## 3 Fabrication of Prototypes Sample by Means of 3D Printing  
After the identification of the most appropriate geometrical variations of unit cells for the PLA and TPU polymer materials, 2D and 3D prototype samples of 3 \(\times\) 3 unit cell systems were designed for further numerical and experimental investigations. For this purpose, two geometrical variations were favored: one for the 2D samples (Figure 4) and a similar one for the 3D samples (Figure 5) to allow for a direct comparison between different materials for each of the 3D printing processes. Samples were additively manufactured through FDM (2D samples) and SLS (3D samples) technologies. The proposed auxetic systems were created out of the following materials: PLA, PET, TPU through FDM process, and PA12, Duraform Flex(r) through powder bed fusion (PBF). Table 3 summarizes the various types of the manufactured auxetic samples used for experimental investigation in terms of their auxetic properties under compression. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Von Mises Plastic Material** & \multicolumn{3}{c}{**Hyperelastic Mooney–Rivlin Material**} \\ \hline
**Property** & **Value** & **Property** & **Value** \\ \hline Density, \(d\) & 1240 kg/m\({}^{3}\) & Density, \(d\) & 1200 kg/m\({}^{3}\) \\ Elastic modulus, \(E\) & 973 MPa & Poisson’s ratio, \(v\) & 0.45 \\ Poisson’s ratio, \(v\) & 0.36 & Tensile strength, \(\sigma_{\mathrm{T}}\) & 30 MPa \\ Yield strength, \(Y\) & 15.7 MPa & Mooney–Rivlin coef. \(C_{10}\) & \(-\)1.1 MPa \\  & & Mooney–Rivlin coef. \(C_{01}\) & 5.2 MPa \\  & & Mooney–Rivlin coef. \(C_{11}\) & \(-\)846.5 MPa \\  & & Mooney–Rivlin coef. \(C_{20}\) & 451.7 MPa \\  & & Mooney–Rivlin coef. \(C_{02}\) & 398.7 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties used for the FE analysis of unit cells: Von [PERSON] plastic material for hard polymer (PLA) and hyperelastic Mooney–Rivlin material for soft polymer (TPU). Figure 3: (**a**) Calculated Poisson’s ratio of the auxetic unit cell independent of the equivalent strains by varying compression force in the linear regions for hard polymer (PLA) and elastomer (TPU); (**b**) calculated Poisson’s ratio for twelve (12) unit cells, geometrical variations, and selection of the two optimum configurations for PLA (number 6) and TPU (number 12). First, prototype samples of 2D auxetic systems were planned with the same number of unit cells (3 \(\times\) 3). Three specimens were produced for each selected material (PLA, PET, TPU) using the fused deposition modeling (FDM) technique by means of 3D-printer. Raise3D Pro2 Plus. The layer height selected to manufacture these parts was set to 0.2 mm, and the infill percentage was kept to 100%. Table 4 lists the process parameters of the FDM process. All specimens were manufactured along the z-direction, as illustrated in Figure 4, to refrain from using supports with a total size of 90 \(\times\) 94 \(\times\) 30 mm. Figure 4: (**a**) CAD of the 2D auxetic samples in different views; (**b**) creation of 2D samples by means of the FDM process; and (**c**) dimensional details of unit cells. In a similar fashion, two 3D samples with identical geometrical features were fabricated by means of powder bed fusion of polymers with two different materials. The PA12 sample was fabricated on an EOS P 396 SLS machine, while the Duratform FLEX sample was fabricated on a DTM Sinterstation 2500 Plus. The geometrical features of the 3D samples are shown in Figure 5, while the process parameters for the SLS processes are provided in Tables 5 and 6.