All admissible shapes of neutral inclusions with the complete Gurtin-Murdoch surface model
Bibliographic record
Abstract
In linear elastostatics, an inclusion embedded into a host foreign matrix is referred to as ‘neutral’ when it does not disturb the original stress field in the matrix. It has been shown that an inclusion of particular shape can be made neutral by designing an appropriate interphase between the inclusion and the matrix. The Gurtin-Murdoch (G-M) interface model has been used extensively in the literature to describe the elastic behavior of an interphase at small scales. It has been shown in the literature that in the case of plane deformation, when the matrix is subjected to external in-plane loading, the use of the simplified version of the G-M interface model (with constant interface parameters), eliminates the possibility of a neutral inclusion except for the case when the inclusion is circular and the (uniform) external in-plane loading is hydrostatic. In this paper, we revisit this scenario and examine the possibility of constructing neutral inclusions using the complete version of the G-M interface model. We identify sufficient and necessary conditions for neutrality in terms of the inclusion shape, the corresponding elastic constants and loading parameters. We find that with the complete version of the G-M interface model (for constant interface parameters), it is indeed possible to construct neutral inclusions for certain non-circular inclusion shapes or non-hydrostatic uniform external in-plane loadings.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".