Dynamic Mode Decomposition of Deformation Fields in Elastic and Elastic-Plastic Solids
Bibliographic record
Abstract
Without recourse to constitutive assumptions, without knowledge of material properties, and without solving any of the conservation equations, we construct deformation fields for linear solids using Dynamic Mode Decomposition (DMD).Originally developed for analyzing experimental or computational field variables in fluid mechanics, it takes as input vectors of flow variables assembled as columns of a data matrix, and requires a remarkably few lines of code.It is a natural fit for solid mechanics wherein surface displacements can be used for the analysis.Vectors of surface displacements are arrayed in columns to created a data matrix.Singular Value Decomposition of the time-shifted data matrix affords selection of dominant modes (rank) in the deformation field.The DMD algorithm operates on time-shifted data matrices, obtains a reduced-order model that can reconstruct the deformation field, and also provides the dominant temporal and spatial modes of the deformation.In the case of linear elastic solids, DMD can be used to: reconstruct or predict the displacement states.In elastic-plastic solids, the transition from elastic to plastic results in the eigenvalues of the low-rank data matrix going out of the unit circle (implying an unstable growth mode).Using a combination of finite element analyses and displacement measurements obtained using Digital Image Correlation (DIC), we make the case for using DMD for state-estimation and state prediction in elastic solids and identifying onset of plasticity in elastic-plastic solids.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".