9. Bibliography#

  1. Grvouil A., Moes N., Belytschko T., « 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, vol. 53, pp. 2569-2586, 2002

  1. OSHER S., SETHIAN J.A., « Fronts propagations with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations », Journal of Computational Physics, vol. 79, vol. 79, pp. 12-49, 1988

  1. Sukumar N., Chopp D.L., Moran B., Moran B., « Extended finite element method and fast marching method for three-dimensional fatigue crack propagation », Engineering Fracture Mechanics, vol. 70, vol. 70, pp. 29-48, 2003

  1. Erdogan G., Sih G.C., « On the crack extension in plates under plane loading and transverse shear », Journal of Basic Engineering, vol. 85, pp. 519-27, 1963

  1. Barth T.J., SethianJ.A., « Numerical schemes for the Hamilton-Jacobi and level-set equations on triangulated domains », Journal of Computational Physics, vol. 145, pp. 1-40, 1998

  1. Crandall M.G., Lions P.L., « Two approximations of solutions of Hamilton-Jacobi equations », Mathematics of Computation, vol. 43, pp. 1-19, 1984

  1. Deconinck H., Struijs R., Roep.l., « Compact Advection Schemes on Unstructured Grids », Technical Report, VKI, VKI LS 1993-04, Computational Fluid Dynamics, 1993

  1. Roep.l., « Linear Advection Schemes on Triangular Meshes », Technical Report CoA 8720, Cranfield Institute of Technology, 1987

  1. Roep.l., « Optimum Upwind Advection on Triangular Mesh », ICASE 90-75, 1990

  1. PENG D., MERRIMAN B., OSHER S., ZHAO H., H., KANG M., « A PDE -based fast local level-set method », Journal of Computational Physics, vol. 155, pp. 410-438, 1999

  1. ADALSTEINSSON D., SETHIAN J.A., « A fast level-set method for propagating interfaces », Journal of Computational Physics, vol. 118, pp. 269-277, 1995

  1. PRABEL B., COMBESCURE A., GRAVOUIL A., MARIE S., « Level set X- FEM non matching meshes: application to dynamic crack propagation in elastic-plastic media », International Journal for Numerical Methods in Engineering, vol. 1, vol. 1, pp. 1-15, 2006

  1. DUFLOT M., « A study of the representation of cracks with level-sets », International Journal for Numerical Methods in Engineering, vol. 70, pp. 1261-1302, 2007

  1. COLOMBO, PATRICK MASSIN, « Fast and robust level-set update for 3D non-planar X- FEM crack propagation modelling », Computer Methods in Applied Mechanics and Engineering, 200 (2011), 200 (2011), 2160-2180

  1. SUKUMAR N., CHOPP D.L., BE CHET E., MOëS N., N., « Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method », International Journal Numerical Methods in Engineering, 76 (2008), 727-748

  1. SHI J., CHOPP D., LUA J., SUKUMAR N., N., BELYTSCHKO T., « Abaqus implementation of extended finite element method using a level-set representation of three-dimensional fatigue crack growth and life predictions », Engineering Fracture Mechanics, 77 (2010), 2840-2863

  1. CITARELLA R., BUCHHOLZ F.-G., Comparison of crack growth simulation by DBEM and FEM for SEN -specimens undergoing torsion or bending loading, Engineering Fracture Mechanics, 75 (2008), 75 (2008), 489-509

  1. COLOMBO D., « An implicit geometrical approach to level-sets update for 3D non planar X- FEM crack propagation », submitted to Computer Methods in Applied Mechanics and Engineering

  2. SETHIAN J.A., Level Set Methods and Fast Marching Methods, 1999.

  1. GALENNE E., « Automatic propagation of 3D cracks with X- FEM in fatigue: projection method » Report AMA, 2008

  1. HABOUSSA D., « Modeling the traction-shear transition of metals under shock by X- FEM », Thesis, INSA Lyon, 2012

  2. BRONSTEIN A., BRONSTEIN M., KIMMEL R. « Numerical geometry of non-rigid shapes », Springer, 2007