Bibliographic record
Abstract
The paper examines the mechanics of inflation of incompressible planar hyperelastic membranes that are rigidly fixed at their boundary and subjected to a uniform pressure. Strain energy functions characterized by the neo-Hookean, Mooney–Rivlin and the Ogden forms are used. Fixity is provided along either circular or elliptical boundaries. The computational results indicate that the strain energy function has a significant influence on the pressure versus inflated volume response of the deformed membrane. When the strain energy function corresponds to a Mooney–Rivlin form, the circular membrane displays no tendency to develop any instability. The equivalent circular membranes composed of both the neo-Hookean and Ogden-type strain energy functions developed an initial ‘ Wrinkling Instability ’. For planar membranes with an elliptical planform, the wrinkling instability is more pronounced; membranes composed of hyperelastic materials with a Mooney–Rivlin form of the strain energy function continue to deform without the development of an initial instability point, whereas membranes composed of both the neo-Hookean and Ogden materials exhibit wrinkling behaviour at critical locations at the interior of the fixed boundary region. The dependency of the strain energy function on the second invariant of the Cauchy–Green strain tensor has an influence in the suppression of hyperelastic effects. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.
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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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".