Finite element analysis of a layered shoe sole under biomechanical plantar pressure loading

A physiologically-motivated dual-peak Gaussian plantar pressure loading, calibrated to normal-walking ground reaction force (≈ 1 body weight), acting on a two-dimensional finite element analysis (FEA) of a multi-layered athletic shoe sole is presented. The only geometry is a stiff rubber outsole (E = 50 MPa, ν = 0.47) bonded to a compliant Ethylene-Vinyl Acetate (EVA) foam midsole (E = 5 MPa, ν = 0.40) with a total of 672 Constant Strain Triangle (CST) elements and 798 degrees of freedom. The applied load is a dual peak Gaussian pressure distribution with a primary peak in the heel (x = 33.6 mm) and a secondary peak in the metatarsal (x = 210 mm) area, calibrated to a 70 kg subject (686.7 N), to simulate the heel-strike phase. The global stiffness matrix is assembled layer-wise and is directly solved with the LU factorisation. The results indicate that the peak Von Mises stress is 141.25 kPa at the heel, the maximum vertical compression is 0.3662 mm at the heel (x ≈ 33 mm), and the total absorbed strain energy is 76.41 mJ, of which 94% is absorbed in the softer midsole. The outsole has Von Mises stress of around 1.19 times the midsole, a pattern consistent with a load-redistribution role for the outsole within this single-configuration model. The results give insight into the stress localization, load transfer between layers and energy absorption efficiency of footwear, which is relevant for design. This framework is intended as a preliminary computational screening tool for material and structural parameter exploration, rather than a validated predictor of in vivo plantar loading or injury risk.