A Model for the Mullins Effect in Multinetwork Elastomers
Bibliographic record
Abstract
Double and triple network (TN) elastomers can be made by infusing monomers into a single network (SN) polymer, causing it to swell, and then polymerizing and cross-linking the monomers. The result is a double network (DN) elastomer in which one network is stretched and the other is in hydrostatic compression. TN systems are made by repeating the process starting with the DN material. The multinetwork (MN) elastomers exhibit a Mullins effect in which softening occurs upon a first cycle of loading, with the elastomer stiffness recovered above the previous maximum strain. The Mullins effect is attributed to rupture of the stretched network, eliminating the constraint on the compressed network, thereby motivating straining at the lower stiffness of the remaining material. A model for this process is developed, based on the previous work of Horgan et al. (2004, “A Theory of Stress Softening of Elastomers Based on Finite Chain Extensibility,” Proc. R. Soc. A, 460(2046), pp. 1737–1754). In the proposed model, a composite stiffness for the MN system is developed and a damage process introduced to degrade the contribution of the stretched network. The damage model is designed to account for the progressive elimination of chains that are most highly loaded in the stretched network, so that the undamaged stiffness is restored when the strain rises above levels previously experienced. The proposed model reproduces the behavior of the Mullins effect in the MN system.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.003 | 0.001 |
| Insufficient payload (model declined to judge) | 0.010 | 0.002 |
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".