Efficient meshless phase-field modeling of crack propagation by using adaptive load increments and variable node densities

Ali, Izaz (author), Šarler, Božidar (author), Mavrič, Boštjan (author)

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 SCNvar 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.

• Language: English
• Keywords: phase-field method, strong-form meshless method, LRBFCM, adaptive load step size, scattered nodes, PH_
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 18 str.
• Numbering: Vol. 13, issue 23, art. 3795
• PID: 20.500.12556/RUL-176501
• UDC: 531:51
• ISSN on article: 2227-7390
• DOI: 10.3390/math13233795
• COBISS.SI-ID: 259597059
• Publication date in RUL: 02.12.2025

Record is a part of a journal

• Title: Mathematics
• Shortened title: Mathematics
• Publisher: MDPI AG
• ISSN: 2227-7390
• COBISS.SI-ID: 523267865

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.