Bibliographic record
Abstract
In this chapter problems of finite deformation elastostatics for isotropic hyperelastic solids are considered. Exact solutions for some problems of finite deformation of incompressible elastic solids have been obtained by inverse methods. In these methods a deformation field is assumed, and it is verified that the equilibrium equations and stress and displacement boundary conditions are satisfied. There are some elastostatic problems that have deformation fields that are possible in every homogeneous isotropic incompressible elastic body in the absence of body forces. These deformation fields are said to be controllable. In an important paper by Ericksen an attempt is made to obtain all static deformation fields that are possible in all homogeneous isotropic incompressible bodies acted on by surface tractions only. Ericksen further showed that the only deformation possible in all homogeneous compressible elastic bodies, acted on by surface tractions only, is a homogeneous deformation. In this chapter solutions are given for several problems of finite deformation of incompressible isotropic hyperelastic solids and two simple problems for an isotropic compressible solid. These solutions with one exception involve controllable deformation fields and are based on the physical components of stress, deformation gradient, and the left Cauchy-Green strain tensor. This is in contrast to the approach of Green and Zerna, who used convected coordinates and tensor components.
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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".