This paper reports quasi‐static and low‐kinetic energy impact testing of auxetic and conventional open‐cell polyurethane foams. The auxetic foams were fabricated using the established thermo‐mechanical process originally developed by Lakes. Converted foams were subject to compression along each dimension to 85% and 70% of the unconverted dimension during the conversion process, corresponding to linear compression ratios of 0.85 and 0.7, respectively. The 0.7 linear compression ratio foams were confirmed to have a re‐entrant foam cell structure and to be auxetic. Impact tests were performed for kinetic energies up to 4 J using an instrumented drop rig and high speed video. A flat dropper was employed on isolated foams, and a hemispherical‐shaped dropper on foams covered with a rigid polypropylene outer shell layer. The flat dropper tests provide data on the rate dependency of the Poisson's ratio in these foam test specimens. The foam Poisson's ratios were found to be unaffected by the strain rate for the impact energies considered here. Acceleration‐time data are reported along with deformation images from the video footage. The auxetic samples displayed a six times reduction in peak acceleration, showing potential in impact protector devices such as shin or thigh protectors in sports equipment applications.

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Intuitively, materials become both shorter and wider when compressed along their length.Here we show how a composite material or structure can display a simultaneous reversal in the direction of deformation for both the axial and transverse dimensions, corresponding to negative values of effective stiffness and effective Poisson's ratio, respectively. A negative Poisson's ratio [1] (NPR or auxetic [2] ) host assembly stabilising (otherwise unstable) embedded negative stiffness [3] (NS) elements is presented and modelled analytically. Composite assemblies containing 3 alternative NS elements are demonstrated experimentally, confirming both NPR and NS responses under quasi-static loading over certain strain ranges and in good agreement with model predictions. We report systems demonstrating NS values over two orders of magnitude, ranging from -1.4 N mm -1 to -160 N mm -1 . Such systems are scalable and are expected to lead to increased enhancements in other useful properties such as vibration damping, finding application across transport, healthcare, defence and space sectors, amongst others. 2 2 Metamaterials derive macroscale properties from a (usually) periodic arrangement of smaller scale sub-units or building blocks. The properties are sometimes considered unknown or unusual in natural materials, and can be counter-intuitive or opposite to our everyday experience. [4,5] Metamaterials include negative refractive index [6] and negative effective mass density [7] materials finding use in, for example, electromagnetic and acoustic cloaking/lensing applications, respectively. Examples of mechanical metamaterials are negative compressibility transition, [4] NPR [1] and NS [3] materials.Auxetic materials and structures exist, and are stable in the unconstrained state, at the nanoscale (e.g. crystalline forms of silica, [8] zeolites [9] and cellulose [10] ), microscale (microporous polymers [11] and microfabricated truss-like structures [12] ) and macroscale (composite laminates, [13] foams, [14,15] honeycombs [16] and patterned elastomeric spherical shells [17] ). Enhanced shear modulus, [18] energy absorption [19] and indentation resistance [20] are some of the benefits known for auxetic materials and structures. [21] Periodic arrangements of sub-units leading to auxetic behaviour include truss, [16,22] corner-sharing polygon, [23,24] and hybrid truss-polygon [25] frameworks, and particle assemblies. [26,27] NS materials and structures, on the other hand, are thermodynamically unstable unless stabilised by an external constraint. [28] Examples of NS materials include polymethacrylimide (PMI) foams, [16] honeycombs and lattices, [29,AA1,AA2] and certain crystals (VO 2 , BaTiO 3 ) undergoing constrained phase transformation. [30,31] The NS effect can also be displayed by constrained buckled ...

Auxetic materials offer potential to be applied to sports safety equipment. This work reports quasi-static and impact testing of auxetic open-cell polyurethane foam -fabricated with a compression and heat treatment process -in comparison to its conventional counterpart. The foam was compressed to 70% of its original dimension along each dimension during the conversion process. Quasi-static compression testing confirmed the converted foam to be auxetic, with a Poisson's ratio of -0.08. Impact testing was performed for energies up to 5.6 J with an instrumented drop rig and high-speed video. Peak accelerations were ~3 times lower for the auxetic foams, because they prevented bottoming. This work has shown further potential for auxetic foam to be applied to sports safety devices. Future work should look to optimise foam selection and the conversion process, while comparing auxetic foam with existing materials and products.

