Computational Mechanics

, Volume 44, Issue 1, pp 73–92

# Generalized finite element method enrichment functions for curved singularities in 3D fracture mechanics problems

Original Paper

## 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.

### Keywords

Partition of unity methods Generalized/Extended finite element method 3D fracture mechanics Crack front enrichments

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## Authors and Affiliations

• J. P. Pereira
• 1
• C. A. Duarte
• 1
• X. Jiao
• 2
• D. Guoy
• 3
1. 1.Department of Civil and Environmental EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
2. 2.Department of Applied Mathematics and StatisticsStony Brook UniversityStony BrookUSA
3. 3.Center for Simulation of Advanced RocketsUniversity of Illinois at Urbana-ChampaignUrbanaUSA