Muscle Constitutive Model With a Tangent Modulus Approximation: Ansys Implementation and Verification
Bibliographic record
Abstract
Sophisticated muscle material models are required to perform detailed finite element simulations of soft tissue; however, state-of-the-art muscle models are not among the built-in materials in popular commercial finite element software packages. Implementing user-defined muscle material models is challenging for two reasons: deriving the tangent modulus tensor for a material with a complex strain energy function is tedious and programing the algorithm to compute it is error-prone. These challenges hinder widespread use of such models in software that employs implicit, nonlinear, Newton-type finite element methods. We implement a muscle material model in Ansys using an approximation of the tangent modulus, which simplifies its derivation and implementation. Three test models were constructed by revolving a rectangle (RR), a right trapezoid (RTR), and a generic obtuse trapezoid (RTO) around the muscle's centerline. A displacement was applied to one end of each muscle, holding the other end fixed. The results were validated against analogous simulations in FEBio, which uses the same muscle model but with the exact tangent modulus. Overall, good agreement was found between our Ansys and FEBio simulations, though some noticeable discrepancies were observed. For the elements along the muscle's centerline, the root-mean-square-percentage error in the Von Mises stress was 0.00%, 3.03%, and 6.75% for the RR, RTR, and RTO models, respectively; similar errors in longitudinal strain were observed. We provide our Ansys implementation so that others can reproduce and extend our results.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
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".