Research Article

An XFEM method for modeling geometrically elaborate crack propagation in brittle materials

  1. Casey L. Richardson1,*,
  2. Jan Hegemann2,
  3. Eftychios Sifakis1,
  4. Jeffrey Hellrung1,
  5. Joseph M. Teran1

Article first published online: 16 JUN 2011

DOI: 10.1002/nme.3211

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Volume 88, Issue 10, pages 1042–1065, 9 December 2011

Additional Information

How to Cite

Richardson, C. L., Hegemann, J., Sifakis, E., Hellrung, J. and Teran, J. M. (2011), An XFEM method for modeling geometrically elaborate crack propagation in brittle materials. Int. J. Numer. Meth. Engng., 88: 1042–1065. doi: 10.1002/nme.3211

Author Information

  1. 1

    Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, CA 90095-1555, U.S.A.

  2. 2

    Institute for Computational and Applied Mathematics, University of Münster, Einsteinstrasse 62, D-48149 Münster, Germany

*Center for Imaging Science, Clark 319B, Johns Hopkins University, 3400 N. Charles St, Baltimore, MD 21218, U.S.A.

Publication History

  1. Issue published online: 7 NOV 2011
  2. Article first published online: 16 JUN 2011
  3. Manuscript Accepted: 20 MAR 2011
  4. Manuscript Revised: 1 SEP 2010
  5. Manuscript Received: 13 APR 2010

SEARCH

SEARCH BY CITATION

ARTICLE TOOLS

View Full Article (HTML) Get PDF (589K)

Keywords:

  • finite elements;
  • XFEM;
  • fracture

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.

View Full Article (HTML) Get PDF (589K)