Stabilization of the extended finite element method for stiff embedded interfaces and inclusions
Bibliographic record
Abstract
Abstract This article investigates the performance of the XFEM for stiff embedded interfaces and inclusions. It is known that the XFEM may lead to ill‐conditioned stiffness matrices and oscillations in the interface traction field, the severity of which depends on the underlying basis functions, as well as on the orientation of the interface. The jumps at the discontinuity are shown to contain quadratic bubble residuals that can introduce oscillatory behavior. Those residuals are worsened by the ill‐conditioning of the system with very stiff interfaces. A variationally consistent method is proposed to overcome the oscillatory behavior and ill‐conditioning, in which the assumed strain method is developed to directly eliminate bubble residuals and deploy Legendre polynomials and explore their orthogonality properties to improve the conditioning of the stiffness matrices. Numerical examples illustrate the efficiency and generality of the proposed approach at both element and structural levels. The new approach is shown to be robust for imposing Dirichlet type boundary conditions at the crack interface, such as crack closure and initially rigid cohesive laws. The effects of numerical oscillations on the prediction of effective properties of composites in XFEM‐based computational homogenization procedures are also discussed.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".