Analytic solution for a circular nano-inhomogeneity in a finite matrix
Bibliographic record
Abstract
The Gurtin-Murdoch model has found wide applications in analyzing the mechanical behaviors of nanocomposites with surface/interface effect. In the existing literature, the matrix is usually assumed to be infinite and the surface/interface effect is considered only at the inhomogeneity-matrix interface. This assumption is indeed valid as the matrix is usually at macroscale rather than nanoscale. However, if the size of the matrix decreases to the nanoscale too, the surface/interface effect will have to be considered at the outer boundary of the matrix. In this paper, the plane deformation of a circular nano-inhomogeneity embedded inside a finite circular matrix (which implies the matrix is also at nanoscale) is investigated. The stress boundary conditions are given at the inhomogeneity-matrix interface and the outer boundary of the matrix by the G-M model. The analytic solution for the stress field is finally obtained through the complex variable method. The results show that the stress field inside the inhomogeneity is still uniform (size-dependent) when the surface/interface effect is considered. In addition, the stress field inside the bulk (including the inhomogeneity and the matrix) can be influenced not only by the size and elastic constant of the inhomogeneity, but also by those of 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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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 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".