Uniform stress field inside a non-parabolic open inhomogeneity interacting with a mode III crack
Bibliographic record
Abstract
Using conformal mapping techniques, analytic continuation and the theory of Cauchy singular integral equations, we prove that a non-parabolic open inhomogeneity embedded in an elastic matrix subjected to a uniform remote anti-plane stress nevertheless admits an internal uniform stress field despite the presence of a finite mode III crack in its vicinity. Our analysis indicates that: (i) the internal uniform stress field is independent of the specific shape of the inhomogeneity and the presence of the finite crack; (ii) the existence of the finite crack plays a key role in the non-parabolic open shape of the inhomogeneity and in the non-uniform stresses in the surrounding matrix; (iii) the two-term asymptotic expansion at infinity of the stress field in the matrix is independent of the presence of the finite crack. Detailed numerical results are presented to demonstrate the proposed theory.
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How this classification was reachedexpand
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 | 0.000 | 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 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".