Dynamic homogenization of inhomogeneous elastic media based on energy equivalence
Bibliographic record
Abstract
This paper presents a new method of dynamic homogenization of periodic elastic media under harmonic antiplane deformation based on energy equivalence. The dynamic homogenization is based on two main steps, (1) determining the dispersion relation and the detailed local response in a representative volume element (RVE) by analyzing the propagation of Bloch waves and (2) using energy equivalence between the periodic and effective media to determine the effective properties. The method is first applied to a one-dimensional periodic medium, from which the analytical solutions of the effective material properties are obtained. The results are compared with that from the original periodic medium and an excellent agreement is observed. The dynamic homogenization method is then applied to general two-dimensional periodic media to determine the effective properties and to predict wave fields under typical loading conditions. Illustrative examples are presented and compared with the results from the multiple scattering model. The method has also been applied to multiscale modeling of complicated inhomogeneous media containing multiple groups of periodic inhomogeneities. By treating each group as a homogeneous material with effective properties determined by the current homogenization method, the wave field is obtained using the boundary element method. The resulting wave fields from the current method show an excellent agreement with that from the multiple scattering model with matching local response details.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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".