Shape-dependent initial pressure effects of fluid inclusions in an elastic solid under plane deformation
Bibliographic record
Abstract
We reconsider the plane deformation of an isotropic elastic solid matrix enclosing macroscale compressible fluid inclusions. The initial pressure inside the fluid inclusions proves to play a significant role in tuning the elastic response of the solid–fluid composite to external loadings. Such initial pressure effects cannot be captured via the classical treatment based on linear elasticity. We follow a modified boundary condition proposed earlier in the literature to examine the influence of the initial pressure in the inclusions on the external loading-induced local and overall elastic behavior of the composite for general shapes of the inclusions. Specifically, we derive initial pressure-dependent closed-form solutions for incremental stress distributions (caused by an in-plane far-field loading) around an isolated fluid inclusion of practically arbitrary shape and then attain initial pressure-dependent in-plane effective properties of the composite containing randomly distributed fluid inclusions (for a given volume fraction) based on certain homogenization methods. Numerical results are presented mainly for a soft elastic solid containing, respectively, approximately regular polygonal liquid inclusions, approximately rectangular liquid inclusions and elliptical liquid inclusions. We show that the initial pressure in the inclusions always enhances the effective moduli of the corresponding composites and that for given volume fraction of the inclusions such enhancement effects are reduced with an increasing number of sides of the inclusions (in terms of regular polygonal cases) while they are amplified with increasing slenderness of the inclusions (in terms of rectangular and elliptical cases).
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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 | 0.000 | 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".