Analysis of Internal Stress in an Elliptic Inclusion with Imperfect Interface in Plane Elasticity
Bibliographic record
Abstract
This paper reports a semianalytic solution for the internal stresses associated with an elliptic inclusion embedded within an infinite matrix in plane elasticity. The bonding at the inclusion-matrix interface is assumed to be homogeneously imperfect with corresponding interface conditions defined in terms of linear relations between interface tractions and displacement jumps. Complex variable techniques are used to obtain infinite series representations of the internal stresses (specifically, the mean stress and the von Mises equivalent stress) that, when evaluated numerically, demonstrate how the internal stresses vary with the aspect ratio of the inclusion and the parameter h describing the imperfection in the interface. These results can be used to evaluate the effects of the imperfect interface and the aspect ratio of the inclusion on internal failure caused by void formation and plastic yielding within the inclusion. Remarkably, the mean stress and von Mises equivalent stress are both found to be nonmonotonic functions of the imperfect interface parameter h. Consequently, in each case, we can identify a specific value (h*) of h that corresponds to the maximum peak stress (mean or von Mises) inside the inclusion. This special value h* of the interface parameter depends on the aspect ratio of the elliptic inclusion and the imperfect interface condition.
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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 | 0.001 |
| 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) | 0.000 | 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 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".