Couple Stress Theory For Materials With Microstructures
Bibliographic record
Abstract
Classical continuum theory (CCT) provides a mathematical model to study the mechanical response of materials under external effects. In the context of CCT, there is no material length scale, and a solid body is sub-dividable into an infinitesimal element with the same behavior as the bulk material, disregarding the fact that all materials are made of building blocks and have microstructures in different length scales. The lack of material characteristic length-scale in CCT prevents it from recognizing any size-effect. Additionally, even order material property tensors associated with this theory can only characterize the centrosymmetric behavior of the materials, and consequently, CCT overlooks the intrinsic chirality and polarity of materials. Although a handful of generalized continuum theories has been proposed in the last century to address the shortcomings of CCT, none has proved to be consistent and applicable, mainly due to a lack of knowledge about the introduced material coefficients in these non-classical theories. This study introduces a consistent and self-sufficient effective generalized continuum theory for advanced materials with microstructures. Assuming that CCT governs the base material's behavior, we implement a bottom-up approach based on an augmented asymptotic homogenization resulting in the couple-stress theory in 3D space Using the introduced continuum theory, we can accurately model the response of chiral mechanical metamaterial under different type of loads. The proposed model provides a benchmark for the rational design, classification, and manufacture of mechanical metamaterials.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| 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".