Generalized finite element method enrichment functions for curved singularities in 3D fracture mechanics problems
This paper presents a study of generalized enrichment functions for 3D curved crack fronts. Two coordinate systems used in the definition of singular curved crack front enrichment functions are analyzed. In the first one, a set of Cartesian coordinate systems defined along the crack front is used. I...
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| Veröffentlicht in: | Computational mechanics Jg. 44; H. 1; S. 73 - 92 |
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01.06.2009
Springer Nature B.V |
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| ISSN: | 0178-7675, 1432-0924 |
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| Abstract | This paper presents a study of generalized enrichment functions for 3D curved crack fronts. Two coordinate systems used in the definition of singular curved crack front enrichment functions are analyzed. In the first one, a set of Cartesian coordinate systems defined along the crack front is used. In the second case, the geometry of the crack front is approximated by a set of curvilinear coordinate systems. A description of the computation of derivatives of enrichment functions and curvilinear base vectors is presented. The coordinate systems are automatically defined using geometrical information provided by an explicit representation of the crack surface. A detailed procedure to accurately evaluate the surface normal, conormal and tangent vectors along curvilinear crack fronts in explicit crack surface representations is also presented. An accurate and robust definition of orthonormal vectors along crack fronts is crucial for the proper definition of enrichment functions. Numerical experiments illustrate the accuracy and robustness of the proposed approaches. |
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| AbstractList | This paper presents a study of generalized enrichment functions for 3D curved crack fronts. Two coordinate systems used in the definition of singular curved crack front enrichment functions are analyzed. In the first one, a set of Cartesian coordinate systems defined along the crack front is used. In the second case, the geometry of the crack front is approximated by a set of curvilinear coordinate systems. A description of the computation of derivatives of enrichment functions and curvilinear base vectors is presented. The coordinate systems are automatically defined using geometrical information provided by an explicit representation of the crack surface. A detailed procedure to accurately evaluate the surface normal, conormal and tangent vectors along curvilinear crack fronts in explicit crack surface representations is also presented. An accurate and robust definition of orthonormal vectors along crack fronts is crucial for the proper definition of enrichment functions. Numerical experiments illustrate the accuracy and robustness of the proposed approaches. |
| Author | Pereira, J. P. Guoy, D. Jiao, X. Duarte, C. A. |
| Author_xml | – sequence: 1 givenname: J. P. surname: Pereira fullname: Pereira, J. P. organization: Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign – sequence: 2 givenname: C. A. surname: Duarte fullname: Duarte, C. A. email: caduarte@uiuc.edu, caduarte@illinois.edu organization: Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign – sequence: 3 givenname: X. surname: Jiao fullname: Jiao, X. organization: Department of Applied Mathematics and Statistics, Stony Brook University – sequence: 4 givenname: D. surname: Guoy fullname: Guoy, D. organization: Center for Simulation of Advanced Rockets, University of Illinois at Urbana-Champaign |
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| Keywords | Crack front enrichments 3D fracture mechanics Generalized/Extended finite element method Partition of unity methods |
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| SubjectTerms | Classical and Continuum Physics Computational Science and Engineering Coordinates Engineering Enrichment Finite element method Fracture mechanics Mathematical analysis Original Paper Representations Robustness (mathematics) Simulation Singularities Theoretical and Applied Mechanics |
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