## 3 Results  
### Mechanical Properties and Energy Absorption  
Figure 4 illustrates quasi-static compression test results for all four structures. Each structure demonstrates a highly reproducible stress-strain response. By careful observation of all these stress-strain curves, it can be seen that an elastic-plastic collapse behavior with three distinct stages \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & **Young’s Modulus, Es** & **Poisson’s Ratio** & **Density, \(\rho_{s}\)** & **Yield Stress, \(\sigma_{ys}\)** \\ \hline PLA+ & 2.0 GPa & 0.35 & 1.26 g/cm\({}^{3}\) & 39 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties of PLA+ polymer. Figure 3: Stress-strain curves of the hexagonal honeycomb under compression. of deformation occurs, which are, linear-elastic, plateau stress and densification. Such mechanical response is analogous to that of traditional bending-dominated lattice or foams [40]. In detail, all the structures show a uniform deformation in the initial elastic region until its elastic limit. Then the cell edges yield and collapse with a sharp drop of stress. Prior to the occurrence of densification, the plateau stress stage performs a sustained oscillation in stress values due to the sudden occurrence of strut buckling and layer-to- layer collapse. Figure 5 illustrates the difference of the mechanical properties and energy absorption capabilities for all four structures. Detailed information of experiment data is also summarized in Table 4. It can be concluded that the overall performance of the samples with meta-precipitates outperforms those without meta-precipitates. With the introduction of meta-precipitates during unit cell design, the yield strength (compressive strength) and plateau stress increase. The favorable plateau response contributes to an improvement in the energy absorption capabilities. This idea is similar to other research efforts for energy absorber applications, while the solution to the unit cell design is different [39]. In addition, the values of the major properties are in positive correlation to the number of precipitates that are introduced in the samples, at the same time the relative density of the samples increases negligibly. Therefore, the P-4 structure that consists of 4 meta-precipitates exhibit excellent energy absorption capability compared to other structures, with the total energy absorption of \(2.04\times 10^{4}\) J/m\({}^{3}\) (approximately 20% higher than initial P-0 structure with completely periodic arrangement), and with specific energy absorption of 39.97 J/kg. It reveals that the architected metamaterial can be significantly strengthened with the design of meta-precipitate, ensuring its capability of carrying more load especially in large deformation. Figure 4: Constitutive stress-strain responses for (**a**) P-0 type, (**b**) P-1 type (**c**) P-2 type (**d**) P-4 type (Each curve contains 3 experimental data and 1 numerical result. The numbers are corresponding to the deformation behavior depicted in Figure 7). Perfect match between experimentally-measured stress-strain responses (thin curves) and simulation results (thick blue curves) could be found in Figure 4. The comparison of deformation behavior is illustrated in Figure 6. Prime property indexes obtained from experiments and simulations are summarized in Table 5, which are in good agreement with each other. The maximum difference of the deformation is \(\sim 0.01\), which is consistent with the experimental results.