Algorithms for a strain-based plasticity criterion for bone

Pankaj Pankaj, Finn E. Donaldson

Research output: Contribution to journalArticlepeer-review

Abstract

A range of stress-based plasticity criteria have been employed in the finite element analysis of the post-elastic behaviour of bone. There is some recognition now that strain-based criteria are more suitable for this material because they better represent its behaviour. Moreover, because bone yields at relatively isotropic strains, a strain-based criterion requires fewer material parameters unlike those required for a stress-based criterion. Based on a minimum and maximum principal strain criterion, a robust strain-based plasticity algorithm is developed. As the criterion comprises six piecewise linear surfaces in principal strain space, it has a number of singular regions. Singularity indicators are developed to direct the algorithm to make appropriate plastic corrector returns when singularity regions are encountered. The developed algorithms permit a plastic corrector to be achieved in a single iterative step in all cases. A range of benchmark tests are developed and conducted after implementing the algorithm in a finite element package. These tests show that the constitutive behaviour is as expected. Copyright (C) 2012 John Wiley & Sons, Ltd.

Original languageEnglish
Pages (from-to)40-61
Number of pages22
JournalInternational Journal for Numerical Methods in Biomedical Engineering
Volume29
Issue number1
Early online date15 Jun 2012
DOIs
Publication statusPublished - Jan 2013

Keywords

  • stress-based
  • anisotropy
  • singularity indicators
  • benchmark tests

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