Prise en compte de discontinuités en espace et en temps par la méthode des éléments finis étendus
Application à la dynamique de la rupture
DOI:
https://doi.org/10.13052/REMN.16.827-843Keywords:
extended finite element, lasto-dynamics, time discontinuity, dynamic crack propagationAbstract
This paper is aimed at presenting an application of the extended finite element method to the time variable in the framework of dynamic crack propagation. We take advantage of the partition of the unity properties of finite elements and use an enriched basis of shape functions in space as well as time. To solve the problem in time, we use a weak formulation including a continuity condition for the velocity. It allows to model mechanical problems with space and time discontinuities. Applications to dynamic crack growth simulation are presented.
Downloads
References
Babuska I., Melenk J., “The Partition of unity method”, International Journal for Numerical
Methods in Engineering, vol. 40, 1997, p. 727-758.
Belytschko T., Chen H., “Singular enrichment finite element method for elastodynamic crack
propagation”, International Journal of Computational Methods, vol. 1, n° 1, 2001, p. 1-15.
Belytschko T., Chen H., Jingxiao X., Goangseup Z., “Dynamic crack propagation based on loss
of hyperbolicity and a new discontinuous enrichment”, International Journal for Numerical
Methods in Engineering, vol. 58, 2003, p. 1873-1905.
de Borst R., Remmers J., Needleman A., “Mesh-independent numerical representations of
cohesive-zone models”, Engineering Fracture Mechanics, vol. 173, n° 2, 2006, p. 160-177.
Chessa J., Belytschko T., “Arbitrary discontinuites in space-time finite elements”, International
Journal for Numerical Methods in Engineering, vol. 61, n° 15, 2004, p. 2595-2614.
Freund L., Dynamic fracture mechanics, Cambridge Monographs on Mechanics and Applied
Mathematics, 1990.
Grégoire D.,Maigre H., Réthoré J., Combescure A., “Dynamic crack propagation under mixedmode
loading - Comparison between experiments and X-FEM simulations”, International
Journal of Solids and Structures, vol. 44, 2007, p. 6517-6534.
Kalthoff J., “Modes of dynamic shear failure in solids”, International Journal of Fracture,
vol. 101, 2000, p. 1-31.
Kanninen M., Popelar C., Advanced fracture mechanics, Oxford University Press, New York,
Maigre H., Rittel D., “Dynamic fracture detection using the force displacement reciprocity : application
to the compact compression specimen”, International Journal of Fracture, vol. 73,
, p. 67-79.
Moës N., Dolbow J., Belytschko T., “A finite element method for crack growth without remeshing”,
International Journal for Numerical Methods in Engineering, vol. 46, n° 1, 1999,
p. 133-150.
Remmers J., de Borst R., Needleman A., “A cohesive segments method for the simulation of
crack growth”, Computational Mechanics, vol. 31, 2003, p. 69-77.
Réthoré J., Méthode éléments finis étendus en espace et en temps : application à la propagation
dynamique des fissures, Thèse, Institut National de Sciences Appliquées de Lyon, 2005.
Réthoré J., Gravouil A., Combescure A., “A combined space time eXtended Finite Element
Method”, International Journal for Numerical Methods in Engineering, vol. 64, 2005a,
p. 260-284.
Réthoré J., Gravouil A., Combescure A., “An Energy Conserving Scheme for Dynamic Crack
Growth with the eXtended Finite Element Method”, International Journal for Numerical
Methods in Engineering, vol. 63, 2005b, p. 631-659.
