Hyperelastic modelling of nonlinear running surfaces

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 sacrifices a little accuracy to admit a robust, low-order hyperelastic strain-energy functional. This helps prevent the premature termination of finite 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 fit to the quasi-static response of the treadmill was achieved with an initial shear modulus =2 MPa and a power-stiffening index =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 significant effect on comfort and damage to nearby tissue