@inproceedings{bcdfb61ef0c146e5b49fb7987e8aa301,
title = "A global-local approach for the construction of enrichment functions for the generalized FEM and its application to three-dimensional cracks",
abstract = "Existing generalized or extended finite element methods for modeling cracks in three-dimensions require the use of a sufficiently refined mesh around the crack front. This offsets some of the advantages of these methods specially in the case of propagating threedimensional cracks. In this paper, a strategy to overcome this limitation is investigated. The approach involves the development of enrichment functions that are computed using a new global-local approach. This strategy allows the use of a fixed global mesh around the crack front and is specially appealing for non-linear or time dependent problems since it avoids mapping of solutions between meshes. The resulting technique enjoys the same flexibility of the so-called meshfree methods for this class of problem while being more computationally efficient. The proposed generalized FEM with global-local functions, by numerically constructing the enrichment functions, brings the benefits of existing generalized FEMto a broader class of problems. The procedure is applied to the solution of three-dimensional linear elastic fracture mechanics problems. Numerical experiments demonstrating the computational efficiency and accuracy of the method are presented.",
keywords = "Extended finite element method, Fracture mechanics, Generalized finite element method, Global-local method, Meshfree method",
author = "Duarte, {C. Armando} and Kim, {Dae Jin} and Ivo Babu{\v s}ka",
note = "Funding Information: Acknowledgments The partial support of this work by The University of Illinois (C.A. Duarte and D.-J. Kim), the National Science Foundation under grant DMS-0341982 (C.A. Duarte and I. Babu?ka) and the Korea Science and Engineering Foundation (D.-J. Kim) Project Number M06-2003-000-10312-0, are gratefully acknowledged.; Ecommas Thematic Conference on Meshless Methods, 2005 ; Conference date: 11-07-2005 Through 14-07-2005",
year = "2007",
doi = "10.1007/978-1-4020-6095-3_1",
language = "English (US)",
isbn = "9781402060946",
series = "Computational Methods in Applied Sciences",
publisher = "Springer",
pages = "1--26",
editor = "V.M.A. Leitao and Alves, {Carlos J.S.} and Duarte, {C. Armando}",
booktitle = "Advances in Meshfree Techniques",
address = "Germany",
}