# A Simple Method to Convert Cellular Polymers into Auxetic Metamaterials
## 3 Results and Discussion
### Auxetic Foams
#### 3.2.3 Mechanical Properties
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & **Tensile** & **Strain** & **Energy** & **Damping** & **Tensile** \\  & **Modulus** & **Energy (\(E_{p}\))** & **Dissipated** & **Capacity** & **NPR** \\  & **(kPa)** & **(kPa)** & **(\(E_{d}\)) (m/cm\({}^{3}\))** & **(\%)** & **(\%)** \\ \hline PE-D16-O & 3.26 & 25.0 & 0.95 & 3.80 & 0.38 \\ PE-D16-P1.0 & 3.97 & 31.2 & 1.22 & 3.91 & \(-\)2.55 \\ PE-D16-P1.3 & 15.6 & 64.6 & 3.47 & 5.68 & \(-\)2.83 \\ PE-D16-P1.5 & 40.4 & 136 & 15.5 & 11.4 & \(-\)2.89 \\ \hline PE-D21-O & 1.73 & 20.3 & 0.47 & 2.38 & 0.34 \\ PE-D21-P1.6 & 2.06 & 13.7 & 1.97 & 16.7 & \(-\)1.60 \\ PE-D21-P1.9 & 6.07 & 67.4 & 4.91 & 7.28 & \(-\)2.55 \\ PE-D21-P2.1 & 30.1 & 81.3 & 11.2 & 13.8 & \(-\)1.07 \\ \hline PE-D30-O & 2.39 & 49.5 & 0.43 & 0.871 & 0.37 \\ PE-D30-P1.5 & 1.13 & 3.41 & 0.46 & 13.4 & \(-\)1.60 \\ PE-D30-P1.8 & 3.49 & 24.9 & 1.30 & 5.20 & \(-\)0.97 \\ PE-D30-P2.0 & 3.54 & 20.6 & 1.83 & 8.88 & \(-\)1.52 \\ \hline PE-D36-O & 2.18 & 64.5 & 0.078 & 0.12 & 0.40 \\ PE-D36-P1.5 & 6.39 & 31.6 & 1.69 & 5.30 & \(-\)1.50 \\ PE-D36-P1.8 & 5.11 & 33.3 & 1.77 & 5.33 & \(-\)0.72 \\ PE-D36-P2.1 & 9.44 & 52.5 & 8.13 & 15.5 & \(-\)0.49 \\ \hline \hline \multirow{2}{*}{**Sample**} & **Compressive** & **Strain** & **Energy** & **Dissipated** & **Damping Capacity** \\  & **Modulus** & **Energy (\(E_{p}\))** & **(\(E_{d}\)) (m/cm\({}^{3}\))** & **(\%)** & **(\%)** \\ \hline PE-D16-O & 0.209 & 2.41 & 0.086 & 3.56 \\ PE-D16-P1.0 & 0.159 & 1.64 & 0.24 & 14.3 \\ PE-D16-P1.3 & 0.268 & 3.89 & 0.51 & 13.0 \\ PE-D16-P1.5 & 1.04 & 2.55 & 0.26 & 10.2 \\ \hline PE-D21-O & 0.678 & 3.09 & 0.34 & 10.9 \\ PE-D21-P1.6 & 0.760 & 2.26 & 0.46 & 20.2 \\ PE-D21-P1.9 & 0.439 & 3.42 & 0.37 & 12.3 \\ PE-D21-P2.1 & 0.942 & 4.54 & 0.45 & 10.0 \\ \hline PE-D30-O & 0.788 & 5.63 & 0.34 & 6.11 \\ PE-D30-P1.5 & 0.471 & 3.41 & 0.46 & 13.4 \\ PE-D30-P1.8 & 2.42 & 5.65 & 0.61 & 12.0 \\ PE-D30-P2.0 & 1.71 & 8.60 & 1.96 & 29.7 \\ \hline PE-D36-O & 1.68 & 4.28 & 0.68 & 15.8 \\ PE-D36-P1.5 & 2.56 & 7.19 & 1.90 & 26.4 \\ PE-D36-P1.8 & 3.10 & 8.92 & 2.50 & 28.1 \\ PE-D36-P2.1 & 2.54 & 17.6 & 3.43 & 19.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Tensile properties of the auxetic foams produced. than the auxetic foams (Table 4). As previously mentioned, it was believed that when the VMC changed the cellular structure, some cells were broken, and this was why some of the auxetic foams showed low stresses at low strains (0.1-3%). The presence of hysteresis loops confirmed the typical energy dissipation (\(E_{d}\)) behavior of these materials under slow deformation. The energy dissipation of the auxetic foams was better than that of the original foams (Table 4). The auxetic foams based on D16 had Ed values of 1.22 mJ/cm\({}^{3}\), 3.47 mJ/cm\({}^{3}\) and 15.5 mJ/cm\({}^{3}\) compared to 0.95 mJ/cm\({}^{3}\) for D16. The damping capacity is the capacity to absorb vibration using internal friction and to convert mechanical energy into heat. The damping capacities of the four original foams were 3.8%, 2.4%, 0.87% and 0.12%, while those of the auxetic foams were 11.4%, 13.8%, 13.4% and 15.5% (Table 4). For the D16, D21 and D30 foams, an improved damping capacity corresponded to an increasingly negative tensile NPR. This trend did not hold for D36, and the reason behind this difference was unclear. Figures 9 and 10 and Table 4 report the mechanical properties obtained from the compressive stress-strain curves and the quasi-static cyclic testing. The compressive modulus and strain energy (\(E_{p}\)) values presented in Table 4 showed the same trend as the tensile data; the strain energies of the original foams were larger than those of the auxetic foams (PE-D16-P1.0 and PE-D21-P1.6). However, as the VMC treatment pressure increased, so did the strain energies, surpassing those of the original foams. The energy dissipated (\(E_{d}\)) and damping capacities (%) of the auxetic foams tested under compression all showed a great improvement over their original foams.