# Co-Design of Mechanical and Vibration Properties of a Star Polygon-Coupled Honeycomb Metamaterial
## 3 Stress-Strain Characteristics of the Metamaterials by Simulation and Experiment  
Three-dimensional printing, which is also known as additive manufacturing, is a rapid prototyping technology to construct 3D objects through the method of layer-by-layer printing. The stereolithography (SLA) 3D printing technology, which is one of the most widely used rapid prototyping technologies to cure layers of resin and create 3D objects using ultraviolet light, was adopted to manufacture the proposed metamaterials. The metamaterials used in the experiments were manufactured by the company named WENEXT in Shenzhen, China, and an industrial SLA 3D printer Lite600 HD (UnionTech, Shanghai, China) was employed. The layer thickness precision of the Lite600 HD is up to 0.05 mm and the printing speed is 7 mm/s. The resin material WEILAI8000 (WL8000), which is produced by the Royal DSM Group of the Netherlands with excellent properties, smooth surface, high precision, and water and moisture resistance, was used. The build orientation affects the strength, accuracy, and surface finish of the 3D printing parts. When the tension forces are perpendicular to the printing layers, part weakness tends to occur. In contrast, the printed parts are stronger if the tension forces are parallel. Therefore, the proposed metamaterials were printed in an orientation so that layers aligned with the axis where tension forces were highest or in an orientation so that layers intersected the axis where compression forces were highest. In order to achieve excellent characteristics while ensuring the printing accuracy, the thicknesses of the rods and rings of the proposed metamaterials were designed to be 1.2 mm and 1 mm, respectively. The dimensional accuracy of the 3D-printed samples is 0.05 mm and the relative density errors are below 2%, which ensures that the samples meet the requirements and can be used for experiments. The WL8000-based structures are fastened to the upper and lower aluminum strips and the assembly pins are made of copper, as shown in Figure 2a-c. The properties of the materials are listed in Table 2. Furthermore, numerical simulations and actual experiments were carried out to investigate the stress-strain characteristics of the involved structures. Firstly, a two-dimensional cell was built in Abaqus CAE 2018 (Dassault aircraft company, Paris, France), as shown in Figure 1, and then the required number of cells was extended in the horizontal and vertical directions. A total of five cells in the horizontal direction and eight cells in the vertical direction were set to generate the proposed structure in this paper. With the aluminum strips and metal pins assembled in the desired positions, the entire model is combined into a whole structure, as shown in Figure 2a-c. The thickness of the model was set to 20 mm, which is equal to that of the experimental samples. The specific material properties are shown in Table 2. To ensure that there were at least 10 elements in the shortest wavelength to guarantee accuracy, the maximum mesh size was set to 0.3 mm. In addition, the bottom surface of the upper aluminum strip and the two sides of the lower aluminum strip were set to be completely fixed. The load force \(F\) was applied to the midpoint of the upper surface of the aluminum strip and the maximum deformation displacement was set to 15 mm, starting at 0 mm and gradually increasing to 15 mm. \begin{table}
\begin{tabular}{c c c c c} \hline \(a_{x}\) (mm) & \(a_{y}\) (mm) & \(d\) (mm) & \(\theta\) (\({}^{\circ}\)) & \(r_{1}\) (mm) & \(r_{2}\) (mm) \\ \hline
75 & 60 & 1.2 & 60 & 4 & 5 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameter values of the unit cell. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Density (kg/m)** & **Elastic Modulus (GPa)** \\ \hline WL8000 & 1120 & 2.65 \\ Aluminum & 2700 & 71 \\ Copper & 8960 & 117 \\ Tungsten & 19,350 & 411 \\ \hline \end{tabular}
\end{table} 
Table 2: Properties of the materials.