An XFEM method for modelling geometrically elaborate crack propagation in brittle materials
International Journal for Numerical Methods in Engineering, Volume 88, Number 10, page 1042--1065 — 2011
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 straightfoward 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.
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@Article{RHSHT11, author = "Richardson, Casey and Hegemann, Jan and Sifakis, Eftychios and Hellrung, Jeffrey and Teran, Joseph", title = "An XFEM method for modelling geometrically elaborate crack propagation in brittle materials", journal = "International Journal for Numerical Methods in Engineering", number = "10", volume = "88", pages = "1042--1065", year = "2011", url = "http://graphics.cs.wisc.edu/Papers/2011/RHSHT11" }