Reducible and irreducible forms of stabilised gradient elasticity in dynamics
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Bibliographic record
Abstract
The continualisation of discrete particle models has been a popular tool to \nformulate higher-order gradient elasticity models. However, a straightforward continualisation \nleads to unstable continuum models. Pade approximations can be used to stabilise ´ \nthe model, but the resulting formulation depends on the particular equation that is transformed \nwith the Pade approximation. In this contribution, we study two different stabilised ´ \ngradient elasticity models; one is an irreducible form with displacement degrees of freedom \nonly, and the other is a reducible form where the primary unknowns are not only displacements \nbut also the Cauchy stresses — this turns out to be Eringen’s theory of gradient \nelasticity. Although they are derived from the same discrete model, there are significant \ndifferences in variationally consistent boundary conditions and resulting finite element implementations, \nwith implications for the capability (or otherwise) to suppress crack tip \nsingularities
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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.
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