Effective Mechanical Properties of Periodic Cellular Solids with Generic Bravais Lattice Symmetry via Asymptotic Homogenization
Bibliographic record
Abstract
In this paper, the scope of discrete asymptotic homogenization employing voxel (cartesian) mesh discretization is expanded to estimate high fidelity effective properties of any periodic heterogeneous media with arbitrary Bravais's lattice symmetry, including those with non-orthogonal periodic bases. A framework was developed in Python with a proposed fast-nearest neighbour algorithm to accurately estimate the periodic boundary conditions of the discretized representative volume element of the lattice unit cell. Convergence studies are performed, and numerical errors caused by both voxel meshing and periodic boundary condition approximation processes are discussed in detail. It is found that the numerical error in periodicity approximation is cyclically dependent on the number of divisions performed during the meshing process and, thus, is minimized with a refined voxel mesh. Validation studies are performed by comparing the elastic properties of 2D hexagon lattices with orthogonal and non-orthogonal bases. The developed methodology was also applied to derive the effective properties of several lattice topologies, and variation of their anisotropic macroscopic properties with relative densities is presented as material selection charts.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".