Towards a complete characterization of the effective elasticity tensors of mixtures of an elastic phase and an almost rigid phase
Bibliographic record
Abstract
The set GU f of possible effective elastic tensors of composites built from two materials with positive definite elasticity tensors C 1 and C 2 = δC 0 comprising the set U = {C 1 , δC 0 } and mixed in proportions f and 1 -f is partly characterized in the limit δ → ∞.The material with tensor C 2 corresponds to a material which (for technical reasons) is almost rigid in the limit δ → ∞.This paper, and the underlying microgeometries, has many aspects in common with the companion paper "On the possible effective elasticity tensors of 2-dimensional and 3-dimensional printed materials".The chief difference is that one has a different algebraic problem to solve: determining the subspaces of stress fields for which the thin walled structures can be rigid, rather than determining, as in the companion paper, the subspaces of strain fields for which the thin walled structure is compliant.Recalling that GU f is completely characterized through minimums of sums of energies, involving a set of applied strains, and complementary energies, involving a set of applied stresses, we provide descriptions of microgeometries that in appropriate limits achieve the minimums in many cases.In these cases the calculation of the minimum is reduced to a finite-dimensional minimization problem that can be done numerically.Each microgeometry consists of a union of walls in appropriate directions, where the material in the wall is an appropriate p-mode material that is almost rigid to 6 -p ≤ 5 independent applied stresses, yet is compliant to any strain in the orthogonal space.Thus the walls, by themselves, can support stress with almost no deformation.The region outside the walls contains "Avellaneda material", which is a hierarchical laminate that minimizes an appropriate sum of elastic energies.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 0.005 |
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".