A New Continuum-Based Thick Shell Finite Element for Soft Biological Tissues in Dynamics: Part 2 - Anisotropic Hyperelasticity and Incompressibility Aspects
Bibliographic record
Abstract
In a companion article (Part 1), we presented the development of a thick continuum-based (CB) shell finite element (FE) based on Mindlin-Reissner theory. We verified the accuracy, efficiency and locking insensitivity of the element in modeling large 3D deformations, using linear elastic material properties. In the present article, we developed and implemented the kinetics description, within the updated Lagrangian (UL) formulation, of anisotropic incompressible hyperelastic constitutive relations that enable the CB shell FE to accurately model very large 3D strains and deformations. Specifically, we developed the measures of deformation in the lamina coordinate system, presented three techniques to model nonlinear hyperelastic strains, and enabled the direct enforcement of incompressibility and of the zero normal stress condition without using a penalty factor or a Lagrange multiplier. Moving towards the application of the present work to the biomedical realm, we performed multiple experiments concerning mechanical behavior of rubber-like materials and soft biological tissues in different geometries and loading conditions. Excellent agreements between the present FE results and the analytical and/or experimental data proved the CB shell FE combined with the present constitutive techniques to be a highly reliable and efficient tool for modeling, analyzing, and predicting mechanical behavior of soft biological tissues.
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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) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| 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 | 0.001 |
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".