A convex anisotropic damage model based on the compliance tensor
Bibliographic record
Abstract
This work is devoted to anisotropic continuum-damage mechanics in the quasi-static, isothermal, small-strain setting. We propose a framework for anisotropic damage evolution based on the compliance tensor as primary damage variable, in the context of generalized standard models for dissipative solids. Based on the observation that the Hookean strain energy density of linear elasticity is jointly convex in the strain and the compliance tensor, we design thermodynamically consistent anisotropic damage models that satisfy Wulfinghoff’s damage-growth criterion and feature a convex free energy. The latter property permits obtaining mesh-independent results on component scale without the necessity of introducing gradients of the damage field. We introduce the concepts of stress-extraction tensors and damage-hardening functions, implicitly describing a rigorous damage-analogue of yield surfaces in elastoplasticity. These damage surfaces may be combined in a modular fashion and give rise to complex damage-degradation behavior. We discuss how to efficiently integrate Biot’s equation implicitly, and show how to design specific stress-extraction tensors and damage-hardening functions based on Puck’s anisotropic failure criteria. Last but not least we demonstrate the versatility of our proposed model and the efficiency of the integration procedure for a variety of examples of interest.
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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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".