Fig. 1 Locations for the four cross-sectional areas calculated denoted by the X. The annulus ring was assumed to be cylindrical, and the area of an ellipse was calculated from the thickness and radial width data obtained via laser displacement and imagej , respectively. This average cross-section... More

Fig. 2 ( a ) Unloaded annulus ring. The rakes were driven toward the center of the ring and the annulus was manually hooked onto the rakes to ensure they did not pierce the tissue. ( b ) and ( c ) Mounted annulus ring with increasing rake-to-rake displacement to remove slack. ( d ) Preloaded (50 m... More

Fig. 3 Sample stress–strain curve with identification of tensile properties examined More

Fig. 1 The spring-mass-damper model representing the body-midsole-ground connection, developed by Ly et al. [ 1 ] to simulate ground reaction force under varying midsole conditions. Rigid and wobbling masses of the lower and upper body were represented by m1 and m2, and m3 and m4, respectively. Th... More

Fig. 2 ( a ) Conventional shoe elastic stiffnesses (midsole spring) of different hardness under compressive displacement described by exponential functions and ( b ) auxetic exponential function fit overlayed on recorded quasi-static compression data More

Fig. 3 The 3D reentrant auxetic structure under investigation and its characteristic dimensions of beam angle ( θ ), beam diameter (ø), and base length ( b ) which dictate the force tunability. The width ( w ) and thickness ( t ) of the base, as well as the height of the cell ( h ) are constant. More

Fig. 4 Typical simulated GRF for conventional (shod) and auxetic (aux) midsoles. Conventional midsoles have a single impact peak, resembling shod running. The auxetic has more than one impact peak, more alike to barefoot running. The curve from 0 ms to the time of the first peak is considered in c... More

Fig. 5 Interaction plots for ground reaction force ( a ) impact magnitude, ( b ) ILR, ( c ) average loading rate (ALR) and elastic energy storage with damping (Ns/m) and plateau height (BW). Multiple lines indicate different simulated masses ranging from 45 to 90 kg, where the lowest line at each ... More

Fig. 6 Ground reaction force metrics of ( a ) impact peak magnitudes, ( b ) instantaneous loading rate (ILR), ( c ) average loading rate (ALR), and ( d ) elastic midsole storage at the low damping condition (450 Ns/m) for simulated conditions of an auxetic midsole versus conventional midsoles for ... More

Fig. 1 NAS curve for representative stance phase (solid line). Point A corresponds to heel strike, point B corresponds to the beginning of EL, the middle X corresponds to the transition point between EL and LL, Xs to the left and right correspond to the transition point shifted ±1 deg, point C cor... More

Fig. 2 Average RMSE of Shamaei, CF, and standard SL-NAS models. Vertical brackets represent ±1 standard deviation. Asterisks above horizontal brackets represent a significant difference ( p <  0.05). Significant differences represent differences between models at the same gait speed. More

Fig. 3 ( a )–( d ) Examples of specific NAS curves (blue) with various EL beginning (*), transition point (→), and LL ending (+), as calculated by both models. Dark points are for the CF model, lighter points (red) are for the Shamaei model. Most stance phases were a mixture of ( a ) and ( b ). ( ... More

Fig. 4 Average sagittal ankle angle at which EL begins for both the Shamaei and CF methods. Vertical brackets represent ±1 standard deviation. Asterisks above horizontal brackets represent a significant difference ( p <  0.05). Significant differences represent differences between models at the... More

Fig. 5 Average ankle angle at which EL ends and LL begins, aka transition angle, for both the Shamaei and CF methods. Vertical brackets represent ±1 standard deviation. Asterisks above horizontal brackets represent a significant difference ( p <  0.05). Significant differences represent differe... More