Stresses, Singularities, and a Complementary Energy Principle for Large Strain Elasticity
Bibliographic record
Abstract
Abstract This article reviews three aspects of large strain elasticity. First, various conjugate stress tensors to strain tensors are reviewed. Many researchers have studied the theory of large strain elasticity. Many stress tensors including the Cauchy stress tensor, the first and the second Piola–Kirchhoff stress tensor, and the Jaumann stress tensor have been proposed to describe the stress state at a point. Recently, the first author of this article proposed a concept of “base forces” to reveal the essence of stress state. By the concept of base forces, the description of the stress state becomes clearer than other stress tensors. We attempt to take base forces as a basic point of view to deal with a review in which different descriptions of stress state are discussed and compared. The governing equations and boundary conditions expressed by the base forces are given. Second, this article reviews the solution of some singularity problems for large strain elasticity, i.e., problems of stress singularity at a crack or a notch tip, at the point of application of a concentrated force and at the vertex of contact in rubberlike materials. Methods of getting the singularity index of stress by using base forces are introduced and compared to earlier work. Complementary energy principles for large strain elasticity have eluded researchers for nearly 100years. A review of some important advances in this is also given, and a new complementary energy principle related to base forces is introduced.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".