A simple model for elastic wave propagation in hard sphere-filled random composites
Bibliographic record
Abstract
A simple model is proposed to study wave propagation in hard sphere-reinforced elastic random composites. Compared to existing related models, the proposed model is featured by a modified form of classical elastodynamic equations in which the inertia term is substituted by the acceleration field of the mass centre of a representative unit cell, supplied with a derived simple differential relation between the displacement field of the composite and the displacement field of the mass centre of a representative unit cell. The present model enjoys conceptual and mathematical simplicity although it is restricted to hard sphere-filled elastic composites in which the elastic moduli of embedded spheres are much (at least 4-5 times) stiffer than those of a softer matrix. Explicit formulas are derived for the attenuation coefficient and the effective phase velocity of plane longitudinal P-waves and transverse S-waves. The efficiency and reasonable accuracy of the present model are demonstrated by reasonably good agreement between the predicted results and some established known data. The proposed model could offer a potential general method to study various three-dimensional dynamic problems of hard sphere-filled elastic random composites.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".