Algorithms for a strain-based plasticity criterion for bone

作者：Pankaj Pankaj^*; Donaldson Finn E

来源：International Journal for Numerical Methods in Biomedical Engineering, 2013, 29(1): 40-61.

DOI：10.1002/cnm.2491

• stress-based
• anisotropy
• 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.

• 出版日期2013-1