| Several spring-damper-mass models of the human body have been developed in order to reproduce the measured ground vertical reaction forces during human running (McMahon and Cheng, 1990; Ferris and Farley, 1999; Liu and Nigg, 2000). In particular, Liu and Nigg introduced at the lower level of their model, i.e. at the interface between the human body and the ground, a nonlinear element representing simultaneously the shoe mid-soles and the ground flexibility. The ground reaction force is modelled as the force supported by this nonlinear element, whose parameters are identified from several sets of experimental data. This approach proved to be robust and quite accurate. However, it does not explicitly take into account the shoe and the ground properties. It turns out to be impossible to study the influence of shoe materials on the impact force, for instance for footwear design purposes. In this paper, a modification of the Liu and Nigg's model is suggested, where the original nonlinear element is replaced with a bi-layered spring-damper-mass model: the first layer represents the shoe mid-sole and the second layer is associated with the ground. Ground is modeled as an infinite elastic half-space. We have assumed a visco-elastic behaviour of the shoe material, so the damping of shoe material is taken into account. A methodology for the shoe soles characterization is proposed and used together with the proposed model. A parametric study is then conducted and the influence of the shoe properties on the impact force is quantified. Moreover, it is shown that impact forces are strongly affected by the ground stiffness, which should therefore be considered as an essential parameter in the footwear design. |
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