A crack with surface elasticity in finite plane elastostatics
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Bibliographic record
Abstract
We consider the effect of surface elasticity on a finite crack in a particular class of compressible hyperelastic materials of harmonic type subjected to uniform remote Piola stresses. The surface mechanics is incorporated into the model of finite deformation by employing a version of the continuum-based surface/interface theory of Gurtin and Murdoch. A complete solution valid throughout the entire domain of interest is obtained by reducing the problem to two series of coupled Cauchy singular integrodifferential equations that are solved numerically using a collocation method. Our model predicts that, in general, the size-dependent Piola stresses exhibit a weak logarithmic singularity at the crack tips. For a crack in a special class of materials subjected to mode II loading, the stresses are bounded whereas the deformation gradients exhibit a logarithmic-type singularity at the crack tips.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. 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.
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)
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 it