Atomistic constitutive relations for multilattice crystals
Bibliographic record
Abstract
In this chapter, we derive expressions for the free energy, stress and elasticity tensors for crystalline systems under equilibrium conditions. These expressions can be used as constitutive relations in continuum mechanics (see Section 2.5) under the assumption that a continuum system is in a state of “local thermodynamic equilibrium” at each point. The advantage of the “atomistic constitutive relations” derived here is that they inherently possess basic properties of the material such as its symmetries and lattice-invariant shears which are difficult to incorporate into standard continuum models for crystals. It is also hoped that atomistic models are more predictive than macroscopic phenomenological models, but of course this depends on the transferability of the interatomic model as discussed in Section 5.7.2. The use of atomistic constitutive relations within a continuum finite element framework will be our first example of a multiscale method in Chapter 12.
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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".