## 6 Geometries Used in Additively Manufactured Crash Boxes
### Lattice Structures  
Lattice structures are periodic, porous configurations that consist of systematically arranged 2D or 3D unit cells. According to studies, these structures are lightweight and have superior energy absorption capabilities, which makes them ideal for use in crash box designs [57]. Lattice structures are challenging to produce through traditional manufacturing techniques due to their intricate geometries and complex internal networks, which often require precision at a fine scale. AM techniques offer a suitable alternative by enabling the construction of these intricate forms. Several investigations have focused on lattice structures fabricated via AM [58; 59; 60]. Lattice structures are widely used as energy absorbers due to their reliable mechanical properties. [PERSON] et al. [61] introduced symmetry-corrugate hierarchical honeycombs (SCHHs), shown in Figure 10a, fabricated from stainless steel 316L via SLM. The study investigated the effects of amplitude coefficients (\(\varphi\)A) and period coefficients (\(\varphi\)T) on  
Figure 9: Origami-inspired structures: (**a**) origami crash box [54]; (**b**) origami-inspired multi-cell tubes [55]; (**c**) double-layer biomimetic multi-cell tubes with pre-folded external walls [56]. crashworthiness, revealing that \(\varphi\)T had a more pronounced influence on crash performance than \(\varphi\)A. SCHH structures achieved a 53.8% improvement in \(E_{\text{T}}\) compared to conventional honeycombs. Graded lattice structures feature systematic variations in internal geometry within the same part, allowing for tailored mechanical performance and optimized energy absorption. [PERSON] et al. [62] introduced a novel graded origami-inspired lattice structure, illustrated in Figure 10e, fabricated from stainless steel 304 L using SLM. The \(SEA\) values across different orientations and geometries were recorded as 9.53 J/g for X-0.85-60, 4.63 J/g for Y-0.85-60, 9.08 J/g for Z-0.85-60, 7.15 J/g for Z-0.65-60, and 7.68 J/g for Z-0.85-50. Among graded configurations, G-50-65-50 achieved 10.89 J/g, G-65-50-65 reached 11.78 J/g, and G-50-65 exhibited the highest \(SEA\) at 13.08 J/g. Auxetic lattice structures are promising for crash box design due to their unique deformation behavior and enhanced energy absorption capacity. Unlike traditional lattices, auxetic structures expand laterally when compressed, promoting superior distribution and dissipation of impact energy. [PERSON] et al. [63] investigated the energy absorption performance of three lattice types, hexagonal (non-auxetic), re-entrant (auxetic), and double arrowhead (auxetic), under axial and in-plane loading, as illustrated in Figure 10c. Specimens are fabricated using FDM with carbon-fiber-reinforced nylon (Onyx) and standard nylon. The results show that the double arrowhead auxetic structure exhibits the highest energy absorption capacity, achieving an \(SEA\) 125% higher than the hexagonal lattice and 244% higher than the re-entrant design when fabricated with Onyx. Triply periodic minimal surface (TPMS)-based porous lattice structures have been attracting attention due to their excellent performance and lightweight characteristics. [PERSON] et al. [64] introduced three novel composite TPMS-based porous structures, namely PI-type, PIP-type, and PN-type structures, as shown in Figure 10d, drawing inspiration from the micro-porous architecture of bones. These structures are produced from 316L stainless steel using SLM. The results show that deformation patterns and energy absorption capacities are strongly influenced by the thickness ratio between the inner and outer surfaces. PI structures with a thickness ratio of 0.4 (PI-0.4) demonstrate superior energy absorption capacity, achieving 10.8% and 12.1% improvements in \(E_{\text{T}}\) and \(CFE\), respectively, compared to conventional foams. Building upon interest in TPMS structures, [PERSON] et al.