Giesekus Constitutive Model for Thermoviscoelastic Fluids based on Ordered Rate Constitutive Theories
Bibliographic record
Abstract
This paper presents derivation of Giesekus constitutive model in Eulerian description based on ordered rate constitutive theories for thermoviscoelastic fluids for compressible and incompressible cases in contra-, co-variant and Jaumann bases. The ordered rate constitutive theories for thermoviscoelastic fluids of orders (m, n) consider convected time derivative of order m of the deviatoric Cauchy stress tensor in a chosen basis (i.e. co-, contra-variant or Jaumann) as dependent variable in the development of constitutive theories for the stress tensor. Its argument tensors consist of density, temperature, convected time derivatives of the deviatoric Cauchy stress tensor of up to order m-1 and convected time derivative of up to order n of the conjugate strain tensor. In addition, constitutive theory for the heat vector compatible with the constitutive theory for the deviatoric stress tensor is also presented in co-, contra-variant and Jaumann bases. It is shown that the Giesekus constitutive model is a subset of the rate constitutive theory of orders m = n = 1. It is also shown that the deviatoric Cauchy stress tensor (contra-, co-variant or Jaumann basis) naturally results as dependent variable in the constitutive theory, and that currently used Giesekus constitutive model in deviatoric polymer Cauchy stress tensor is not derivable based on axioms and principles of the constitutive theory in continuum mechanics. Numerical studies are presented for fully developed flow between parallel plates for a dense polymeric liquid using the Giesekus constitutive model derived in this paper as well as currently used model.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".