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Improvements for the solution of crack evolution using extended finite element method
Yuxiao Wang1, Akbar A Javadi2, Corrado Fidelibus3
1Department of Engineering, University of Exeter, Harrison Building, North Park Road, Exeter, EX4 4QF, United Kingdom.
Scientific Reports
|November 6, 2024
Summary
The eXtended Finite Element Method (XFEM) efficiently simulates crack growth. This study enhances XFEM accuracy and efficiency by optimizing element subdivision and Gauss point distribution for crack analysis.
Area of Science:
- Computational Mechanics
- Materials Science
- Fracture Mechanics
Background:
- The eXtended Finite Element Method (XFEM) is a powerful tool for simulating crack evolution without mesh refinement.
- However, approximations in XFEM can lead to inaccuracies in nodal displacements, particularly near crack tips.
- Improving the computational efficiency and accuracy of XFEM remains an active area of research.
Purpose of the Study:
- To mathematically investigate and enhance the solution efficiency of the eXtended Finite Element Method (XFEM).
- To identify the causes of discrepancies in nodal displacements within XFEM simulations.
- To propose and validate improvements for accurate and efficient crack analysis using XFEM.
Main Methods:
- Comprehensive mathematical analysis of the XFEM solution process, focusing on the global stiffness matrix.
- Development of two novel improvement strategies: element subdivision based on Gauss point distribution and optimal Gauss point determination.
- Application of proposed improvements with the interaction integral method for stress intensity factor calculation.
- Numerical validation against analytical and standard XFEM solutions.
Main Results:
- Discrepancies in nodal displacements were identified and attributed to XFEM approximation.
- The proposed methods of element subdivision and optimal Gauss point allocation significantly improved accuracy.
- The enhanced XFEM approach, combined with the interaction integral method, reduced computational time and eliminated surface traction influence.
- Validated numerical results showed enhanced accuracy and efficiency compared to standard XFEM.
Conclusions:
- The proposed improvements effectively address the accuracy limitations of XFEM in crack simulation.
- Optimizing element subdivision and Gauss point strategy enhances computational efficiency and solution precision.
- The refined XFEM approach provides a more reliable and faster method for fracture mechanics analysis.
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