An arbitrarily shaped Eshelby inclusion interacting with a circular piezoelectric inhomogeneity penetrated by a semi-infinite crack
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Bibliographic record
Abstract
We study the interaction between an Eshelby inclusion of arbitrary shape and a circular piezoelectric inhomogeneity penetrated by a semi-infinite crack under antiplane mechanical and in-plane electrical loading in a linear piezoelectric solid.The Eshelby inclusion undergoes uniform antiplane eigenstrains and inplane eigenelectric fields.Through the use of a conformal mapping, the cracked piezoelectric plane is first mapped onto the lower half of the image plane.The corresponding boundary value problem is then studied in this image plane.The interaction problem is solved through the construction of an auxiliary function and the application of analytic continuation across straight and circular boundaries.We obtain concise expressions for the resultant stress and electric displacement intensity factors at the crack tip.
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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) | 0.001 | 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