## 3 Results
### Deformation Mode  
The deformation process of the four structures under quasi-static compression is presented in Figure 7 to understand the difference of deformation mode. All four structures show uniform deformation at the linear-static stage. Elastic or plastic strut buckling occurs beyond the first stress peak, which gradually results in deformation localization. Due to the introduction of meta-precipitates, there is obvious difference in the elastic limit and the initial location for deformation localization, leading to the entire difference for the deformation mode, which will be discussed respectively. The P-0 structure exhibits a conventional diagonal crushing, which is a typical failure mode usually observed in other periodically-arranged cellular solid [42]. The localized deformation results in the formation of plastic hinge at the nodes adjacent to the diagonal. The nodes located along the diagonal is easy to concentrate more plastic deformation when the compression continues. Consequently, the strain at the nodes attains the failure strain [43], and they undergo rigid body rotations at the same time the unit cell is twisted. Once the first diagonal of twisting cells come into contact with the next row caused by this \"twist mode\", additional stress is required to continue the deformation, leading to the increase of stress value. The twist behavior is then repeated, resulting in an irregular oscillation of the stress-strain curves before the densification occurs. The deformation of P-1, P-2 and P-4 structure is different from that of the P-0 structure. For P-1 structure, the buckling of the struts initially occurs at the first two layers of the matrix, followed by a progressive crushing of the first two layers when the strain increases. Once the structure is further compressed, a diagonal crushing comes into existence. It is to some extent analogous to the deformation of P-0 structure with one distinct difference. The crushing meanders and deviates from the diagonal line when it approaches the meta-precipitate. The meta-precipitate remains almost undeformed during this process. In other word, the deformation localization changes its initial direction to bypass the meta-precipitates. This phenomenon illustrates that the meta-precipitate is stronger and can hinder the progress of deformation localization and the subsequent failure. The P-2 structure exhibits a progressive crushing more obvious than the P-1 structure. No sign of diagonal crushing is observed before the strain comes to 0.25. The progressive crushing leads to layer-by-layer collapse. At the strain of 0.25, the diagonal crushing is also hindered or even stopped at the location adjacent to the meta-precipitate, followed by progressive crushing at the upper layers. The P-4 structure exhibits a diagonal crushing at the gaps among four meta-precipitates. The meta-precipitates remain undeformed prior to the strain of 0.31. However, it eventually rotates for further compression, leading to a stress peak and a relatively higher plateau stress in the stress-strain curve. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Sample**}} & \multicolumn{2}{c}{**Young’s Modulus (GPa)**} & \multicolumn{1}{c}{**Yield Strength (MPa)**} & \multicolumn{1}{c}{**Energy Absorption (\(\times 10^{4}\) J/m\({}^{3}\))**} & \multicolumn{1}{c}{**Energy Absorption (\%)**} \\ \hline P-0 & Exp & 2.39 & 4.89 & 1.70 & 61.87 \\  & FEA & 2.71 & 4.84 & 1.64 & 60.43 \\  & Error & 13.39\% & 9.20\% & 3.53\% & 2.33\% \\ \hline P-1 & Exp & 3.14 & 4.96 & 1.82 & 66.67 \\  & FEA & 3.38 & 4.96 & 1.83 & 64.04 \\  & Error & 7.64\% & 0.00\% & 0.01\% & 3.94\% \\ \hline P-2 & Exp & 3.18 & 5.01 & 1.93 & 69.73 \\  & FEA & 3.36 & 5.07 & 1.86 & 68.51 \\  & Error & 5.66\% & 1.20\% & 3.63\% & 1.75\% \\ \hline P-4 & Exp & 3.27 & 5.27 & 2.04 & 78.99 \\  & FEA & 3.48 & 5.25 & 1.94 & 73.90 \\  & Error & 6.42\% & 0.00\% & 4.90\% & 6.44\% \\ \hline \hline \end{tabular} Note: Error = \(|\text{Exp}-\text{FEA}|/\text{Exp}\times 100\%\).  
\end{table}