Evaluating the macroscopic yield behaviour of trabecular bone using a nonlinear homogenisation approach
Open accessAbstract
Computational homogenisation approaches using high resolution images and finite element (FE) modelling have been extensively employed to evaluate the anisotropic elastic properties of trabecular bone. The aim of this study was to extend its application to characterise the macroscopic yield behaviour of trabecular bone. Twenty trabecular bone samples were scanned using a micro-computed tomography device, converted to voxelised FE meshes and subjected to 160 load cases each (to define a homogenised multiaxial yield surface which represents several possible strain combinations). Simulations were carried out using a parallel code developed in-house. The nonlinear algorithms included both geometrical and material nonlinearities. The study found that for tension-tension and compression-compression regimes in normal strain space, the yield strains have an isotropic behaviour. However, in the tension-compression quadrants, pure shear and combined normal-shear planes, the macroscopic strain norms at yield have a relatively large variation. Also, our treatment of clockwise and counter-clockwise shears as separate loading cases showed that the differences in these two directions cannot be ignored. A quadric yield surface, used to evaluate the goodness of fit, showed that an isotropic criterion adequately represents yield in strain space though errors with orthotropic and anisotropic criteria are slightly smaller. Consequently, although the isotropic yield surface presents itself as the most suitable assumption, it may not work well for all load cases. This work provides a comprehensive assessment of material symmetries of trabecular bone at the macroscale and describes in detail its macroscopic yield and its underlying microscopic mechanics.
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Casting the yield criterion in terms of strain, rather than stress, eliminates nearly all of the dependence of the yield surface on porosity and much of its dependence on fabric.
“As several of these studies have found, casting the yield criterion in terms of strain, rather than stress, eliminates nearly all of the dependence of the yield surface on porosity and much of its dependence on fabric.”
From Bone Mechanical Properties in Healthy and Diseased States (2018) · cites this paper as [123]
The Introduction (p. 3) describes strain-space behaviour as more isotropic and density-independent than stress-space behaviour, and the Results (p. 7) find little relationship between uniaxial yield strains, BV/TV, and fabric. But the Conclusions (p. 12) report substantial variation in other loading regimes, so the claim that strain-based casting eliminates nearly all porosity dependence across the yield surface is too broad. (LLM, conf=0.86)
Experimental — accuracy not yet measuredThis barrier was subsequently overcome using numerical simulation, and there now exist several multiaxial yield criteria for trabecular bone.
“This barrier was subsequently overcome using numerical simulation, as discussed in Section 2.2.9, below, and there now exist several multiaxial yield criteria for trabecular bone (see References 121–123 and references therein).”
From Bone Mechanical Properties in Healthy and Diseased States (2018) · cites this paper as [123]
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Self-citation
- Authors
- Levrero-Florencio, F., Margetts, L., Sales, E., Xie, S., Manda, K., & Pankaj, P.
- Affiliations
- University of Edinburgh (GB)
- University of Manchester (GB)
- Corresponding author
- Levrero-Florencio, Francesc
- Venue
- Journal of the Mechanical Behavior of Biomedical Materials
- Publisher
- Elsevier BV
- Published
- 2016-08
- Volume
- 61
- Pages
- 384-396
- ISSN
- 1751-6161 (ISSN-L)
- OpenAlex
- W2339878253
- Cited by
- 46
- References
- 75
- Citations by year
- 2026: 2 · 2025: 2 · 2024: 2 · 2023: 2 · 2022: 5 · 2021: 1 · 2020: 6 · 2019: 8 · 2018: 8 · 2017: 6 · 2016: 4
- FWCI
- 7.47
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Journal of the mechanical behavior of biomedical materials/Journal of mechanical behavior of biomedical materials (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Edinburgh Research Explorer (University of Edinburgh) (publishedVersion, other-oa)
- Research Portal (Queen's University Belfast) (submittedVersion, cc-by)
- Research Explorer (The University of Manchester) (submittedVersion, cc-by)
- Funders
- University of Edinburgh
- National Centre for Supercomputing Applications (e398, EP/K036939/1)
- Biotechnology and Biological Sciences Research Council (BB/K006029/1)
- Engineering and Physical Sciences Research Council
- Science and Technology Facilities Council (HCP010)
- Topics
- Physical Sciences › Engineering › Mechanics of Materials › Composite Material Mechanics
- Health Sciences › Medicine › Orthopedics and Sports Medicine › Bone health and osteoporosis research
- Physical Sciences › Engineering › Biomedical Engineering › Elasticity and Material Modeling
- Keywords
- trabecular bone, yield criterion, material symmetry, tension-compression asymmetry, shear loading, micro-computed tomography, geometric and material nonlinearity
- MeSH terms
- Cancellous Bone, Biomechanical Phenomena, Humans, Stress, Mechanical, Anisotropy, Finite Element Analysis, X-Ray Microtomography
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