Auxetic materials have a negative Poisson's ratio, which can enhance other properties. Greater indentation resistance and energy absorption, as well as synclastic curvature, could lend auxetic materials well to protective sports equipment and clothing. Sheets of foam often form padding within protective equipment, but producing large homogenous auxetic foam samples is challenging. The aim of this work was to investigate techniques to fabricate large thin sheets of auxetic foam, to facilitate future production and testing of prototype sports equipment utilizing this material. A mold was developed to fabricate sheets of auxetic foam − with planar dimensions measuring 350 × 350 mm − using the thermo‐mechanical process. The mold utilized through‐thickness rods to control lateral compression of foam. Sheets of auxetic foam measuring 10 × 350 × 350 mmd were fabricated and characterized. Each sheet was cut into nine segments, with density measurements used to determine how evenly the foam had been compressed during fabrication. Specimens cut from corner and centre segments were subject to quasi‐static extension up to 30% to obtain stress versus strain relationships, with Digital Image Correlation used to determine Poisson's ratio. Specimens cut from the corner tended to have a marginally higher density, lower stiffness and more consistent negative Poisson's ratio compared to those from the centre, indicating some inconsistency in the conversion process. Future work could look to improve fabrication techniques for large thin homogenous sheets of auxetic foam.

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Intuitively, materials become both shorter and wider when compressed along their length.Here we show how a composite material or structure can display a simultaneous reversal in the direction of deformation for both the axial and transverse dimensions, corresponding to negative values of effective stiffness and effective Poisson's ratio, respectively. A negative Poisson's ratio [1] (NPR or auxetic [2] ) host assembly stabilising (otherwise unstable) embedded negative stiffness [3] [4,5] Metamaterials include negative refractive index [6] and negative effective mass density [7] materials finding use in, for example, electromagnetic and acoustic cloaking/lensing applications, respectively. Examples of mechanical metamaterials are negative compressibility transition, [4] NPR [1] and NS [3] materials.Auxetic materials and structures exist, and are stable in the unconstrained state, at the nanoscale (e.g. crystalline forms of silica, [8] zeolites [9] and cellulose [10] ), microscale (microporous polymers [11] and microfabricated truss-like structures [12] ) and macroscale (composite laminates, [13] foams, [14,15] honeycombs [16] and patterned elastomeric spherical shells [17] ). Enhanced shear modulus, [18] energy absorption [19] and indentation resistance [20] are some of the benefits known for auxetic materials and structures. [21] Periodic arrangements of sub-units leading to auxetic behaviour include truss, [16,22] corner-sharing polygon, [23,24] and hybrid truss-polygon [25] frameworks, and particle assemblies. [26,27] NS materials and structures, on the other hand, are thermodynamically unstable unless stabilised by an external constraint.[28] Examples of NS materials include polymethacrylimide (PMI) foams, [16] honeycombs and lattices, [29,AA1,AA2] and certain crystals (VO 2 , BaTiO 3 )undergoing constrained phase transformation. [30,31] The NS effect can also be displayed by constrained buckled tube [32] , buckled beam [33] or multiple magnet [34] systems. Whereas our system is demonstrated to display NS under quasi-static loading, it should be pointed out that a number of these previous studies [3,[30][31][32] measured the dynamic modulus. Dynamic loading of NS materials can give rise to beneficial temporary effects demonstrated, for example, in 3 3 composite systems containing NS inclusions or elements which display extreme stiffness [30] and vibration damping [3,32] responses.Our 'double-negative' mechanical metamaterial displaying simultaneous negative Poisson's ratio and negative stiffness properties comprises an auxetic host framework constraining embedded NS elements. The framework consists of a regular array of interlocked rigid hexagonal sub-units with 3 male and 3 female keys per sub-unit, arranged in an alternating fashion around the six sides of the hexagon [27] (Figure 1...