A Singular-Element-Free Approach to Contour Integral Evaluation Using Adaptive Remeshing

  • Rajendran, Vishakh (Polymer Competence Centre)
  • Lang, Margit (Polymer Competence Centre)
  • Afsharnia, Reza (Technical University of Leoben)
  • Pinter, Gerald (Technical University of Leoben)
  • Fuchs, Peter (Polymer Competence Centre)

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In this study, fracture metrics are evaluated using the J-Integral framework with Virtual Crack Extension and Interaction Integral formulations based on contour integration [1]. Accurate evaluation of fracture metrics requires sufficient resolution in the vicinity of the crack tip. A common approach relies on singular crack-tip elements, which capture the square-root stress singularity and improve the accuracy of contour-integral-based quantities [2]. However, their use introduces additional modeling complexity due to element degeneration and specific midside node placements. In incremental crack growth simulations with stepwise evaluation of crack propagation direction, repeated reconstruction of singular elements limits automation and complicates large-scale or parametric analyses. Adaptive remeshing provides an alternative by enabling automated mesh refinement and coarsening driven by prescribed error indicators. In this work, the capability of adaptive remeshing to replace singular crack-tip elements is systematically assessed through a comparative evaluation of fracture metrics. In addition, the influence of commonly used error indicators on the accuracy and robustness of fracture quantities is examined. Two adaptive remeshing error indicators—element strain energy–based and von Mises stress–based—are investigated for both notch and crack configurations. Stress concentration factors (SCF) and stress intensity factors (SIF) are employed as evaluation metrics. For notch problems, the strain energy–based indicator converges in fewer remeshing iterations, whereas the von Mises–based indicator yields values closer to analytical solutions. In contrast, for crack problems, the von Mises–based indicator performs poorly in SIF evaluation, exhibiting large contour-to-contour variations and excessive mesh coarsening near the crack tip. Overall, the results demonstrate that adaptive remeshing can effectively replace singular crack-tip elements, providing comparable fracture metrics with reduced implementation complexity. The element strain energy–based indicator is shown to be more suitable for contour-integral-based SIF evaluation, while the von Mises–based indicator remains appropriate for stress concentration analyses.