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Extended finite element method in computational fracture mechanics: a retrospective examination

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Abstract

In this paper, we provide a retrospective examination of the developments and applications of the extended finite element method (X-FEM) in computational fracture mechanics. Our main attention is placed on the modeling of cracks (strong discontinuities) for quasistatic crack growth simulations in isotropic linear elastic continua. We provide a historical perspective on the development of the method, and highlight the most important advances and best practices as they relate to the formulation and numerical implementation of the X-FEM for fracture problems. Existing challenges in the modeling and simulation of dynamic fracture, damage phenomena, and capturing the transition from continuum-to-discontinuum are also discussed.

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Acknowledgments

The authors are grateful to the late Professor Ted Belytschko, with whom they coauthored many of the initial contributions on the X-FEM. His research ideas and technical writing have influenced our thinking and has helped us to shape this article. We also thank Professors David Chopp and Brian Moran, who introduced us to level set methods. N.S. is grateful for the research support of the National Science Foundation through contract Grant CMMI-1334783 to the University of California at Davis. J.E.D. is grateful to the support from Sandia National Laboratories and Idaho National Laboratory, to Duke University; N.M. gratefully acknowledges the support of the ERC advanced Grant XLS No. 291102.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of California, Davis, CA, 95616, USA

    N. Sukumar

  2. Department of Civil and Environmental Engineering, Duke University, Durham, NC, 27708, USA

    J. E. Dolbow

  3. GeM Institute, Ecole Centrale de Nantes, 44321, Nantes, France

    N. Moës

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  1. N. Sukumar
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  2. J. E. Dolbow
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  3. N. Moës
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Correspondence to N. Sukumar.

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Sukumar, N., Dolbow, J.E. & Moës, N. Extended finite element method in computational fracture mechanics: a retrospective examination. Int J Fract 196, 189–206 (2015). https://doi.org/10.1007/s10704-015-0064-8

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