Using fractional derivatives for improved viscoelastic modeling of textile composites. Part I: Fabric yarns
Bibliographic record
Abstract
In this article, the viscoelastic behavior of fabric yarns is modeled by a new means of fractional calculus. First, the constitutive relation of the fractional “Poynting-Thomson” model is developed to investigate the behavior of yarns. The proposed material constitutive relation is a differential equation of fractional order, where the response to a unit step of stress (for determination of creep compliance), or a unit step of strain (for stress relaxation modulus) can be readily found in the literature. Here, focusing on the stress relaxation, the response function is fitted to the experimental data of yarns in a typical woven fabric prepreg, at both dry and partially consolidated conditions. The yarns were made of E-glass fibers comingled with polypropylene fibers. The results showed a significant agreement with experimental data along with improved predictions of the new fractional modeling approach when compared to other approaches such as the integer order model and Prony series. For early relaxation times, especially for [Formula: see text] a considerable discrepancy was observed between the values of relaxation modulus obtained by the experiments and that by the integer-order derivative model. However, the results extracted via the fractional derivatives were in close agreement with experimental results at all relaxation times. Using the fractional properties of the yarns, the variation of storage and loss moduli of the yarns with external frequency loading was also predicted, capturing both the rubbery and glassy regions of the material frequency response.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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 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".