# Review of Auxetic Materials for Sports Applications: Expanding Options in Comfort and Protection
## 4 Expected Characteristics and Supporting Evidence
Increased energy absorption has been shown experimentally for auxetic foam; under flat plate [33] and studded impacts [274], quasi-statically with flat compression plates [8], within aluminium tubes [299] and with a studded indenter and a stiff shell [7]. When compressed cyclically at high strain rates (0.036 to 0.36 s\({}^{-1}\)[300] and 0.033 s\({}^{-1}\)[2; 274]) auxetic foams absorbed up to sixteen times more  
Figure 7: **(a)** Typical compressive stress vs. strain response of auxetic and conventional open cell foam (note cellular collapse between 5 to 10% then hardening beyond 80% strain via densification in open cell foam); **(b)** Strain energy density (Volumetric (\(U_{v}\), Equation (5)), Distortion (\(U_{d}\), Equation (6)) & \(U_{l}\), Total) vs. [PERSON]’s ratio for a linear elastic isotropic material subject to a uniaxial stress. Uniaxial stress and Young’s modulus set to 1 kPa. energy than open cell foams of a different polymeric composition and equivalent density, therefore appearing more useful in cushioning layers of sporting (and general) PE & PPE. The differences in energy absorption do not account for changes in stress/strain relationship or strain rate dependency between conventional and auxetic samples. As strain rates increased, Young's modulus and the magnitude of NPR increased marginally in samples of auxetic PU foam [301]. In some cases the increased linear elastic range of the auxetic foam compared to the parent foam with a plateau region in the stress-strain relationship could have contributed to higher energy absorption [2; 8; 33]. Energy absorption, strain rate dependency and (often) indentation resistance combine to influence performance under impact. Theoretically beneficial for impact protection [282], auxetic foam samples have been shown to exhibit between \(\sim\)three and \(\sim\)eight times lower peak force under 2 to 15 J impacts adapted from BS 6183-3:2000 for cricket thigh pads [3; 8; 55]. During a comparison of high strain rate compression (20 to 40 J) to a conventional commercial foam of similar density, auxetic samples exhibited (1.2 to 1.8 times) higher peak acceleration, but also exhibited higher compressive elastic modulus [2]. Peak forces can be further decreased (1.2 to 1.5 times) during 5 J impacts by impregnating auxetic foam with shear thickening fluid [302]. Inward material flow has been shown under impact by rudimental visual inspection of high-speed camera stills, and the samples with the greatest magnitude of NPR exhibited higher lateral contraction, lower through thickness deformation and a similar peak force to other samples [33]. Newly developed 3D auxetic textile composites exhibit lower peak forces than their conventional counterpart under 12 to 25 J impacts [5]. In helical yarns, a wrap angle of 27\({}^{\circ}\) gave the best combination of Poisson's ratio and stiffness for energy absorption [209] during 7 to 65 J impacts. Honeycomb sandwich panels with auxetic cores were found to resist ballistic impacts better than regular or rectangular cores [303], and absorb more impact energy when the re-entrant cell structure was non-uniform [304]. Laminated composites containing warp knit auxetic Kevlar(r) fabric reinforcement, under 167 m/s impact with a 14.9 g bullet (\(\sim\)200 J), showed similar energy absorption to laminates containing conventional woven Kevlar(r) reinforcement [305; 306]. The auxetic Kevlar(r) laminates, however, displayed enhancements in fracture toughness (225%) and fracture initiation toughness (577%), and a reduction in front and rear face damage area [305; 306]. Auxetic composite laminates displayed reduced back face damage during 7-18 J impacts by a stud [32; 307; 308]. Auxetic composite laminates could, therefore, improve the durability of protective shells in PPE and other sports equipment (i.e., bicycle frames or boat hulls). Related to energy absorption, auxetic foams have been tested for vibration damping (to ISO 13753 for vibration protecting gloves [309]).