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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Bibliographic Details
Published in:Computational mechanics Vol. 44; no. 1; pp. 73 - 92
Main Authors: Pereira, J. P., Duarte, C. A., Jiao, X., Guoy, D.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.06.2009
Springer Nature B.V
Subjects:
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
Crack front enrichments
3D fracture mechanics
Generalized/Extended finite element method
Partition of unity methods
ISSN:0178-7675, 1432-0924
Online Access:Get full text
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Summary: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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ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-008-0356-1