An Eshelby inclusion of arbitrary shape in a degenerate orthotropic elastic plane
Bibliographic record
Abstract
Using Suo’s complex variable formulation, we first derive a general solution to the plane problem of an infinite homogeneous degenerate orthotropic elastic plane containing an Eshelby inclusion of arbitrary shape undergoing uniform in-plane eigenstrains. The elastic field within the Eshelby inclusion is identified once the two polynomials representing the principal parts of the remote asymptotic behaviors of two auxiliary functions are determined. We next derive an explicit solution to the problem of an inclusion having an ( n +1)-fold axis of quasi-symmetry (with n ≥1) in an infinite degenerate orthotropic elastic material. The inclusion boundary has an ( n +1)-fold axis of symmetry in the z -plane, where z is the single complex variable appearing in Suo’s formulation, and is described by a four-term mapping function. The non-uniform distributions of the total strains and rigid body rotation within the quasi-symmetric inclusion are completely determined. We further prove that when n ≥2, the arithmetic mean of the Eshelby tensors at n +1 rotational symmetric points within the inclusion in the z -plane is equal to the constant Eshelby tensor within a special elliptical inclusion, the boundary of which is circular in the z -plane, and that it is independent of the rotation of the inclusion boundary in the z -plane.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".