Numerical simulation of film casting using an updated lagrangian finite element algorithm
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Bibliographic record
Abstract
Abstract This paper presents a new numerical algorithm for 2D nonisothermal time‐stepping simulations of a nonlinear viscoelastic cast film process. A significant contribution of the algorithm is that an updated Lagrangian description of motion is employed, as opposed to the more conventional Eulerian description generally used for continuous polymer processing simulations. Furthermore, use is made of a Perzynatype constitutive equation, which is different from what is usually employed for molten polymers. The constitutive equation accommodates viscoelasticity, extensional thinning/thickening, and strain‐hardening. This new numerical algorithm can find the steady‐state film properties, and it can predict the onset of instability by observing draw resonance. The critical draw ratio is determined from the response problem, which means that the mathematical complications of the more common linear stability analysis are avoided. In terms of the stability of the film, it was observed that stability is decreased by extensional thinning, strain‐hardening, and higher relaxation times, and stability is increased by higher heat transfer coefficients and higher ratios of air‐gap length to die width.
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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 it