Nonlinear elasticity of biological tissues with statistical fibre orientation
Bibliographic record
Abstract
The elastic strain energy potential for nonlinear fibre-reinforced materials is customarily obtained by superposition of the potentials of the matrix and of each family of fibres. Composites with statistically oriented fibres, such as biological tissues, can be seen as being reinforced by a continuous infinity of fibre families, the orientation of which can be represented by means of a probability density function defined on the unit sphere (i.e. the solid angle). In this case, the superposition procedure gives rise to an integral form of the elastic potential such that the deformation features in the integral, which therefore cannot be calculated a priori. As a consequence, an analytical use of this potential is impossible. In this paper, we implemented this integral form of the elastic potential into a numerical procedure that evaluates the potential, the stress and the elasticity tensor at each deformation step. The numerical integration over the unit sphere is performed by means of the method of spherical designs, in which the result of the integral is approximated by a suitable sum over a discrete subset of the unit sphere. As an example of application, we modelled the collagen fibre distribution in articular cartilage, and used it in simulating displacement-controlled tests: the unconfined compression of a cylindrical sample and the contact problem in the hip joint.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".