## 3 Results
### Physical Test Results of Optimized Lattices  
The reaction force plots of the optimized lattices from the physical tests are shown in Figure 17 with their respective results from the simulations. The Simple Cubic lattice samples again show lower force peaks compared with the simulations, analogously to the samples with uniform thickness discussed previously. The Simple Cubic lattice FEA  
Figure 16: Reaction force versus compression plate displacement of the optimized Simple Cubic lattice geometries (**a**) and the Isotruss lattice geometries (**b**) compared with results from the uniform lattice structures.  
Figure 15: Diameter values of Simple Cubic (**a**) and Isotruss (**b**) lattices after optimization (T1: bottom, T10: top).  
model sufficiently predicts when force peaks from sequential layer collapse will occur but produces significantly higher reaction forces. The Isotruss lattice FEA model underestimates the achieved force peaks slightly but remains close to the plateau force seen in the later stages of the compression test.  
All of the models' absorbed energies and SEA values are listed in Table 6. The lattice samples all weigh considerably less than what was assumed in the FEA model, which impacts their SEA performance positively. The absorbed energy of the Simple Cubic lattice simulation is nearly twice as large as that of the test samples, as can be estimated from the corresponding graph in Figure 17a, where the FEA model predicts a large initial force peak and then consistently overestimates the force level greatly. Thickness measurements of the samples revealed that their diameters were 0.1-0.2 mm lower than expected in regions with a required thickness under 1 mm. The simulation was repeated with uniform diameter reductions of 0.1 mm and 0.2 mm. The results are shown in Figure 18, and a much closer fit is apparent. Their absorbed energies were 4.7 J and 3.4 J for 0.1 mm and 0.2 mm thickness reductions. The SEA performance amounted to 796 J/kg with a 0.1 mm reduction and 690 J/kg with a 0.2 mm reduction. The former model reaches energy absorption and SEA levels that are comparable to the samples' average, indicating that the negative thickness deviation is at the root of the performance difference.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{3}{c}{**Simple Cubic Lattice**} & \multicolumn{3}{c}{**Isotruss Lattice**} \\ \cline{2-7}  & **Absorbed Energy (J)** & **Weight (g)** & **SEA (J/kg)** & **Absorbed Energy (J)** & **Weight (g)** & **SEA (J/kg)** \\ \hline Sample 1 & 4.7 & 6.0 & 784 & 61.5 & 18.8 & 3269 \\ \hline Sample 2 & 3.9 & 5.4 & 719 & 58.8 & 18.9 & 3109 \\ \hline Sample 3 & 4.4 & 5.8 & 752 & 73.9 & 20.3 & 3939 \\ \hline Avg. samples & 4.1 & 5.7 & 752 & 64.7 & 19.3 & 3439 \\ \hline Simulated & 8.2 & 6.74 & 1210 & 65.1 & 22.27 & 2921 \\ \hline \end{tabular}
\end{table}
Table 6: Total absorbed energy and specific energy absorption (SEA) values of the Simple Cubic and Isotruss lattice samples after optimization with the quadratic thickness distribution approach.  
Figure 17: Reaction force versus compression plate displacement of the Simple Cubic lattice geometries (**a**) and the Isotruss lattice geometries (**b**) with the quadratic thickness optimization approach.  
The Isotruss lattice samples achieve 17.7% higher SEA values than those predicted with their FE models. However, focusing on their non-normalized absorbed energies alone, their differences are significantly smaller and only amount to 1% and 4%. The disparities in SEA levels, therefore, stem from the differing sample weights compared with FE model weights.