Midsoles are important components in footwear as they provide shock absorption and stability, thereby improving comfort and effectively preventing certain foot and ankle injuries. A rationally tailored midsole can potentially mitigate plantar pressure, improving performance and comfort levels. Despite the importance of midsole design, the potential of using in-plane density gradation in midsole has been rarely explored in earlier studies. The present work investigates the effectiveness of in-plane density gradation in shoe midsoles using a new class of polyurea foams as the material candidate. Their excellent cushioning properties justify the use of polyurea foams. Different polyurea foam densities, ranging from 95 to 350 kg/m3 are examined and tested to construct density-dependent correlative mathematical relations required for the optimization process. An optimization framework is then created to allocate foam densities at certain plantar zones based on the required cushioning performance constrained by the local pressures. The interior-point algorithm was used to solve the constrained optimization problem. The optimization algorithm introduces a novel approach, utilizing the maximum specific energy absorption as the objective function. The optimization process identifies specific foam densities at various plantar regions for maximum biomechanical energy dissipation without incurring additional weight penalties. Our results suggest midsole design can benefit from horizontal (in-plane) density gradation, leading to potential weight reduction and localized cushioning improvements. With local plantar peak pressure data analysis, the optimization results indicate low-density polyurea foams (140 kg/m3) for central and lateral phalanges, whereas stiffer foams (185-230 kg/m3) are identified as suitable candidates for metatarsal and arch regions in an in-plane density graded midsole design.
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