# A Simple Method to Convert Cellular Polymers into Auxetic Metamaterials
## 1 Introduction  
Expanded polyethylene is frequently used for the packaging of sensitive products such as glassware and electronics [1, 2]. Polyethylene (PE) foams contain a high number of small cells that can deform and produce highly absorbing materials. Due to their low density (high porosity), they occupy large volumes and are mostly gas-filled cells separated by thin walls of polymer. Although they are very efficient packaging materials, they generate large volumes of waste at their end-of-life, which is an important problem when it comes to their handling, storage, transport and disposal [3]. This waste leads to pollution/environmental issues if not carefully collected and recycled. PE foams are water- and moisture-resistant, so they are not biodegradable/compostable. Furthermore, conventional disposal methods, such as landfilling or burning, are no longer acceptable under the concept of a circular economy. They contribute to environmental problems, as PE does not breakdown in landfill, while burning contributes to carbon emissions. PE has good thermal stability/resistance, enabling it to maintain its chemical structure, and since most PE foams are un-crosslinked thermoplastics, they can be mechanically recycled (remelted and reshaped) numerous times into different geometries. Another option for PE is to directly reuse the PE foams and generate added value [4, 5]. This can be achieved by modifying the structure/morphology of these foams. In our previous work, preliminary results were presented showing the application of a thermo-mechanical treatment to LDPE foams, yielding auxetic foams [6]. Auxetic foams are materials with a negative Poisson ratio; they expand laterally under elongation and conversely contract under compression. These metamaterials can beproduced by converting a standard PE foam structure (honeycomb/polyhedral shaped cells) into a re-entrant cellular structure. In the past, different post-fabrication treatments were proposed including mechanical, thermal, physical and chemical treatments, which were performed alone or in combination [7; 8; 9; 10; 11; 12]. The success of these methods depended mostly on whether the foam was of an open- or closed-cell structure. For open cells, the main methods combined mechanical compression with thermal treatments. The mechanical compression was either uniaxial [7], biaxial [7; 8] or triaxial [9; 10], but the half-mold process [11] is similar. Although several methods have been proposed in the literature, very few polymers have been investigated. Most of the work has explored polyether urethane foam (PU) with the exception of [PERSON] et al. [9] who used polyester (PES) foams. In all cases, a limited range of negative Poisson's ratios was obtained (\(-0.2\) to \(-1.0\)). [PERSON] et al. [7] reported on thin auxetic flat and curved sheets via uniaxial compression at 150 \({}^{\circ}\)C. The flat foam sheets had an NPR of \(-0.3\), while the curved foams had values down to \(-3\) at 1% strain (multilayer foams). [PERSON] et al. [11; 12; 13] used multiaxial compression for conventional PU foam (open-cell) and heating of the compressed specimens above the polymer matrix softening point. The samples were made at different temperatures (135 and 150 \({}^{\circ}\)C) and compression ratios (1.7-6.5) and with different cooling methods (water or room-temperature exposure) [12; 13; 14; 15; 16; 17; 18; 19; 20; 21]. The minimum NPR reached was \(-1.3\) for a density of 27 kg/m\({}^{3}\)[11]. The authors also observed that removing the foam from the mold immediately after heating created a different microstructure between the internal and external parts; a lower density core with a rigid skin was obtained. This behavior was a result of a temperature profile inside the sample, as the external region, in contact with the mold walls, was at a higher temperature than the interior. Therefore, the samples only produced an NPR of \(-0.34\) under compression [14]. Recently, [PERSON] et al. [15; 16; 17] used open-cell PU foams to convert into auxetic foams.