## 3 Results and Discussion
### Empirical Modelling  
The classical model of Gibson-Ashby [8; 29] may be used to analyse these results. The outcomes of this investigation highlight a markedly pronounced contrast in properties between a solid and lattice. Specifically, this disparity is mainly exhibited in a normalised fashion about their solid properties (\(\mathsf{x}^{\star}/\mathsf{x}_{\mathrm{s}}\)). The empirical findings demonstrate that relative stress (\(\sigma^{\star}/\mathsf{\sigma}_{\mathrm{s}}\)) and relative elastic modulus (\(\mathrm{E}^{\star}/\mathrm{E}_{\mathrm{s}}\)) were equally consistent. It is worth noting that the BCC + CP and FCC + CP topological configurations yielded a superior performance in both properties when compared to their respective primary structures (BCC and FCC) [27]. It can be seen that even though the relative density of the FCC + CP was twice that of the FCC relative density, and the elastic modulus of the FCC + CP was significantly increased by a factor of three.  
After that, the plot between relative stress and the relative density provides analysis for all of the experimental data; this data reviled that there was a relative density between 0.10 and 0.15, and the stress of the lattice varied between about 0.005 and 0.039 times of the solid. As previously stated, the Gibson-Ashby model has the capability to prognosticate the fracture mode of the lattice structures, which is apparent in references, particularly in the metallic lattice structures. However, this model may not be optimally suitable for the current outcome, as the associated density approaches the minimum limit of 0.003 Figure 8 shows the experimental results along with the Gibson-Ashby model [29], which The data indicates a weak correlation between the model and the experiment, with a correlation coefficient of 0.6 and a model correlation of 0.15. However, it is worth noting that the linear model appears to align with the experimental data. Although the model produced a satisfactory plot, the comparative stress of the CP differed from the other samples. To enhance the correlation coefficient, it is recommended to exclude the results of the CP sample. In relation to the relative elastic modulus, the Gibson-Ashby model for stretch dominance yielded a suboptimal correlation coefficient of 0.3. Nevertheless, it surprisingly presented the same connection between relative elastic modulus and relative density, also at 0.3 [22].  
One thing that should be mentioned is that although the Gibson-Ashby [29] model is very famous and is accepted in the study of foam and lattice structures [8], as it was theoretically proven based on [PERSON]'s bulking [53]. However, if there are one or more structures, which have no significant difference in relative density (see Figure 8), it could lead to two or more response points at the same dependence variable, which would reduce an accurate model. For example, the relative density of the BCC and FCC samples are were insignificantly different with about 0.1; in this case, they show two different responses in the relative stress at approximately 0.005 and 0.010. Not only had CP a special collapse function, it did not agree with the other responses included relative stress and relative elastic modulus. That could be cause by the critical length of bucking column as mention  
Figure 7: Energy absorption per unit mass of the lattice structures.  
on the literature [55; 57]. This critical of any bucking column is limited by the boundary conditions: both ends fixed, both ends pinned, fixed and pinned, and fixed and free [55; 57].