Longitudinal Bending Stiffness Analysis of Composite Carbon Plates and Shoe Sole, Based on Three-Point Bending Test

The forefoot longitudinal bending stiffness of shoe soles, measured through the widely used three-point bending test, is a key factor influencing running economy and lower-limb biomechanics. This study utilizes the finite element method to simulate three-point bending, examining the influence of different loading rates on stiffness and analyzing the impact of various plate thicknesses and forefoot curvature radii on the stiffness of plates and the ‘plate-sole’ system. The results indicate that within the same displacement range, varying the loading rates did not affect stiffness. However, increased thickness significantly enhanced both the stiffness of the plate and the ‘plate-sole’, while a larger curvature radius of the plate resulted in a modest 5–10% stiffness increase for both. To conclude, the present study provides a theoretical foundation for further exploring the mechanical properties of carbon plate configurations in footwear. Plate stiffness is affected by both thickness and curvature radius, with thickness having a greater impact. The same applies to the ‘plate-sole’. The stiffness of the ‘plate-sole’ is not a simple sum of the individual contributions from the shoe and the plate. This non-additive response emphasizes the significant role of the shoe material in altering the plate’s mechanical properties, which is an important consideration for optimizing shoe design.