Improvements for the solution of crack evolution using extended finite element method
Abstract It is demonstrated that the eXtended Finite Element Method (XFEM) is of remarkable efficiency in simulating crack evolution by eliminating the need for remeshing and refinement. In this paper, it is shown how to enhance the solution efficiency through a comprehensive mathematical investigat...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-11-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-76626-0 |
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| author | Yuxiao Wang Akbar A. Javadi Corrado Fidelibus Huiqi Liang |
| author_facet | Yuxiao Wang Akbar A. Javadi Corrado Fidelibus Huiqi Liang |
| author_sort | Yuxiao Wang |
| collection | DOAJ |
| description | Abstract It is demonstrated that the eXtended Finite Element Method (XFEM) is of remarkable efficiency in simulating crack evolution by eliminating the need for remeshing and refinement. In this paper, it is shown how to enhance the solution efficiency through a comprehensive mathematical investigation of the solution process using XFEM. A typical example is presented to illustrate the disparities in nodal displacements along the two symmetric faces of the crack resulting from the approximation of XFEM. By analysing the structure and components of the global stiffness matrix, the underlying causes of these discrepancies are identified. Building upon these findings, two improvements of the solution are proposed to gain an acceptable accuracy in computing the nodal displacements. The first improvement consists of the subdivision of the enriched elements depending on the characteristic of the distribution of Gauss points. The second improvement is set by determining the optimal number of Gauss points in each sub-element near the crack tip. To calculate the stress intensity factor of the crack under surface pressure, such improvements are applied in conjunction with the interaction integral method, which significantly reduces computational time and eliminates the influence of surface tractions. The numerical solution is validated by comparing it with the analytical solution and the standard XFEM solution. The proposed improvements can enhance both the accuracy of the solution and the computational efficiency of XFEM. |
| format | Article |
| id | doaj-art-3f6f8fdee19b4484b83c078bd6204e63 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-3f6f8fdee19b4484b83c078bd6204e632024-11-10T12:19:30ZengNature PortfolioScientific Reports2045-23222024-11-0114111710.1038/s41598-024-76626-0Improvements for the solution of crack evolution using extended finite element methodYuxiao Wang0Akbar A. Javadi1Corrado Fidelibus2Huiqi Liang3Department of Engineering, University of ExeterDepartment of Engineering, University of ExeterDepartment of Innovation Engineering, University of SalentoDepartment of Engineering, University of ExeterAbstract It is demonstrated that the eXtended Finite Element Method (XFEM) is of remarkable efficiency in simulating crack evolution by eliminating the need for remeshing and refinement. In this paper, it is shown how to enhance the solution efficiency through a comprehensive mathematical investigation of the solution process using XFEM. A typical example is presented to illustrate the disparities in nodal displacements along the two symmetric faces of the crack resulting from the approximation of XFEM. By analysing the structure and components of the global stiffness matrix, the underlying causes of these discrepancies are identified. Building upon these findings, two improvements of the solution are proposed to gain an acceptable accuracy in computing the nodal displacements. The first improvement consists of the subdivision of the enriched elements depending on the characteristic of the distribution of Gauss points. The second improvement is set by determining the optimal number of Gauss points in each sub-element near the crack tip. To calculate the stress intensity factor of the crack under surface pressure, such improvements are applied in conjunction with the interaction integral method, which significantly reduces computational time and eliminates the influence of surface tractions. The numerical solution is validated by comparing it with the analytical solution and the standard XFEM solution. The proposed improvements can enhance both the accuracy of the solution and the computational efficiency of XFEM.https://doi.org/10.1038/s41598-024-76626-0Extended finite element method, Crack evolution, Symmetric nodes, Accuracy improvement for the interaction integral method |
| spellingShingle | Yuxiao Wang Akbar A. Javadi Corrado Fidelibus Huiqi Liang Improvements for the solution of crack evolution using extended finite element method Scientific Reports Extended finite element method, Crack evolution, Symmetric nodes, Accuracy improvement for the interaction integral method |
| title | Improvements for the solution of crack evolution using extended finite element method |
| title_full | Improvements for the solution of crack evolution using extended finite element method |
| title_fullStr | Improvements for the solution of crack evolution using extended finite element method |
| title_full_unstemmed | Improvements for the solution of crack evolution using extended finite element method |
| title_short | Improvements for the solution of crack evolution using extended finite element method |
| title_sort | improvements for the solution of crack evolution using extended finite element method |
| topic | Extended finite element method, Crack evolution, Symmetric nodes, Accuracy improvement for the interaction integral method |
| url | https://doi.org/10.1038/s41598-024-76626-0 |
| work_keys_str_mv | AT yuxiaowang improvementsforthesolutionofcrackevolutionusingextendedfiniteelementmethod AT akbarajavadi improvementsforthesolutionofcrackevolutionusingextendedfiniteelementmethod AT corradofidelibus improvementsforthesolutionofcrackevolutionusingextendedfiniteelementmethod AT huiqiliang improvementsforthesolutionofcrackevolutionusingextendedfiniteelementmethod |