The Effects of Surface Elasticity on an Elastic Solid With Mode-III Crack: Complete Solution
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A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Full frame distilled prediction
Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
- Candidate categories
- none
- Consensus categories
- none
- Domain
- Candidate signal: noneConsensus signal: none
- Study design
- Candidate signal: Simulation or modelingConsensus signal: Simulation or modeling
- Genre
- Candidate signal: EmpiricalConsensus signal: none
- Teacher disagreement score
- 0.797
- Threshold uncertainty score
- 0.551
- Validation status
machine_predicted_unvalidated·codex-gemma-dda1882f352a
Codex and Gemma teacher scores by category
| 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 | 0.000 |
| Scholarly communication | 0.000 | 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)
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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.
- Teacher spread
- 0.235 · how far apart the two teachers sit on this one work
- Validation status
score_only:v0-immature-baseline· verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it
Abstract
We examined the effects of surface elasticity in a classical mode-III crack problem arising in the antiplane shear deformations of a linearly elastic solid. The surface mechanics are incorporated using the continuum based surface/interface model of Gurtin and Murdoch. Complex variable methods are used to obtain an exact solution valid everywhere in the domain of interest (including at the crack tip) by reducing the problem to a Cauchy singular integro-differential equation of the first order. Finally, we adapt classical collocation methods to obtain numerical solutions, which demonstrate several interesting phenomena in the case when the solid incorporates a traction-free crack face and is subjected to uniform remote loading. In particular, we note that, in contrast to the classical result from linear elastic fracture mechanics, the stresses at the (sharp) crack tip remain finite.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
The record
- Venue
- Journal of Applied Mechanics
- Topic
- Numerical methods in engineering
- Field
- Engineering
- Canadian institutions
- University of Alberta
- Funders
- Natural Sciences and Engineering Research Council of Canada
- Keywords
- Antiplane shearElasticity (physics)Cauchy distributionLinear elasticityTraction (geology)Fracture mechanicsMathematical analysisMechanicsMaterials scienceFree surfaceMathematicsStress intensity factorPhysicsFinite element methodComposite material
- Has abstract in OpenAlex
- yes