Numerical propagation of dynamic cracks using X-FEM
DOI:
https://doi.org/10.13052/REMN%20–%2016/2007Keywords:
partition of unity, extended finite element method, dynamic crack propagation, cohesive modelAbstract
This paper presents an application of the eXtended Finite Element Method for numerical modeling of the dynamic cracks propagation. The numerical cracks representation is adapted to the time-dependent mechanical formulation, using the Heaviside step function for completely cutted elements and the cohesive model for crack tips. In order to find the propagation parameters, a crack evolution model is proposed. The numerical implementation is achieved in new explicit FE module. A numerical example is proposed for proving the computational efficiency of this new module.
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References
Babuska I., Melenk J., « The Partition of Unity Method », International Journal for Numerical
Methods in Engineering, vol. 40, p. 727-758, 1997.
Belytschko T., Black T., « Elastic Crack Growth in Finite Elements withMinimal Remeshing »,
International Journal for Numerical Methods in Engineering, vol. 45, p. 601-620, 1999.
Belytschko T., Chen H., « Singular enrichment finite element method for elastodynamic crack
propagation », International Journal of Computational Methods, vol. 1, n° 1, p. 1-15, 2004.
Belytschko T., Chen H., Xu J., Zi G., « Dynamic Crack Propagation Based on Loss of Hyperbolicity
and a New Discontinuous Enrichment », International Journal for Numerical
Methods in Engineering, vol. 58, p. 1873-1905, 2003.
Belytschko T., Fish J., Engelmann B., « A Finite Element with Embedded Localisation Zones »,
Computer Methods in Applied Mechanics and Engineering, vol. 70, p. 59-89, 1988.
Borst R., Remmers J. J., Needleman A., «Mesh-independent discrete numerical representations
of cohesive-zone models », Engineering Fracture Mechanics, vol. 73, p. 160-177, 2006.
Camacho G. T., Ortiz M., « Computational modeling of impact damage in brittle materials »,
International Journal of Solids and Structures, vol. 33, p. 2899-2938, 1996.
Daux C., Moës N., Dolbow J., Sukumar N., Belytschko T., « Arbitrary Branched and Intersecting
Cracks with the Extended Finite Element Method », International Journal for Numerical
Methods in Engineering, vol. 48, p. 1741-1760, 2000.
Dolbow J. E., Devan A., « Enrichment of Enhanced Assumed Strain Approximations for Representing
Strong Discontinuities: Addresing Volumetric Incompressibility and the Discontinuous
Patch test », International Journal for Numerical Methods in Engineering, vol. 59,
p. 47-67, 2004.
Dvorkin. E. N., « Finite Elements with Displacements Interpolated Embedded Localization
Lines Insensitive to Mesh Size and Distorsions », International Journal for Numerical
Methods in Engineering, vol. 30, p. 541-564, 1990.
Elguedj T., Gravouil A., Combescure A., « Appropriate extended functions for X-FEM simulation
of plastic fracture mechanics », Computer Methods in Applied Mechanics and Engineering,
vol. 195, p. 501-515, 2006.
Hulbert G. M., Chung J., « Explicit Time Integration for Structural Dynamics with Optimal
Numerical Dissipation », Computer Methods in Applied Mechanics and Engineering, vol.
, p. 175-188, 1996.
Jirasek M., « Comparative Study on Finite Elements with Embedded Discontinuities », Computer
Methods in Applied Mechanics and Engineering, vol. 188, p. 307-330, 2000.
Menouillard T., Réthoré J., A.Combescure, Bung H., « Efficient explicit time stepping of the
eXtended Finite ElementMethod (X-FEM) », International Journal for NumericalMethods
in Engineering, 2006.
Moës N., Belytschko T., « Extended Finite Element Method for Cohesive Crack growth »,
Engineering Fracture Mechanics, vol. 69, p. 813-833, 2002.
Moës N., Dolbow J., Belytschko T., « A Finite Element Method for Crack Growth without
Remeshing », International Journal for Numerical Methods in Engineering, vol. 46, p. 131-
, 1999.
Nistor I., Identification expérimentale et simulation numérique de l’endommagement en dynamique
rapide: application aux structures aéronautiques, PhD thesis, Institut National
Polytechnique de Toulouse, 2005.
Nistor I., Pantalé O., Caperaa S., Sattouf C., « Identification of a Dynamic Viscoplastic Flow
Law Using a Combined Levenberg-Marquardt and Monte-Carlo Algorithm », VII international
Conference on Computational Plasticity, Barcelone, 2003.
OrtizM., Leroy Y., Needleman A., « A Finite ElementMethod for Localized Failure Analysis »,
Computer Methods in Applied Mechanics and Engineering, vol. 61, p. 189-214, 1987.
Ortiz M., Pandolfi A., « Finite-Deformation Irreversible Cohesive Elements for Threedimensional
Crack-Propagation Analysis », International Journal for Numerical Methods
in Engineering, vol. 44, p. 1267-1282, 1999.
Pandolfi A., Krysl P., Ortiz M., « Finite Element Simulation of Ring Expansion and Fragmentation
», International Journal of Fracture, vol. 95, n° 1-4, p. 279-297, 1999.
Pantalé O., « An Object-Oriented Programming of an Explicit Dynamics Code: Application to
Impact Simulation », Advances in Engineering Software, vol. 33, n° 5, p. 275-284, 8, 2002.
Pantalé O., « Parallelization of an Object-Oriented FEM Dynamics Code: Influence of the
strategies on the SpeedUp », Advances in Engineering Software, vol. 36, n° 6, p. 361-373,
Remmers J., Borst R., Needleman A., « Simulation of Fast Crack Growth Using Cohesive
Segments », VII International Conference on Computational Plasticity, COMPLAS, 2003.
Réthoré J., Gravouil A., Combescure A., « A stable numerical scheme for the finite element
simulation of dynamic crack propagation with remeshing », Computer Methods in Applied
Mechanics and Engineering, vol. 193, p. 4493-4510, 2004.
Réthoré J., Gravouil A., Combescure A., « An energy-conserving scheme for dynamic crack
growth using the eXtended finite element method », International Journal for Numerical
Methods in Engineering, vol. 63, p. 631-659, 2005.
Simo J., Oliver J., Armero F., « An Analysis of Strong Discontinuities Induced by Strain Softening
in Rate-Independent Inelastic Solids », Computational Mechanics, vol. 12, p. 277-296,
Sukumar N., Moës N., Moran B., Belytschko T., « Extended Finite Element Method for Three-
Dimensional Crack Modelling », International Journal for Numerical Methods in Engineering,
vol. 48, p. 1549-1570, 2000.
Sukumar N., Prévost J.-H., « Modelling Quasi-Static Crack Growth with the Extended Finite
Element Method. Part I: Computer Implementation », International Journal of Solids and
Structures, vol. 40, p. 7513-7537, 2003.
Xu X. P., Needleman A., « Numerical Simulation of Fast Crack Growth in Brittle Solids »,
Journal of the Mechanics and Physics of Solids, vol. 42, p. 1397-1434, 1994.