Efficient Meshless Phase-Field Modeling of Crack Propagation by Using Adaptive Load Increments and Variable Node Densities

Izaz Ali, Božidar Šarler () and Boštjan Mavrič
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Izaz Ali: Faculty of Mechanical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia
Božidar Šarler: Faculty of Mechanical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia
Boštjan Mavrič: Faculty of Mechanical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia

Mathematics, 2025, vol. 13, issue 23, 1-18

Abstract: This study employs the fourth-order phase-field method (PFM) to investigate crack propagation. The PFM incurs significant computational costs due to its need for a highly dense node arrangement for accurate crack propagation. This study proposes an adaptive loading step size strategy combined with a scattered node (SCN var ) arrangement with variable spacings. The mechanical and phase-field models are solved using the strong-form meshless local radial basis function collocation method in a staggered approach. The method’s performance is evaluated based on accuracy and computational cost, using regular nodes (RGN) and scattered nodes (SCN uni ) with uniform spacing, as well as SCN var with variable node spacing. Two benchmark tests are used to analyze the proposed method: a symmetric double-notch tension and a single-edge notch shear test. The analysis shows that the adaptive step size strategy improves numerical stability while the SCN var significantly reduces computational cost. Using SCN var , the CPU time is decreased by about thirty times compared to uniform nodes in the tensile case and by approximately three times in the shear case, without sacrificing accuracy. This confirms that directing computational resources to critical regions can significantly reduce CPU time, suggesting that adaptive node redistribution could further enhance computational performance.

Keywords: phase-field method; strong-form meshless method; LRBFCM; adaptive load step size; scattered nodes; PH (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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