Finite element analysis-based optimization of longitudinal bending stiffness and rearfoot stability in carbon-plated running shoes

Introduction The carbon-plated midsole in running shoes plays a pivotal role in enhancing the runner’s performance by storing and releasing energy. A key factor in running shoes is the Longitudinal Bending Stiffness (LBS), where higher LBS usually improves energy efficiency by enhancing energy return during a running cycle. However, a critical trade-off exists: excessive LBS can diminish performance and may increase the risk of injury. Methods To this end, this study aims to model and optimize the balance between energy efficiency and stability through finite element analysis (FEA). Specifically, the LBS was systematically adjusted by varying midsole foam materials and carbon plate thicknesses. A total of two FEA models were employed: a three-point bending simulation accessing LBS, and a lateral loading model accessing rearfoot stability. Boundary conditions for both models were defined through preliminary simulations. A parametric analysis was conducted by varying the midsole foam material and carbon plate thickness to identify optimal configurations. Results Preliminary results indicate that EVA midsoles exhibited the greatest LBS and stability, followed by PEBA, both outperforming TPU. Furthermore, thicker carbon plates showed a higher value of LBS but had little effect on stability. Discussion This research provides a novel standard of LBS testing and a novel FEA modeling framework for designing carbon-plated running shoes that enhance performance while reducing injury risks.