Algorithms for a strain‐based plasticity criterion for bone. (15th June 2012)

• Record Type: Journal Article
• Authors: Pankaj, Pankaj; Donaldson, Finn E.
• Is Part Of: International journal for numerical methods in biomedical engineering. Volume 29:Number 1(2013:Jan.)
• Page Start: 40
• Page End: 61
• Publication Date: 2012-06-15
• Subjects: stress‐based -- anisotropy -- singularity indicators -- benchmark tests; Biomedical engineering -- Periodicals; Imaging systems in medicine -- Periodicals; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 610.28
• DOI: 10.1002/cnm.2491
• Languages: English
• ISSNs: 2040-7939

Abstract

SUMMARY: 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. Abstract : A simple and robust strain‐based plasticity algorithm, based on minimum and maximum principal strain, is developed for simulating the post‐elastic behaviour of bone. Unlike stress‐based criteria, the isotropic nature of the criterion is particularly advantageous. Singularity indicators are derived to direct the algorithm to make plastic corrector returns to the singular locations of the criterion, and the developed algorithms permit a plastic corrector to be achieved in a single iterative step in all cases.