On the non-uniqueness of solution in surface elasticity theory
Bibliographic record
Abstract
Recent researches have shown that the surface energy of some real elastic solids is unlikely to be positive semi-definite. Motivated by this, the present work studies counter-examples for uniqueness of the solution of surface elasticity theory in simple three-dimensional spherically symmetric and two-dimensional axi-symmetrical deformations. Simple sufficient conditions are derived for non-uniqueness of the solution in terms of bulk elastic modulus, surface elastic modulus and geometrical parameters of the elastic body. Unlike the non-uniqueness conditions for classical linear elasticity, which are given in terms of elastic constants alone, the geometrical dimensions of the elastic body play a key role in the non-uniqueness of the solution of surface elasticity theory. Roughly speaking, the solution of surface elasticity models can be non-unique if the smallest characteristic dimension of the body (such as thickness of a thin body, or diameter of a small body or a small hole in an elastic body) is below a certain critical value so that the magnitude of negative surface energy can compete with the positive bulk strain energy of the elastic body. For example, using the available data for the negative surface modulus suggested in the literature, our results predict that the solution could be non-unique for softer materials (such as rubbers) when the smallest characteristic dimension of the elastic body is below typically 1 µm. This result could predict self-buckling of softer elastic thin films in the presence of significant surface stresses.
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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 | 0.000 |
| 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 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".