External Crack in Torsion in an Infinite Non-Homogeneous Medium with a Non-Homogeneous Cylindrical Inclusion
Bibliographic record
Abstract
This paper deals with the determination of stresses in a non-homogeneous infinite medium containing an external crack surrounding a non-homogeneous cylindrical inclusion. The crack occupies the region outside the circle surrounding the cylindrical inclusion. The cylindrical inclusion (fiber) and the infinite medium (matrix) have different shear moduli. The external crack is opened by internal shear stresses acting along the crack. The continuity of stress and displacement is assumed at the common cylindrical surface due to perfect bonding. With reference to the cylindrical coordinates the shear modulus of the inclusion and matrix are assumed to be of the forms G1 eβ|z| and G_2rα eβ|z| where G1, G2, α, and β are real constants and α > — 2. The geometry of the problems is more clearly shown in Fig. 1. The problem is reduced to the solution of a Fredholm integral equation of the second kind, which is solved numerically. A closed form expression is obtained for the stress intensity factor and numerical values for stress intensity factor are graphed to demonstrate the effect of non-homogeneity of the inclusion and infinite medium. Finally the order of the singularity is obtained when the crack approaches the inclusion.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 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".