Analysis of a mode-I crack in a one-dimensional orthorhombic quasicrystal strip
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Bibliographic record
Abstract
A mode-I crack in a one-dimensional (1D) orthorhombic quasicrystal (QC) strip under in-plane phonon and phason stress loading is considered. Fourier transforms are applied to reduce the mixed boundary value problem of the mode-I crack to solving a system of simultaneous singular integral equations. Asymptotic expressions of the phonon and phason stresses and displacement fields near the crack tips have been obtained in an explicit form. The crack-tip singularities of the mode-I crack have been investigated and the intensity factors of the stresses in the phonon and phason fields are derived explicitly. The stress intensity factors (SIFs) and the hoop stress intensity factors (HSIFs) have been determined to investigate the effect of the geometric size and the crack kinking phenomenon. The effect of the thickness ratio of the cracked strip on the SIFs and energy release rates has been investigated. When the thickness of the cracked strip becomes infinite large, the results obtained for the crack problem can be reduced to the analytic solution for a mode-I crack in an infinite 1D orthorhombic QC media.
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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 | 0.001 | 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) | 0.001 | 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 it