Couple-stress theory for cellular metamaterials
Bibliographic record
Abstract
All materials from natural to synthetic, metals to polymers, and crystalline to amorphous, have microstructure in different length scales; however, classical Cauchy continuum theory does not have any characteristic length and cannot recognize the size effect. Crystalline materials are categorized into thirty-two symmetry classes based on their intrinsic microstructure. However, they can only be categorized into nine classes based on their overall anisotropic behavior in the classical theory of elasticity. This is due to the central nature of deformation and force measures, i.e., the symmetry of strain and stress tensors. Implementing a bottom-up approach based on an augmented asymptotic homogenization, we present a consistent and self-sufficient effective generalized continuum theory for materials with microstructures in 3D, 2D and 1D spaces. Our theories connect the three-dimensional continuum theories and the one-dimensional beam and two-dimensional plate theories. The accuracy of these models is investigated by comparing them to the detailed finite element models and experiments performed on 3D printed samples. The proposed models provide a benchmark for the rational design, classification, and manufacturing of mechanical metamaterials with programmable deformation modesKeywords: Metmaterials, Multistable chain, Continues path, Snap-back energy release.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.001 |
| Open science | 0.001 | 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".