used in Additively Manufactured Crash Boxes
### Tubular Structures  
Tubular structures, available in either single- or multi-cell configurations, are a common design choice for crash boxes. These structures are engineered to deform progressively under axial loads, effectively dissipating dynamic energy during an impact [18]. AM offers a range of material options and provides an efficient fabrication process for tubular  
Figure 7: Illustration of a standard continuous fiber-reinforced FDM configuration [42].  
structures. Several investigations have examined tubular structures produced through AM [43; 44; 45].  
[PERSON] and [PERSON] [46] investigated carbon-fiber-reinforced PLA single-cell circular structures fabricated by using the FDM technique, as shown in Figure 8a, examining deformation patterns and \(E_{\text{T}}\). After testing wall thicknesses of 1.6, 1.8, and 2 mm, they found that \(E_{\text{T}}\) increased with thickness, reaching 357.99 J at 2 mm, although fragmentation at the thickest wall indicated a trade-off between energy absorption and structural integrity. All specimens exhibit local buckling and discontinuous folding. While [PERSON] and [PERSON] [46] focused on conventional single-cell circular tubes, [PERSON] et al. [47] extended the study of single-cell tubular structures by introducing geometric modifications through corrugation, as shown in Figure 8b. They investigated shape memory corrugated tubes (SMCTs) fabricated from PLA/TPU blends using the FDM technique. The results reveal that the number of corrugations and their amplitude significantly influence the energy absorption capacity and recovery behavior. SMCTs demonstrate over 98% shape recovery within 20 s after thermal activation. After more than ten compression-recovery cycles, \(SEA\) values stabilize in the corrugated tubes, while straight tubes show a continuous decline.  
Figure 8: Tubular structures: (**a**) circular tubes [46]; (**b**) shape memory corrugated tubes [47]; (**c**) multi-cell thin-walled tubes [48]; (**d**) multi-cell-filled thin-walled tubes [49]; (**e**) multi-cell multi-stage tubes [50].  
Multi-cell tubular structures have attracted significant attention due to their superior performance, offering enhanced energy absorption capabilities and stable deformation under loading conditions compared to single-cell structures. These characteristics make them highly suitable for crash box applications. [PERSON] and [PERSON] [48] investigated multi-cell tubes featuring concentric corner-edge connections in square and hexagonal cross-sections, as shown in Figure 8c. Manufactured from PLA+ and ABS materials using FDM, their results show that increasing the number of internal corners enhances energy absorption, with PLA+ tubes outperforming ABS. Specifically, tubes with S-WW and H-WW geometries demonstrated significantly higher \(SEA\) values compared to other geometries. These findings align with [PERSON] et al. [49], who investigated multi-cell-filled tubes with different internal cell geometries--circular, hexagonal, and triangular--fabricated from carbon-fiber-reinforced PA using FDM as shown in Figure 8d. Their results show that higher filling densities significantly improve \(SEA\), with circular-filled configurations achieving higher \(SEA\) values than the hexagonal and triangular variants. [PERSON] et al. [50] further advanced the study of multi-cell tubular structures by investigating stepwise graded multi-cell tubes (SGMTs) and continuous graded multi-cell tubes (CGMTs), as illustrated in Figure 8e. The specimens are fabricated using carbon-fiber-reinforced PA filaments via the FDM technique. The results showed that the stepwise graded multi-cell tubes exhibited distinct multi-stage deformation during axial compression, with the \(SEA\) displaying an upward trend as the number of stepwise segments increased. Additionally, for the same range of cross-sectional variations, the continuous graded multi-cell tubes developed more plastic hinges and demonstrated superior energy absorption performance, which was attributed to the absence of discontinuous interfaces.