## 2 Materials and Methods  
The effect of using auxetic foam within a typical sports safety helmet was investigated through fabrication, characterization, and comparison of conventional and auxetic foams within a helmet. The original helmet (Coolfo Batting Helmet, Rawlings, St. Louis, MO, USA) contained three layers: (1) an open cell polyurethane foam as a conformable layer acting as an interface between the head and the helmet; (2) a closed cell ethylene-vinyl acetate (EVA) foam; and (3) a semi-rigid plastic exterior. This helmet was chosen for its simple construction which allowed easy substitution of candidate foams to act as the conformable layer. The exact grade of open cell polyurethane foam used as the native conformable foam layer in the helmet was unknown and it was not possible to source additional foam of this grade for auxetic conversions. The conformable layer was therefore replaced with an alternative foam (PUR30 FR, Custom Foams) which is well established for auxetic research, to ensure consistent conversion in line with previous studies [34; 38; 44]. A sample of the native conformable foam and the un-converted PU R30 FR foam (41 \(\times\) 127 \(\times\) 25 mm) was compression tested through thickness (25 mm dimension) with a uni-axial test device (Instron 3367, Norwood, MA, USA, with a 500 N load cell) to 50% compression (0.0083 s\({}^{-1}\)). A linear trend line was fitted to the initial linear region of the stress vs. strain data to obtain [PERSON]'s modulus (34.3 kPa, plateau at 3-3.5 kPa, \(\sim\)10% strain) and check it was comparable to PU R30 FR (\(\sim\)30 kPa, plateau at 3-3.5 kPa, -5 to 10% strain). The auxetic foam was fabricated using a thermo-mechanical method for uniform sheets (\(\sim\)350 \(\times\) 350 \(\times\) 20 mm) with compression controlled by pins in the initial heating cycle, previously developed, and described in detail [34; 42]. The same foam (PUR30 FR, Custom Foams), mold compression regimes (isotropic Linear Compression Ratio, LCR of 0.7, defined as the ratio of the compressed to initial dimension), and heat cycles (25 min then 15 min at 180 \({}^{\circ}\)C) were employed. The annealing cycle was reduced to 10 min at 100 \({}^{\circ}\)C. Two foam sheets were produced, the first used for establishing the setup and pilot testing, and the second for final testing, to limit degradation. Prior to impact testing within the helmet, the converted foam was characterized in order to ensure auxetic characteristics similar to previously created samples [34]. A 200 \(\times\) 20 \(\times\) 20 mm auxetic sample cut from the center of the pilot sheet was subjected to a quasi-static tensile test (Instron 3369, Norwood, MA, USA, 10 kN load cell) up to 50% extension (0.0017 s\({}^{-1}\)). The sample was held in place with bonded card-board end tabs (Araldite, Super Strength). Four white pins were placed in a square (10 mm sides) on the front face of the sample, and their movement during testing was recorded using an HD camcorder (JVC Everio, 1920 \(\times\) 1080 pixels). Lateral vs. axial strain data (Marker Tracking, MATLAB, Mathworks 2015b [44]) were fitted with linear trend lines (between 0 and 50% extension) to obtain Poisson's ratio. Images of the foams and helmet can be seen in Figure 1 and the foam layer makeup is shown in Figure 2. Test foams were cut from the sheets in specific shapes using a bandsaw (Bauer Machinenbau). The forehead (Figure 1b) and side (Figure 1a,c) conformable foams were replaced with test foams. The top foam was only \(\sim\)5 mm thick, and assumed to contribute less than other areas, to the helmet's ability to reduce impact induced acceleration. Therefore, the native foam at the top location was left in situ. Velcro strip tape was used to hold foam samples in place, for ease of attachment and removal. Locating marks were placed on the ATD headform to ensure consistency of helmet placement for each test. The properties of both helmets are tabulated in Table 1, along with the specification of the foams used in testing.