Bibliographic record
Abstract
Under consideration are helices made of linear elastic and viscoelastic materials, henceforth called elastic and viscoelastic helices. While the effective (macro level) mechanical response of any helix exhibits coupling of axial with torsional responses, of interest in this study is the derivation of that response from mechanics of a single helical strand (micro level). First, using the earlier results of Costello [Theory of Wire Rope (Springer, New York, 1997)], we develop explicit forms of all the effective constitutive coefficients of a linear elastic helix and plot their dependencies on the geometry and material constants of the strand. Next, using the correspondence principle of viscoelasticity, we derive differential equations of a helix at the macro level by considering three types of viscoelastic models of the strand: Kelvin, Maxwell, and Zener. In general, the helix macro level linear viscoelastic response is different in type (and more complex) from that of the viscoelastic material at the micro level. It is only in the singular case of the strand material's Poisson ratio equal to zero that the type of viscoelastic response is qualitatively the same (i.e. governed by the same order differential equation) as the viscoelastic response of the strand at the micro level. Consequently, direct viscoelastic generalizations of effective constitutive equations of helices, not based on analyses such as those presented here, are likely to be invalid.
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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) | 0.000 | 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 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".