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A robust 3D crack growth method based on the eXtended Finite Element Method and the Fast Marching Method

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Abstract

In the context of the eXtended Finite Element Method (X-FEM), the use of two level set functions allows the representation of the crack to be achieved regardless of the mesh. The initial crack geometry is represented by two distinct level set functions, and the crack propagation is simulated by an update of these two level set functions. In this paper, we propose a new approach, based on the Fast Marching Method (FMM), to update the level set functions. We also propose a new implementation of the FMM, designed for tetrahedral volume meshes. We then extend this method to all types of volume elements (tetrahedra, hexahedra, pentahedra, pyramids) available in a standard finite element library. The proposed approach allows one to use the same mesh to solve the mechanical problem and to update the level set functions. Non-planar quasi-static crack growth simulations are presented to demonstrate the robustness of the approach, compared to existing methods based on the integration of Hamilton-Jacobi equations or geometric approaches.

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Acknowledgements

We sincerely thank the two anonymous reviewers whose suggestions helped us to improve this manuscript.

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Authors and Affiliations

  1. IMSIA, UMR EDF/CNRS/CEA/ENSTA 9219, 828 Boulevard des Maréchaux, 91762, Palaiseau Cedex, France

    M. Le Cren, A. Martin & P. Massin

  2. Université Clermont Auvergne, CNRS, LMBP, 63000, Clermont-Ferrand, France

    A. Martin

  3. École Centrale de Nantes, GéM, UMR CNRS/ECN/UN 6183, 1 Rue de La Noë, 44321, Nantes, France

    N. Moës

  4. Institut Universitaire de France, 1 rue Descartes, 75005, Paris, France

    N. Moës

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  1. M. Le Cren
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  2. A. Martin
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  3. P. Massin
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  4. N. Moës
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Correspondence to A. Martin.

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Le Cren, M., Martin, A., Massin, P. et al. A robust 3D crack growth method based on the eXtended Finite Element Method and the Fast Marching Method. Int J Fract 235, 243–265 (2022). https://doi.org/10.1007/s10704-022-00632-4

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  • DOI: https://doi.org/10.1007/s10704-022-00632-4

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