Hyperelastic modelling of nonlinear running surfaces

Thomson, R.D., Birkbeck, A.E. and Lucas, T.D. (2001) Hyperelastic modelling of nonlinear running surfaces. Sports Engineering, 4(4), pp. 215-224. (doi: 10.1046/j.1460-2687.2001.00088.x)

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 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Birkbeck, Mr Alan
• Authors: Thomson, R.D., Birkbeck, A.E., and Lucas, T.D.
• Subjects: G Geography. Anthropology. Recreation > GV Recreation Leisure; T Technology > TJ Mechanical engineering and machinery
• College/School: College of Science and Engineering > School of Engineering > Systems Power and Energy
• Journal Name: Sports Engineering
• Publisher: Blackwell Publishing
• ISSN: 1460-2687
• Copyright Holders: © Blackwell Publishing
• First Published: First published in Sports Engineering 4(4):215-224
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher