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

Kazi Zahir Uddin, George Youssef, Mitja Trkov, Hamid Seyyedhosseinzadeh, Behrad Koohbor

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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.

Original languageEnglish (US)
Article number109950
JournalJournal of Biomechanics
StatePublished - Aug 26 2020

All Science Journal Classification (ASJC) codes

  • Biophysics
  • Biomedical Engineering
  • Orthopedics and Sports Medicine
  • Rehabilitation


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