A Finite Element Study of the Relationship Between Bone Fibril Elasticity and Degree of Mineralization
Bibliographic record
Abstract
This paper presents a two-dimensional (2D) finite element model of the mineralized collagen fibril. The model was developed to investigate the relationship between fibril elasticity and degree of mineralization, the latter is measured by volume fraction of minerals. Mineralized fibrils were modeled as two-phase composite materials with mineral platelet inclusions embedded in the collagen matrix. Fibril elasticity moduli were determined by finite element analyses. It was found that the fibril elastic modulus increases slowly with the volume fraction of minerals up to a volume fraction of 39.2%. Beyond this point, the elastic modulus increases rapidly with volume fraction. This rapid increase is probably attributed to the sharp gain in von Mises strain within the fibril resulting from a decrease in axial spacing between hydroxyapatite crystals. These results provide insights into the mechanical properties of bone at the nano-mesoscale. The results from the finite element modelling are compared with predictions from theoretical models such as the Mori-Tanaka Scheme, the Self-consistent scheme, and the Voigt-Reuss bounds. Whereas there are considerable differences between theoretical predictions and finite element results, similar trends can still be observed, indicating that finite element modelling is a promising approach to understand the effects of bone chemical composition on its mechanical behaviour.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".