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An XFEM method for modeling geometrically elaborate crack propagation in brittle materials
Author(s) -
Richardson Casey L.,
Hegemann Jan,
Sifakis Eftychios,
Hellrung Jeffrey,
Teran Joseph M.
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3211
Subject(s) - quasistatic process , extended finite element method , finite element method , triangulation , simple (philosophy) , algorithm , quadrature (astronomy) , computer science , numerical integration , scheme (mathematics) , structural engineering , mathematics , geometry , engineering , mathematical analysis , physics , philosophy , electrical engineering , epistemology , quantum mechanics
Abstract We present a method for simulating quasistatic crack propagation in 2‐D which combines the extended finite element method (XFEM) with a general algorithm for cutting triangulated domains, and introduce a simple yet general and flexible quadrature rule based on the same geometric algorithm. The combination of these methods gives several advantages. First, the cutting algorithm provides a flexible and systematic way of determining material connectivity, which is required by the XFEM enrichment functions. Also, our integration scheme is straightforward to implement and accurate, without requiring a triangulation that incorporates the new crack edges or the addition of new degrees of freedom to the system. The use of this cutting algorithm and integration rule allows for geometrically complicated domains and complex crack patterns. Copyright © 2011 John Wiley & Sons, Ltd.