Performance of hyperelastic material laws in simulating biaxial deformation response of polypropylene and high impact polystyrene

K. Y. Tshai*, E. M. A. Harkin-Jones, P. J. Martin

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter


Free surface moulding processes such as thermoforming and blow moulding involve thermal and spatial varying rate dependent biaxial deformation of polymer. These processes are so rapid that the entire forming took place in a matter of seconds. As a result of the elevated rate of deformation, assumption that the deforming polymers experience no time dependent viscous dissipation or perfectly elastic up to large strain has became a common practice in numerical simulation. Following the above assumption, Cauchy’s elastic and hyperelastic theories, originally developed for vulcanised natural rubber has been widely used to represent deforming polymeric materials in free surface moulding processes. To date, various methodologies were applied in the development of these theories, the most significant are those develop purely based on mathematical interpolation (mathematical models) and a more scientific network theories that involves the interpretation of macro-molecular structure within the polymer. In this chapter, the most frequently quoted Cauchy’s elastic and hyperelastic theories, including Ogden, Mooney–Rivlin, neo-Hookean, 3-chain, 8-chain, Van der Waals full network, Ball’s tube model, Edwards–Vilgis crosslinks-sliplinks model and the elastic model of Sweeney–Ward are reviewed. These models were analysed and fitted to a series of experimental high strain rate, high temperature, biaxial deformations data of polypropylene (PP) and high impact polystyrene (HIPS). The performance and suitability of the various models in capturing the polymer’s complex deformation behaviour during free surface moulding processes is presented.

Original languageEnglish
Title of host publicationNumerical Modeling of Materials Under Extreme Conditions
Number of pages32
Publication statusPublished - 2014

Publication series

NameAdvanced Structured Materials
PublisherSpringer Science + Business Media
ISSN (Print)1869-8433

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2014.

Copyright 2015 Elsevier B.V., All rights reserved.


  • Biaxial deformation
  • Free surface moulding
  • High strain rate
  • High temperature
  • Hyperelastic model

ASJC Scopus subject areas

  • Materials Science(all)


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