Effect of surface elasticity on an interface crack in plane deformations
Bibliographic record
Abstract
We consider the effect of surface elasticity on an interface crack between two dissimilar linearly elastic isotropic homogeneous materials undergoing plane deformations. The bi-material is subjected to either remote tension (mode-I) or in-plane shear (mode-II) with the faces of the (interface) crack assumed to be traction-free. We incorporate surface mechanics into the model of deformation by employing a version of the continuum-based surface/interface theory of Gurtin & Murdoch. Using complex variable methods, we obtain a semi-analytical solution valid throughout the entire domain of interest (including at the crack tips) by reducing the problem to a system of coupled Cauchy singular integro-differential equations, which is solved numerically using Chebychev polynomials and a collocation method. It is shown that, among other interesting phenomena, our model predicts finite stress at the (sharp) crack tips and the corresponding stress field to be size-dependent. In particular, we note that, in contrast to the results from linear elastic fracture mechanics, when the bi-material is subjected to uniform far-field stresses (either tension or in-plane shear), the incorporation of surface effects effectively eliminates the oscillatory behaviour of the solution so that the resulting stress fields no longer suffer from oscillatory singularities at the crack tips.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".