Linear theory for the mechanics of third-gradient continua reinforced with fibers resistance to flexure
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Bibliographic record
Abstract
A linear model, framed in the setting of the second strain gradient theory, is presented for the mechanics of an elastic solid reinforced with fibers resistant to flexure. The kinematics and bending resistance of the fibers are formulated via the second and third gradient of the continuum deformation. The corresponding Euler equations and admissible boundary conditions are then obtained by means of iterated integration by parts and variational principles arising in the third gradient of virtual displacement. In particular, within the prescription of superposed incremental deformations, we derive a compatible linear model from which a complete analytical solution describing the deformations of fiber composites is obtained. The proposed linear model predicts smooth and dilatational shear angle distributions over the domain of interest, which are also aligned with the results obtained from the corresponding nonlinear theory.
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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 | 0.001 | 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 it