Uniform in‐plane elastic field inside a monoclinic elliptical inhomogeneity with non‐confocal elliptical interphase layer
Bibliographic record
Abstract
Abstract We employ the Stroh quartic formalism to study the in‐plane deformations of a three‐phase composite consisting of an elliptical inhomogeneity embedded in an infinite matrix via an intermediate interphase layer itself bounded by two elliptical boundaries. The matrix is subjected to uniform remote in‐plane loading. The two corresponding elliptical interfaces (one between the inhomogeneity and the interphase layer and the other between the interphase layer and the surrounding matrix) are non‐confocal. The inhomogeneity and the matrix are assumed to be monoclinic materials with the symmetry plane at x 3 = 0 whilst the intermediate interphase layer is composed of a mathematically degenerate orthotropic material. The non‐confocal character of the two elliptical interfaces is carefully designed according to the orthotropic property of the interphase layer. Two simple conditions are found that ensure that the internal elastic field of stresses and strains inside the elliptical inhomogeneity is uniform. For given material and geometric parameters of the composite, these two conditions give two simple relationships among the three remote in‐plane stresses. In addition, the internal uniform elastic field inside the elliptical inhomogeneity and the non‐uniform elastic field in the interphase layer are determined in real‐form in terms of the two 4 × 4 fundamental elasticity matrices for the inhomogeneity and the matrix and the three 2 × 2 Barnett‐Lothe tensors for (only) the matrix.
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How this classification was reachedexpand
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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".