Fig. 5

The deformation field analysis of the stiffening element reveals its evolution from the undeformed state (blue) to Frame 1 (red) and Frame 2 (green), with Frame 1 representing an intermediate deformation state and Frame 2 closely resembling the natural curvature of the foot during running (To establish a reference, the deformation of all three samples was measured with the heel in a consistent, aligned position): (a) The bending deformation is concentrated near the metatarsophalangeal (MTP) joint, characterized by significant curvature changes in Frame 2; (b) this localized bending mimics the biomechanics of the foot during the push-off phase of running, where the MTP joint plays a vital role in energy transfer and propulsion. The analysis underscores the structural adaptability of the stiffening element, demonstrating its ability to meet the functional demands of foot motion during dynamic activities, particularly in high-stress regions like the MTP joint.