Remodelling in statistically oriented fibre-reinforced materials and biological tissues
Bibliographic record
Abstract
We present a mathematical model of structural reorganisation in a fibre-reinforced composite material in which the fibres are oriented statistically, i.e. obey a probability distribution of orientation. Such a composite material exemplifies a biological tissue (e.g. articular cartilage or a blood vessel) whose soft matrix is reinforced by collagen fibres. The structural reorganisation of the composite takes place as fibres reorient, in response to mechanical stimuli, in order to optimise the stress distribution in the tissue. Our mathematical model is based on the Principle of Virtual Powers and the study of dissipation. Besides incompressibility, our main hypothesis is that the composite is characterised by a probability density distribution that measures the probability of finding a family of fibres aligned along a given direction at a fixed material point. Under this assumption, we describe the reorientation of fibres as the evolution of the most probable direction along which the fibres are aligned. To test our theory, we compare our simulations of a benchmark problem with selected results taken from the literature.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".