Theoretical model for crack branching in magnetoelectroelastic solids
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Bibliographic record
Abstract
A mathematical model is presented to determine the fracture parameters of a finite impermeable crack with one or more branches in a magnetoelectroelastic plane subjected to the remote mechanical, electrical and magnetic loading. An integral equation approach based on the fundamental solution for a generalized dislocation is used to formulate the problem. The problem is reduced to a set of singular integral equations with the dislocation densities along the crack line as the unknown variables. The integral equation system is solved by using numerical quadrature. Selected numerical results are presented to demonstrate the dependence of crack tip field intensity factors on branch length, branch orientation, poling orientation of the medium and type of loading. Numerical results imply that a branch crack cannot propagate in a self-similar manner. Solutions for a crack with double branches show that simultaneous propagation of branches is not possible.
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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