Voxel-Based Asymptotic Homogenization of the Effective Thermal Properties of Lattice Materials with Generic Bravais Lattice Symmetry
Bibliographic record
Abstract
In this paper, voxel-based Asymptotic Homogenization (AH) is employed to calculate the thermal expansion and thermal conductivity characteristics of lattice materials that have a Representative Volume Element (RVE) with non-orthogonal periodic bases. The non-orthogonal RVE of the cellular lattice is discretized using voxel elements (iso-parametric hexahedral element, on a cartesian grid). A homogenization framework is developed in python that uses a fast-nearest neighbor algorithm to approximate the (non-orthogonal) periodic boundary conditions of the discretized RVE. Validation studies are performed where results of the homogenized Thermal Expansion Coefficient (TEC) and thermal conduction performed in this paper are compared with results generated by commercially available software. These included comparison with the results for (a) bi-material unidirectional composite with orthogonal RVE cell envelope; (b) bi-material hexagon lattice with orthogonal cell envelope; (c) bi-material hexagon lattice with non-orthogonal cell envelope; and (d) bi-material square lattice. A novel approach of visualizing the contribution of each voxel towards the individual terms within the homogenized thermal conductivity matrix is presented, which is necessary to mitigate any potential errors arising from the numerical model. Additionally, the effect of the thermal expansion and thermal conductivity for bi-material hexagon lattice (orthogonal and non-orthogonal RVE cell envelope) are presented for varying internal cell angles and all permutations of material assignments for a relative density of 0.3. It is found that when comparing the non-orthogonal RVE with the Orthogonal RVE as a reference model, the numerical error due to approximating the periodic boundary condition for the non-orthogonal bi-material hexagon is generally less than 2% as the numerical error is pseudo-cyclically dependent on the discretization along the cartesian axis.
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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) | 0.000 | 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 | 0.000 | 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".