Validation of a multiscale hysteresis mechanics model to predict oily shoe-floor friction: isolating the effect of varying shoe materials

A predictive understanding of shoe-floor friction is critical to the design of footwear and flooring to prevent slip-and-fall accidents. Recently, friction models have been applied to footwear that predict friction by simulating the impact of the floor’s topography and the shoe’s viscoelastic material properties on viscoelastic energy loss. While these models have shown the effect of the floor’s topography on friction, the validity of these models to predict the impact of shoe material properties on friction is still unproven. The purpose of this study was to evaluate the validity of a viscoelastic friction model for predicting the coefficient of friction (COF) across eight different shoe materials in oily conditions. Eight shoes were produced with identical tread features but varying shoe materials. These were tested on ten porcelain floors of varying surfaces with fully characterised topography across several orders of magnitude in size. Oily COF was measured and a multiscale mechanics model was implemented to predict friction: using all length scales of topography data; systematically restricting the large- or small-scale topography features; and by using a range of scales that had been identified in prior research as optimal. The predictive ability of each method was quantified. The model performed best when small-scale topography of the floor and high-frequency material properties of the shoe were excluded. Therefore, this study demonstrates that this multiscale mechanics model, when tuned to only include certain scale and frequency information, is predictive of the impact of shoe material on oily COF. Practically, the present work validates a modelling approach that can evaluate material candidates for shoe outsoles, dominated by the complex modulus in the range of 80 Hz to 26 kHz.