Discontinuous Galerkin Method in Modeling Materials with Micro-Cracks
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Bibliographic record
Abstract
We analyze wave propagation in heterogeneous brittle materials modeled by a linear elastic body with micro-cracks. The problem is nonlinear due to the boundary conditions on the cracks, such as non-penetration and friction. A numerical upscaling homogenization technique and a discontinuous Galerkin space discretization method are applied to find the effective properties of the damaged material. The wave propagation (speed, amplitude and pulse length) of micro-cracked materials in configurations of varying complexity is studied. While theoretical and numerical wave velocities are found to be very close for small values of the crack density parameter, large values exhibit remarkable differences. Furthermore, we observe that amplitude and speed of the transmitted (damaged) wave are affected by its length when it is close to the length of the micro-cracks.
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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 it