An explicit micro‐FE approach to investigate the post‐yield behaviour of trabecular bone under large deformations

Werner, Benjamin; Ovesy, Marzieh; Zysset, Philippe (2019). An explicit micro‐FE approach to investigate the post‐yield behaviour of trabecular bone under large deformations. International Journal for Numerical Methods in Biomedical Engineering, 35(5), e3188. Wiley 10.1002/cnm.3188

[img] Text
Werner_2019_IntJNumeMethodsBiomedEng.pdf - Published Version
Restricted to registered users only
Available under License Publisher holds Copyright.

Download (1MB) | Request a copy

Homogenised finite element (FE) analyses are able to predict osteoporosis-related bone fractures and become useful for clinical applications. The predictions of FE analyses depend on the apparent, heterogeneous, anisotropic, elastic, and yield material properties, which are typically determined by implicit micro-FE (μFE) analyses of trabecular bone. The objective of this study is to explore an explicit μFE approach to determine the apparent post-yield behaviour of trabecular bone, beyond the elastic and yield properties. The material behaviour of bone tissue was described by elasto-plasticity with a von Mises yield criterion closed by a planar cap for positive hydrostatic stresses to distinguish the post-yield behaviour in tension and compression. Two ultimate strains for tension and compression were calibrated to trigger element deletion and reproduce damage of trabecular bone. A convergence analysis was undertaken to assess the role of the mesh. Thirteen load cases using periodicity-compatible mixed uniform boundary conditions were applied to three human trabecular bone samples of increasing volume fractions. The effect of densification in large strains was explored. The convergence study revealed a strong dependence of the apparent ultimate stresses and strains on element size. An apparent quadric strength surface for trabecular bone was successfully fitted in a normalised stress space. The effect of densification was reproduced and correlated well with former experimental results. This study demonstrates the potential of the explicit FE formulation and the element deletion technique to reproduce damage in trabecular bone using μFE analyses. The proper account of the mesh sensitivity remains challenging for practical computing times.

Item Type:

Journal Article (Original Article)


04 Faculty of Medicine > Pre-clinic Human Medicine > Institute for Surgical Technology & Biomechanics ISTB [discontinued]

Graduate School:

Graduate School for Cellular and Biomedical Sciences (GCB)

UniBE Contributor:

Werner, Benjamin; Ovesy, Marzieh and Zysset, Philippe


500 Science > 570 Life sciences; biology
600 Technology > 610 Medicine & health
600 Technology > 620 Engineering








Philippe Zysset

Date Deposited:

04 Nov 2019 15:58

Last Modified:

10 Nov 2019 02:46

Publisher DOI:


PubMed ID:





Actions (login required)

Edit item Edit item
Provide Feedback