A Cauchy-stress based solution for a necking elastic constitutive model under large deformation
✍ Scribed by P. Olley
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 223 KB
- Volume
- 65
- Category
- Article
- ISSN
- 0029-5981
- DOI
- 10.1002/nme.1473
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✦ Synopsis
Abstract
A finite element based method for solution of large‐deformation hyperelastic constitutive models is developed, which solves the Cauchy‐stress balance equation using a single rotation of stress from principal directions to a fixed co‐ordinate system. Features of the method include stress computation by central differencing of the hyperelastic energy function, mixed integration‐order incompressibility enforcement, and an iterative solution method that employs notional ‘small strain’ stiffness. The method is applied to an interesting and difficult elastic model that replicates polymer ‘necking’; the method is shown to give good agreement with published results from a well‐established finite element package, and with published experimental results. It is shown that details of the manner in which incompressibility is enforced affects whether key experimental phenomena are clearly resolved. Copyright © 2005 John Wiley & Sons, Ltd.