## 3 Static Properties of the Proposed Metamaterials
### Analysis of Static Properties of the Proposed Metamaterials  
In order to systematically study the static properties of the CDCHM, static compression tests were performed on the metamaterials using both experimental and simulation methods. The DHM and CDCHM used in the experiment were made by a company named WENEXT (Shenzhen, China) using 3D-printing technology; the original material is plastic. The printed DHM and CDCHM specimens had the same dimensions of \(375.79\times 450.95\times 20.00\) mm, and the masses of the DHM, CDCHM and CDCHM with copper pins were 0.809 kg, 0.943 kg and 2.02 kg, respectively. Figure 2 represents the simulation and experimental specimens; the blue blocks at the top and bottom ends of the structure are aluminum strips which serve as compression contact surfaces to apply pressure and fix the constraints. The blue circular filling in the ring represents the metal pin. The material properties are listed in Table 2.  
The 2D model shown in Figure 2 was constructed using ABAQUS 2018 to simulate the static compression of the metamaterials. The wall thickness of the CDCHM is 1.2 mm. In order to guarantee the simulation precision and to reduce the computational burden, the maximum size of the finite element is 0.3 mm. A fixed constraint was applied to the bottom aluminum strip, and the load force \(F\), shown in Figure 2, was applied to the center of the upper aluminum strip for the simulation.  
\begin{table}
\begin{tabular}{c c c c c} \hline \(L_{1}\) (mm) & \(L_{2}\) (mm) & \(R\) (mm) & \(d_{1}\) (mm) & \(t\) (mm) \\ \hline
75.158 & 40 & 4 & 1.2 & 20 \\ \hline \end{tabular}
\end{table}
Table 1: Geometric parameters of a unit cell.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Materials** & **Density (kg/m\({}^{3}\))** & **Young’s Modulus (MPa)** & **Poisson’s Ratio** \\ \hline Plastic & 2650 & \(1.12\times 10^{4}\) & 0.42 \\ Aluminum & 2700 & \(7.10\times 10^{4}\) & 0.33 \\ Copper & 8900 & \(1.17\times 10^{5}\) & 0.33 \\ Tungsten & 19,350 & \(4.11\times 10^{5}\) & 0.28 \\ \hline \end{tabular}
\end{table}
Table 2: Material properties.  
The static compression tests of the mentioned metamaterials were carried out by the Instron Legend 2367 universal testing machine, shown as Figure 3a, and the experiments were conducted under the same loading conditions with the above simulation settings. The compression displacement gradually increased from 0 until it stopped when the specimen failed.  
Figure 3b represents the stress-strain curves obtained from the static compression experiment and simulation of the DHM. The two results have the same trend and high consistency, and the morphology of the simulated and experimental specimens is highly similar under the same deformation degree, shown by pictures A-C in Figure 3b. The results indicate that the simulation method is reliable.  
Figure 3: \(Cont.\)  
Figure 2: Static compression test diagram.  
The results of the static compression simulations and experiments of the CDCHM and CDCHM with the metal pins are shown in Figure 3c,d. It can be seen from Figure 3b-d that the stress-strain curves of the metamaterials vary approximately linearly at the initial compression stage. When the structures have been deformed by 2%, the deformation stress corresponding to the DHM is 5.06 KPa, and that corresponding to the CDCHM is 40.11 KPa, which clearly demonstrates that the load-carrying capacity of the CDCHM has been significantly increased by approximately 800%, and the mass is only increased by about 16.6%. However, the load-bearing capacity of the CDCHM with the metal pins is barely enhanced based on the CDCHM, owing to the deformation of the CDCHM mainly being concentrated in the part with the connecting rods.