The energy release rate of a pressurized crack in soft elastic materials: effects of surface tension and large deformation
Bibliographic record
Abstract
In this paper we present a theoretical study on how surface tension affects fracture of soft solids. In classical fracture theory, the resistance to fracture is partly attributed to the energy required to create new surfaces. Thus, the energy released to the crack tip must overcome the surface energy in order to propagate a crack. In soft materials, however, surface tension can cause significant deformation and can reduce the energy release rate for crack propagation by resisting the stretch of crack surfaces. We quantify this effect by studying the inflation of a penny-shaped crack in an infinite elastic body with applied pressure. To avoid numerical difficulty caused by singular fields near the crack tip, we derived an expression for the energy release rate which depends on the applied pressure, the surface tension, the inflated crack volume and the deformed crack area. This expression is evaluated using a newly developed finite element method with surface tension elements. Our calculation shows that, when the elasto-capillary number ω ≡ σ/Ea is sufficiently large, where σ is the isotropic surface tension, E is the small strain Young's modulus and a is the initial crack radius, both the energy release rate and the crack opening displacement of an incompressible neo-Hookean solid are significantly reduced by surface tension. For a sufficiently high elasto-capillary number, the energy release rate can be negative for applied pressure less than a critical amount, suggesting that surface tension can cause crack healing in soft elastic materials.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 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) | 0.001 | 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".