Hyperelastic modelling of nonlinear running surfaces

Abstract

Accurate, 3-D analyses of running impact require a constitutive model of the running surface that includes the material nonlinearity shown by many modern surfaces. This paper describes a hyperelastic continuum that mimics the experimentally measured response of a particular treadmill surface. The material model sacri®ces a little accuracy to admit a robust, low-order hyperelastic strain-energy functional. This helps prevent the premature termination of ®nite element simulations, due to numerical or material instabilities, that can occur with higher-order functionals. With only two free constants, it is also a more practical design tool. The best ®t to the quasi-static response of the treadmill was achieved with an initial shear modulus l 2 MPa and a power-stiffening index a )25. The paper outlines the method used to derive the material constants for the treadmill, a device that is not amenable to the usual materials laboratory tests and must be reverse-engineered. Finite element analyses were then performed to ensure that the treadmill model interacts with the other components of the multibody running system in a numerically stable and physically realistic manner. The model surface was struck by a rigid heel, cushioned by a hyperfoam material that represents a shoe midsole. The results show that, while the ground reaction force is similar to that obtained with a rigid surface, the maximum principal stress in the shoe is reduced by 15%. Such a reduction, particularly when endured over many load cycles, may have a signi®cant effect on comfort and damage to nearby tissue.

Constitutive Models for Rubber XII

“…While the scientific and technical litera ture offer a relatively large abundance of models suitable for rubbers (e.g. Bazkiaei et al 2020, Busfield et al 2000, Carleo et al 2018, De Tommasi et al 2019) their adoption has been so far limited in many industrial sectors, including sports surfaces (Carré et al 2006, Cole et al 2018, Kobayashi & Yukawa 2011, Thomson et al 2001 which will be the focus of the present work.…”

Probing athletics tracks degradation using a microscratch technique

“…Several factors affect the final behaviour of sports surfaces, including composition, geometrical structure and arrangement of their constituting layers [4][5][6]. The complex interplay between these variables prompted the development of numerical models as a tool to understand the behaviour of sports surfaces, predict their performance and allow their optimization [7][8][9]. With the help of these models, the separate effects of geometry and material properties were identified [10][11][12][13]; now we know that shock absorption is mostly determined by the elastic characteristics of the track material, together with its thickness.…”

Modelling the cushioning properties of athletic tracks

“…To overcome this limitation, a few simple 3D FE cases of sports surfaces have been developed [6,10,13]. The present work describes the validation of a 3D extension of the numerical models already developed for athletic tracks in [7][8]14].…”