## 3 Results and Discussions
### Deformation Behaviors  
Deformation is the response of a material to stress or failure under external forces. The general behavior of lattice structures is evaluated using [PERSON]'s criteria (M), specifically defined by the number of struts (\(s\)) and nodes (\(n\)) in the unit cell of the lattice (Equation (4) [55]. If M is less than 0, the number of struts in the lattice structure is insufficient to balance the bending moments at the nodes. In such cases, the struts are subjected to bending stresses and such structures are called \"bending dominated\". On the other hand, if \(M\) is 0 or greater, the lattice is assumed to have a sufficient number of struts to balance the external forces [56]. These supports are primarily subjected to axial stresses and are referred to as \"stretch dominated\". Stretch-dominated structures exhibit higher strength and stiffness than bending ones. Equation (4) is used to evaluate the spatial behavior of lattice structures:  
\[M=s-3n+6 \tag{4}\]  
The deformation behavior of the 12 different lattice structures fabricated in this study is shown in Figures 6-8. All designed structures were modified with additional struts. The calculations show that all of the structures in this study retained the bending-dominated structure, in accordance with the literature. The chiral unit cell had 16 nodes and 28 struts, while the rotation unit cell had 36 nodes and 60 struts and the re-entrant unit cell had 26 nodes and 42 struts. Therefore, the Maxwell numbers for the chiral, rotating and re-entrant unit cells were \(-14\), \(-42\) and \(-30\), respectively, and bending was considered to be dominant. The bending-dominated properties of the lattice structures were also observed experimentally during compression tests. Figures 6-8 show the deformation behavior of the test specimens at different strain rates during the compression test. The main crushing strength test showed similar behavior for chiral and re-entrant FGLSs, with densification occurring at around 50% strain. The rotation structure started to fracture and disintegrate after 24% strain and disintegrated at 60% strain, showing an utterly brittle material feature. The brittle structure is more evident in HG and RG structures. Chiral and re-entrant lattice structures showed ductile behavior in uniform and gradient structures. All chiral lattice structures showed high crushing strength in compression tests and were characterized by crashworthiness. FGLSs deformations started in the thin strut layers and moved towards the thick strut layer. This was particularly evident in VG structures. The thin struts perpendicular to the load were displaced more, while the overlying thick layers stacked up towards the thin layer. As can be seen in Figures 6 and 8, in VG specimens with chiral and re-entrant lattice structures, the high-density area remained intact, while the low-density area was damaged first. In re-entrant lattice structures, the underlying low-density region showed significant lateral expansion after damage. This means that the hardness varies in different density regions, which is different from the uniform lattice structure. In HG specimens, the geometry of the lattice structure was not disturbed in regions of high density. RG chiral and RG re-entrant lattice structures maintained their geometric integrity during the compression test. Chiral and re-entrant structures showed a typical flexural dominant deformation. In the HG configuration of the re-entrant structure, it was observed that the deformation did not continue after the first peak stress in compression. This is thought to be due to the faster transition of the struts in the re-entrant structure into the plastic region. Figure 6: Variations in the chiral lattice structure depending on the amount of compression. Figure 7: Variations in the rotation lattice structure depending on the amount of compression. The shear bands were not observed on the uniform designs of the chiral and re-entrant structures during the compression test.