Dilatation parameterization for two-dimensional modeling of nearly incompressible isotropic materials
Bibliographic record
Abstract
A new method to model the stress–strain relationship in two dimensions is proposed, which is particularly suited for analyzing nearly incompressible materials, such as soft tissue. In most cases of soft tissue modeling, plane strain is reported to approximate the deformation when an external compression is applied. However, it is subject to limitations when dealing with incompressible materials, e.g., when solving the inverse problem of elasticity. We propose a novel 2D model for the linear stress–strain relationship by describing the out-of-plane strain as a linear combination of the two in-plane strains. As such, the model can be represented in 2D while being able to explain the three-dimensional deformation. We show that in simple cases where the applied force is dominantly in one direction, one can approximate the sum of the three principal strain components in a plane by a scalar multiplied by the out-of-plane strain. 3D finite-element simulations have been performed. The proposed model has been tested under different boundary conditions and material properties. The results show that the model parametrization is affected mostly by the boundary conditions, while being relatively independent of the underlying distribution of Young's modulus. An application to the inverse problem of elasticity is presented where a more accurate estimate is obtained using the proposed dilatation model compared to the plane-stress and plane-strain models.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| 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) | 0.001 | 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".