Vol. 16 No. 1 (2017): UIS Engineering Journal
Articles

Geometric description scheme for crack propagation by a geometric description based on Level Sets and Fast Marching Method

Vicente Francisco González Albuixech
Universidad Carlos III de Madrid
Bio
Eugenio Giner
Universidad Politécnica de Valencia
Bio
José Enrique Tarancón
Universidad Politécnica de Valencia
Bio

Published 2016-12-30

Keywords

  • Fracture mechanics,
  • FMM,
  • LSM,
  • XFEM,
  • simulation

How to Cite

González Albuixech, V. F., Giner, E., & Tarancón, J. E. (2016). Geometric description scheme for crack propagation by a geometric description based on Level Sets and Fast Marching Method. Revista UIS Ingenierías, 16(1), 47–58. https://doi.org/10.18273/revuin.v16n1-2017005

Abstract

The Level Set Method is used to describe mathematically the propagation of surfaces, by the resolution and approximation of a set of differential equations. This technique has been widely used on the XFEM framework, specially for crack propagation. However, there are other techniques based on geometrical considerations, as the Fast Marching Method. In this study, it is proposed a geometrical related technique based on the Fast Marching Method and Level Set Method for crack growth description in XFEM. Therefore, the results could be used directly on fracture mechanics analysis using XFEM.

Downloads

Download data is not yet available.

References

  1. J. A. Sethian, Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Materials Science, Cambridge University Press. Cambridge. R.U. 1999.
  2. J. A. Sethian, “Evolution, Implementation, and application of level set and fast marching methods for advancing fronts”, Journal of Computational Physics, vol. 169, pp. 503-555, 2001.
  3. J. A. Sethian, “A Fast Marching Level Set Method for Monotonically Advancing Fronts”, Proc. Nat. Acad, vol. 93, nº. 4, pp.1591-1595, 1996.
  4. J. A. Sethian, “Fast marching methods”, Society of Industrial and Applied Math.. Review, vol 41, nº 2, pp. 199-235,1999.
  5. T. J. Barth, J.A. Sethian, ”Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains”, Journal of Computational Physics. 1998, vol. 145, pp. 1-40, 1998.
  6. N. Moës, J. Dolbow, T. Belytschko, “A Finite Element Method for Crack Growth Without Remeshing”, International Journal for Numerical Methods in Engineering, vol. 46, nº 1, pp. 131-150, 1999.
  7. M. Stolarska, D. Chopp, N. Moës, T. Belytschko, “Modelling crack growth by level sets in the extended finite element method”, International Journal for Numerical Methods in Engineering, vol. 51, pp. 943-960, 2001.
  8. N. Moës, A. Gravouil, T. Belytschko, “Non-planar 3D crack growth by the extended finite element and level sets-part I mechanical model”, International Journal for Numerical Methods in Engineering, vol. 53, pp. 2549-2568, 2002.
  9. A. Gravouil, N. Moës, T. Belytschko, “Non-planar 3D crack growth by the extended finite element and level sets-part II: Level set update”, International Journal for Numerical Methods in Engineering, vol. 53, pp 2569-2586, 2002.
  10. M. Duflot, “A study of the representation of cracks with level sets”, International Journal for Numerical Methods in Engineering, vol. 70, nº11, pp. 1261-1302, 2006.
  11. N. Sukumar, D. L. Chopp, B. Moran, “Extended finite element method and fast marching method for three-dimensional fatigue crack propagation”, Engineering Fracture Mechanics, vol.70, pp. 29-48, 2003.
  12. D. L. Chopp, N. Sukumar, ”Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element / fast marching method”, International Journal of Engineering Science, vol. 41, pp. 845-869, 2003.
  13. N. Sukumar, D. L Chopp, E. Béchet, N. Moës, “Three- dimensional non-planar crack growth by a coupled extended finite element and fast marching method“, International Journal for Numerical Methods in Engineering, vol. 76, pp. 727-748, 2008.
  14. R. Kimmel, J. A. Sethian, “Computing geodesic paths on manifolds”, Proceedings of the national academy of Sciences , vol 95, nº15, pp.8431-8435, 1998.
  15. J. A. Sethian, A. Vladimirsky, “Fast methods for the eikonal and related Hamilton-Jacobi equations on unstructured meshes”, Proceedings of the National Academy of Sciences, vol. 97, nº 11, pp. 5699-5703, 2000.
  16. D. L. Chopp, ”Some improvements of the fast marching method”, Society of Industrial and Applied Math, vol. 23, nº1, pp 230-244, 2001.
  17. R. N. Elias, M. A. D. Martins, A. L. G. A. Coutinho, “Simple finite element-based computation of distance functions in unstructured grids”, International Journal for Numerical Methods in Engineering, vol.72, pp. 1095-1110, 2007.
  18. D. Adalsteinsson, J. A. Sethian, ”The fast construction velocities in level set methods”, The Journal of Computational Physics, vol. 148, pp. 2-22, 1999.