Development of a method for quantifying the midsole reaction model parameters

Abstract

Midsole force–deformation pattern has important implications in determining the kinematics and kinetics of foot during locomotion. Furthermore, the midsole stiffness and viscosity determine the midsole's force–deformation behaviour. Despite the importance of stiffness and damping components of the midsole reaction, which determines the shoe-specific ground reaction forces during locomotion, there is still a lack of methodology to quantify them separately. The purpose of this study was to develop a method of extracting the shoe-specific midsole stiffness and damping components during uniaxial compression testing. For this purpose, the force–deformation behaviour of the sole was modelled as a system consisting of a nonlinear spring and a nonlinear damper. Based on the fact that the stiffness and damping component of the midsole reaction force acts in favour during loading, and work against each other during unloading, the stiffness and damping components were separated. Utilising a curve-fitting technique, a parametric curve represented by the stiffness and damping components of the midsole reaction force model was fitted to each components of force-deformation data to extract the parameters. Statistical tests indicated that the proposed method is reliable for extracting the midsole reaction model parameters with the stiffness and damping components producing favorable results (R² 0.998 ± 0.000 and 0.984 ± 0.018/root mean squared error of 5.550 ± 0.954 and 3.286 ± 2.504, respectively).

Keywords::

• midsole reaction model
• parametric curve fitting
• footwear
• ground reaction force
• midsole deformation

Acknowledgements

This work was funded in part through, the European Community's Seventh Framework Programme under grant agreement no. 222468 (Heelless). The authors would also like to thank Abbas Daragheh for his assistance with data collection.