Several sports-related injuries and orthopedic treatments need the necessity of corrective shoes that can assuage the excessive pressure on sensitive locations of the foot. In the present work, we study the mechanical and energy absorption characteristics of density-graded foams designed for shoe midsoles. The stress-strain responses of polyurea foams with relative densities (nominal density of foam divided by the density of water) of 0.095, 0.23, and 0.35 are obtained experimentally and used as input to a semi-analytical model. Using this model, three-layered foam laminates with various gradients are designed and characterized in terms of their weight, strength, and energy absorption properties. We show that, in comparison with monolithic foams, significant improvement in strength and energy absorption performance can be achieved through density gradation. Our findings also suggest that there is not a single gradient that offers a superior combination of strength, energy absorption, and weight. Rather, an optimal gradient depends on the plantar location and pressure. Depending on the magnitude of the local plantar pressure, density gradients that lead to the highest specific energy absorption are identified for normal walking and running conditions.

一些与运动有关的伤害和矫形治疗需要矫正鞋的使用，以减轻脚的敏感部位的过大压力。在目前的工作中，我们研究了用于鞋中底的密度梯度泡沫的机械和能量吸收特性。通过实验获得相对密度（泡沫的名义密度除以水的密度）为0.095、0.23和0.35的聚脲泡沫的应力应变响应，并将其用作半分析模型的输入。使用该模型，可以设计并使用重量，强度和能量吸收特性来表征具有不同梯度的三层泡沫层压板。我们表明，与整体式泡沫相比，通过密度等级可以显着提高强度和能量吸收性能。我们的发现还表明，没有一个梯度能够提供强度，能量吸收和重量的出色组合。而是，最佳坡度取决于脚底的位置和压力​​。根据局部足底压力的大小，可以确定正常行走和跑步条件下导致最高比能量吸收的密度梯度。