A level set method for simulating wrinkling of extruded viscoelastic sheets
Bibliographic record
Abstract
Abstract When a polymer is extruded freely from a rectangular die of large cross‐sectional aspect ratio, wrinkles are observed. While not present in extruded Newtonian materials, such wrinkles develop in extruded viscoelastic sheets and are understood as an elastic stress‐driven instability. The present study is devoted in developing a transient finite element method, which combines the matrix‐logarithm‐based formulation of the conformation tensor and the single‐phase level set method, for simulating wrinkles that form during sheet extrusion of viscoelastic fluids. Numerical analyses of sheet extrusion were conducted over a wide range of flow rate and width‐to‐thickness ratio of the die exit cross section, χ, to determine critical conditions for the onset of wrinkling of extruded sheets. For large aspect ratios, that is, χ >> 1, wrinkles develop at moderate extrusion flow rate, corresponding to a Weissenberg number of about 29. Calculations based on Rayleigh's energy method show that the critical compressive stress, σc, for the onset of wrinkling of an elastic sheet scales like σc~1/χ2, with a significant drop for χ >> 1. As next to the die exit lip, compressive normal stresses are induced in the extruded sheet, wrinkling will take place for large χ (σc being small), in accordance with numerical predictions.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".