Finite-element implementation of schapery-type constitutive theories based on an internal variable approach
Bibliographic record
Abstract
This paper presents two new strategies for implementing Schapery-type nonlinearly viscoelastic constitutive theories into Finite Element (FE) codes. The first strategy uses the original differential equations that lead to the integral formulation of Schapery-type constitutive theories and Finite Difference (FD) scheme. This strategy is quite different from all the other strategies found in the literature. The second strategy is an improvement of recursive strategies, used by many authors, based on the integral formulation of the constitutive theory. The performances of the new algorithms are compared to that of existing strategies for various loading histories and nonlinearities. It is shown that the newly developed strategy relying on FD schemes can exhibit quadratic convergence rate when one time step is stored and 4th order convergence rate when two time steps are stored, which is a major improvement over the recursive strategies.
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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) | 0.002 | 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 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".