A Neutral Nonlinear Elastic Circular Inhomogeneity Obeying Neuber’s Stress–Strain Law in Anti-Plane Shear
Bibliographic record
Abstract
Summary We consider a three-phase composite in which the internal circular inhomogeneity obeying Neuber’s nonlinear stress-strain law is bonded to an infinite linear isotropic elastic matrix via a middle linear isotropic elastic annular coating when the matrix is subjected to uniform remote anti-plane stresses. A neutral circular inhomogeneity that does not disturb the prescribed uniform stress field in the matrix is identified by numerically solving the resulting two coupled nonlinear equations via iteration or equivalently by solving a single sextic equation to arrive at the constant effective strain within the inhomogeneity and the ratio of the shear modulus of the matrix to that of the coating. The upper bound of the shear modulus ratio is the classical Hashin–Shtrikman formula while the lower bound is the classical Hashin–Shtrikman formula for a cavity. A neutral coated nonlinear spherical inhomogeneity in conductivity obeying Neuber’s law is also designed.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 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".