Algorithms for a strain-based plasticity criterion for bone
Article first published online: 15 JUN 2012
Copyright © 2012 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Biomedical Engineering
Volume 29, Issue 1, pages 40–61, January 2013
How to Cite
Pankaj, P. and Donaldson, F. E. (2013), Algorithms for a strain-based plasticity criterion for bone. Int. J. Numer. Meth. Biomed. Engng., 29: 40–61. doi: 10.1002/cnm.2491
- Issue published online: 3 JAN 2013
- Article first published online: 15 JUN 2012
- Manuscript Accepted: 26 MAR 2012
- Manuscript Received: 21 FEB 2012
- singularity indicators;
- benchmark tests
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 © 2012 John Wiley & Sons, Ltd.