Bibliographic record
Abstract
A general method is presented for the analytic solution of Eshelby’s problem concerned with a smooth inclusion of arbitrary shape embedded within the elastic half-plane of a bonded piezoelectric—elastic bimaterial. Since the well-known Stroh formulation, on which almost all existing works on Eshelby’s problem in piezoelectric media has been based, breaks down for isotropic elastic materials, the solutions available in the literature cannot be applied directly. Consequently, the method of solution for the current problem involves a combination of Stroh’s formulation for piezoelectric materials and the well-known Muskhelishvili method for isotropic elastic bodies. The general solution is derived in terms of an auxiliary function which can be constructed using conformal mappings that map the exterior of the inclusion onto the exterior of the unit circle. To illustrate the method, the case of a dilatational inclusion is examined and detailed results are shown for the mean stress within a thermal elliptic inclusion.
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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 | 0.000 |
| 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 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".