Gradient optimization of multi-layered density-graded foam laminates for footwear material design

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.