## 4 Experimental Mechanical Testing of 3D Printed Auxetic Structures
### Experimental Results  
Figure 7 illustrates the force-displacement measurements for PLA, PET, TPU materials made by FDM and PA12 material by means of PBF. All four materials showed strong \begin{table}
\begin{tabular}{c c c} \hline
**Process Parameter** & **Value** & **Units** \\ \hline Machine type & DTM Sinteraction 2500 Plus & - \\ Material (powder) & Duraform FLEX, infiltrated & - \\ Laser type & CO\({}_{2}\) & - \\ Laser power & 30 & W \\ Laser spot diameter & 300 & \(\upmu\)m \\ Laser speed & 5000 & mm/s \\ Layer thickness & 150 & \(\upmu\)m \\ Hatch distance & 0.3 & mm \\ \hline \end{tabular}
\end{table} 
Table 6: Process parameters for SLS process with Duraform Flex powder (rubber). Figure 6: Experimental setup for compression testing of auxetic samples. reproducibility. The Duraform Flex rubber 3D sample made by SLS demonstrated only minor force response (less than 2 N) due to very low overall stiffness. Since the measuring accuracy of the available force sensor was unable to capture forces of that range, the results for this material are omitted. The experimental study for the 2D auxetic geometries has shown that PLA samples provide the highest stiffness and force response, due to their high elastic modulus, compared to the other materials tested in this experiment. The experiments showed that between 15 mm and 20 mm of travelled compression distance of punch, the FDM 2D samples (PLA, PET, and TPU) produced an increase in the gradient. This elevated stiffness in samples was caused by the contact of the unit cells in the vertical direction during compression. In PLA and PET, the contact took place after the plastic deformation, while for TPU, the contact occurred in the elastic region of the auxetic samples due to the considerably lower Young's Modulus. The SLS 3D auxetic sample made of PA12 powder indicates that lower levels of stiffness were due to the overall lower utilization of material, as illustrated in Figure 5 compared to the FDM 2D samples (Figure 4). The maximum force measured on the samples follows a trend comparable to the stiffness. This can be justified in a similar manner as the stiffness according to the mechanical properties and the overall geometry configuration between the 2D and 3D auxetic samples. The auxeticity was derived by the observed shrinkage only in the transverse x-direction for the 2D samples over the displacements in the loading z-direction, whereas the shrinkage that occurred in both the transverse plane x- and y-directions was used for obtaining the auxeticity of the 3D samples. Here it is worth mentioning that for all samples, the loading z-direction concurs with the building direction of the 3D printing processes for both FDM and SLS. The lower Poisson's ratio estimated for the 3D sample compared to the 2D samples can be explained by the 3D nature of the sample and the fact that auxeticity occurred only in one transverse direction (x-direction) for the 2D samples, while shrinkage was observed in both of the plane directions x and y for the 3D probes. Table 7 summarizes the results on the average stiffness and maximum force recorded during the experiments, as well as the average resulting Poisson's ratios for each auxetic sample. The average Poisson's ratio for the 2D samples was obtained using the measured length reduction in the transverse x-direction  
Figure 7: Experimental measurements of force vs. displacements on auxetic samples. during loading of the three samples for each material. Nevertheless, the average Poisson's ratio for the 3D auxetic sample was calculated by means of the captured shrinkage in both transverse x- and y-directions with respect to the axial loading direction for three samples.