# A Simple Method to Convert Cellular Polymers into Auxetic Metamaterials
## 1 Introduction
This was conducted by using an open mold and a single-direction (uniaxial) thermoforming compression (density of 27 kg/m\({}^{3}\)) [15]. The mechanical tests showed an auxetic behavior with an NPR from \(-1\) to 0 with a slope of the stress-strain curve (tangent modulus) between 0.2 to 2 MPa when the volumetric compression ranged from 40% to 80%. In a second study, they proposed another conversion method, also using a PU foam of 28 kg/m\({}^{3}\). This was achieved via vacuum bags in an autoclave after thermforming at 148 \({}^{\circ}\)C [16]. The final foams were transversely isotropic, showing deformed semi-reticulated configurations. The NPR of the auxetic foams reached \(-1.3\) (at 0.03 of tensile strain) for the thinner specimens (5 mm). The authors reported that the low thickness and high tensile strain reduced the rigidity but improved the auxetic behavior of these cellular materials. Unfortunately, anisotropy inside the pristine foam seemed to have an important effect on the final performances of these auxetic materials. Finally, three series of auxetic foams that were uniaxially deformed in three directions were investigated by [PERSON] et al. [17]. The results showed that different mechanical performances and auxetic behaviors were observed due to the anisotropy of the original foam, i.e., the final properties were a function of the initial state. Some publications reporting the conversion of closed-cell PE foams into NPR foams were found [18; 19; 20; 21]. [PERSON] et al. [18] explored two polymer foams with three types of closed-cell structures: polymethacrylimide (PMI) (52, 205 and 301 kg/m\({}^{3}\)) sold under the tradename Rohacell(r) and Ethafoam(r) low-density polyethylene (LDPE) (59, 109 and 158 kg/m\({}^{3}\)). The LDPE produced a re-entrant geometry leading to NPR, while the PMI did not. Furthermore, only the lowest density (59 kg/m\({}^{3}\)) LDPE foam was successfully converted. The pressure method was performed at 110 \({}^{\circ}\)C and 662 kPa, leading to an NPR between \(-2.5\)\(\pm\) 1.5 (note the large error bars), while for vacuum with heating, only the 59 kg/m\({}^{3}\) LDPE showed an auxetic behavior with an NPR of \(-0.5\)\(\pm\) 0.5 under \(-82\) kPa and \(86\)\({}^{\circ}\)C for small deformation (8% strain). [PERSON] et al. [19] produced auxetic foams by a steam (water vapor) method at 1 atm with closed-cell polyethylene foams with different initial densities (20, 30 and 45 expansion ratios, which is the ratio between the matrix density and the final foam density). After 6 h at 100 \({}^{\circ}\)C, the cells were deformed inwards and cell-wall bending led to a re-entrant structure. The minimum NPR values under tension were \(-\)0.278, \(-\)0.439 and \(-\)0.487 for the 20, 30 and 45 expansion ratios, respectively. Under compression, the minimum NPR values of the specimens were only \(-\)0.026, \(-\)0.090 and \(-\)0.118 at 20, 30 and 45 expansion ratios, respectively. The Poisson ratio was also found to increase with deformation under tensile and compressive stresses [19]. [PERSON] et al. reported on the preparation of auxetic foams via steam (water vapor) treatment [20] and a pressure-vessel method (vacuum) [21]. The original foam was a closed-cell LDPE (low-density polyethylene) foam of 60 kg/m\({}^{3}\). For the steam treatment, NPR values as low as \(-\)0.3 in tension and \(-\)1.1 in compression were obtained, while the value of Young's modulus in tension was improved (between 2 and 6 MPa). For the vacuum method, [PERSON]'s ratios down to \(-\)0.2 and [PERSON]'s modulus up to 1.2 MPa were reported. [PERSON] et al. prepared auxetic foams directly from polypropylene [22] and a nylon elastomer (NE) [23] by a single-step process using CO\({}_{2}\). The polypropylene and polyamide (nylon) elastomer (NE) auxetic foams had NPR values of \(-\)0.46 and \(-\)1.29, respectively. As for any mechanical properties of viscoelastic materials, the effect of the strain rate is also important when reporting the properties. [PERSON] et al.