A Second Order Cone Programming Approach for Simulating Biphasic Materials
Bibliographic record
Abstract
Abstract Strain limiting is a widely used approach for simulating biphasic materials such as woven textiles and biological tissue that exhibit a soft elastic regime followed by a hard deformation limit. However, existing methods are either based on slowly converging local iterations, or offer no guarantees on convergence. In this work, we propose a new approach to strain limiting based on second order cone programming (SOCP). Our work is based on the key insight that upper bounds on per‐triangle deformations lead to convex quadratic inequality constraints. Though nonlinear, these constraints can be reformulated as inclusion conditions on convex sets, leading to a second order cone programming problem—a convex optimization problem that a) is guaranteed to have a unique solution and b) allows us to leverage efficient conic programming solvers. We first cast strain limiting with anisotropic bounds on stretching as a quadratically constrained quadratic program (QCQP), then show how this QCQP can be mapped to a second order cone programming problem. We further propose a constraint reflection scheme and empirically show that it exhibits superior energy‐preservation properties compared to conventional end‐of‐step projection methods. Finally, we demonstrate our prototype implementation on a set of examples and illustrate how different deformation limits can be used to model a wide range of material behaviors.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.003 | 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".