Analysis of an interface crack of arbitrary shape in a three-dimensional transversely isotropic magnetoelectrothermoelastic bimaterial—part 2: Numerical method
Bibliographic record
Abstract
The extended displacement discontinuity (EDD) boundary integral equation and boundary-element method are extended and developed to analyze an arbitrarily shaped, planar interface crack in a three-dimensional, transversely isotropic, magnetoelectrothermoelastic bimaterial under combined, thermoelectromagnetomechanical loadings. The fundamental solutions for uniformly distributed EDDs applied over a constant triangular element are obtained through integrating the fundamental solutions for the unit-point EDDs given by Part 1 over the triangular area. To eliminate the oscillatory singularity near the crack front, the Dirac delta function in the integral–differential equations is approximated by the Gaussian distribution function, and accordingly, the Heaviside step function is replaced by the Error function. The extended stress intensity factors without oscillatory singularities, the energy release rate, and the local J-integral in terms of intensity factors are all obtained. To validate the solution, the EDD boundary-element method is proposed. As an application, an elliptical interface crack is numerically simulated. The influences of the applied combined loadings and material-mismatch as well as the ellipticity ratio on the multiphysical response are studied.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".