Fourth-order phase field modelling of brittle fracture with strong form meshless method

Ali, Izaz (author), Vuga, Gašper (author), Mavrič, Boštjan (author), Hanoglu, Umut (author), Šarler, Božidar (author)

This study aims to find a solution for crack propagation in 2D brittle elastic material using the local radial basis function collocation method. The staggered solution of the fourth-order phase field and mechanical model is structured with polyharmonic spline shape functions augmented with polynomials. Two benchmark tests are carried out to assess the performance of the method. First, a non-cracked square plate problem is solved under tensile loading to validate the implementation by comparing the numerical and analytical solutions. The analysis shows that the iterative process converges even with a large loading step, whereas the non-iterative process requires smaller steps for convergence to the analytical solution. In the second case, a single-edge cracked square plate subjected to tensile loading is solved, and the results show a good agreement with the reference solution. The effects of the incremental loading, length scale parameter, and mesh convergence for regular and scattered nodes are demonstrated. This study presents a pioneering attempt to solve the phase field crack propagation using a strong-form meshless method. The results underline the essential role of the represented method for an accurate and efficient solution to crack propagation. It also provides valuable insights for future research towards more sophisticated material models.

• Language: English
• Keywords: strong form meshless method, fourth-order phase field, crack propagation, staggered approach, polyharmonic splines
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 14 str.
• Numbering: Vol. 169, Part B, [art. no.] 106025
• PID: 20.500.12556/RUL-164671
• UDC: 539.4
• ISSN on article: 0955-7997
• DOI: 10.1016/j.enganabound.2024.106025
• COBISS.SI-ID: 213966083
• Publication date in RUL: 07.11.2024

Record is a part of a journal

• Title: Engineering analysis with boundary elements
• Shortened title: Eng. anal. bound. elem.
• Publisher: Elsevier
• ISSN: 0955-7997
• COBISS.SI-ID: 5605380

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• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.