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Midsoles are important components in footwear as they provide shock absorption and stability, thereby improving comfort and effectively preventing certain foot injuries. A strategically engineered midsole designed to mitigate plantar pressure can enhance athletic performance and comfort levels. Despite the importance of midsole design, the potential of using in-plane density gradation (deliberate variation of material density across the horizontal plane) in midsoles has been rarely explored. The present work investigated the effectiveness of in-plane density gradation in shoe midsoles using novel polyurea foams as the material candidate. Different polyurea foam densities, ranging from 95 to 350 kg/m²were examined and tested to construct density-dependent correlative mathematical relations required for optimizing the midsole design for enhanced cushioning and reduced weight. This study combined mechanical testing and plantar pressure measurements to validate the efficacy of density-graded midsoles. The methodology introduced here is relevant to realistic walking conditions, ensured by biomechanical tests supplemented by digital image correlation analyses. An optimization framework was then created to allocate foam densities at certain plantar zones based on the required cushioning performance constrained by the local pressure. The optimization algorithm was specifically tailored to accommodate varying local pressures experienced by different areas of the foot. The optimization strategy in this study aimed at reducing the overall weight of the midsole while ensuring there were no compromises in cushioning efficacy or distribution of plantar pressure. The approach presented herein has the potential to be applied to a wide range of gait speeds and user-specific plantar pressure patterns. 

This research investigates the dynamic response of a novel polyurea foam with different densities by separately submitting samples to single and multiple impacts at different energies ranging from 1.77 to 7.09 J. The impact and transmitted force‐time histories are acquired during the impact events. Deformation of the samples is also recorded using high‐speed photography and analyzed using digital image correlation (DIC) to characterize density‐dependent strain rate and Poisson's ratio. The analyses of the force‐time histories highlight the interrelationship between the incoming impact energy and force characteristics, including amplitude and durations. The experimental results reveal that polyurea foams can absorb nearly 50% of the incoming impact energy irrespective of their density. The dynamic impact efficacy of the foam persists even after sequential impact events are imparted on the same samples, with only a 20% drop in the load‐bearing capacity after seven consecutive impacts. Furthermore, as verified via electron microscopy observations, the higher‐density foam does not exhibit any permanent damage. This high‐density polyurea foam shows reversible auxetic transition at all impact energies considered herein. The outcomes of this research indicate the suitability of polyurea foams for cushioning and impact mitigation applications, especially in repeated biomechanical impact scenarios. 

Auxetic mechanical metamaterials show significant potential to impact many engineering fields and have been a topic of considerable research interest in recent years. Existing literature on the topic often aims to achieve larger negative Poisson's ratios or tailorable responses by carefully designed and distributed unit cells. Herein, it is aimed to investigate the relationships between global and local strain fields in rectangular center‐symmetric perforated planar structures, thus highlighting the role of local morphology on the macroscopic material response. Additively manufactured samples with hyperelastic constitutive behavior are characterized under tension. The structures are designed and developed with several perforation aspect ratios, leading to various degrees of auxeticity. Global and local strain fields are characterized using a multiscale digital image correlation measurement approach. The local rotation and in‐plane strain fields generated within the solid portions of the unit cells are correlated with the global strain fields and macroscopic Poisson's ratios for a range of cell geometries. The interplay between cell rotation and strain at the meso (unit cell) scale is shown to be the dominant factor in the strain‐dependent evolution of the Poisson's ratio in the structures.