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
Hauptverfasser: Pereira, J. P., Duarte, C. A., Jiao, X., Guoy, D.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer-Verlag 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.
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.
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  surname: Pereira
  fullname: Pereira, J. P.
  organization: Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign
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  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
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  givenname: X.
  surname: Jiao
  fullname: Jiao, X.
  organization: Department of Applied Mathematics and Statistics, Stony Brook University
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  surname: Guoy
  fullname: Guoy, D.
  organization: Center for Simulation of Advanced Rockets, University of Illinois at Urbana-Champaign
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Issue 1
Keywords Crack front enrichments
3D fracture mechanics
Generalized/Extended finite element method
Partition of unity methods
Language English
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PublicationTitle Computational mechanics
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Snippet This paper presents a study of generalized enrichment functions for 3D curved crack fronts. Two coordinate systems used in the definition of singular curved...
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StartPage 73
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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Title Generalized finite element method enrichment functions for curved singularities in 3D fracture mechanics problems
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