Step-by-Step Simplification of the Micropolar Elasticity Theory to the Couple-Stress and Classical Elasticity Theories
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Bibliographic record
Abstract
The micropolar elasticity theory provides a useful material model for dealing with fibrous, coarse granular, and large molecule materials. Though being a well-known and well-developed elasticity model, the linear theory of micropolar elasticity is not without controversy. Specially simplification of the microppolar elasticity theory to the couple-stress and classical elasticity theories and the required conditions on the material elastic constants for this simplification have not been discussed consistently. In this paper the linear theory of micropolar elasticity is reviewed first. Then the correct approach for a consistent and step-by-step simplification of the micropolar elasticity model with six elastic constants to the couple-stress elasticity model with four elastic constants and the classical elasticity model with two elastic constants is presented. It is shown that the classical elasticity is a special case of the couple-stress theory which itself is a special case of the micropolar elasticity 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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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