Correction force for releasing crack tip element with XFEM and only discontinuous enrichment
How to smoothly release the crack tip element with only discontinuous enrichment in XFEM?
DOI:
https://doi.org/10.13052/EJCM.18.465-483Keywords:
XFEM, cohesive law, discontinuous enrichment, Heaviside function, dynamic crack propagationAbstract
This paper deals with numerical crack propagation and makes use of the extended finite element method in the case of explicit dynamics. The advantage of this method is the absence of remeshing. The use of XFEM with Heaviside functions only gives a binary description of the crack tip element: cut or not. Here, we modify the internal forces with a correction force in order to smoothly release the tip element while the virtual crack tip travels through an element. This avoids creating non physical stress waves and improves the accuracy of the evaluation of the stress intensity factors during propagation.
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References
Barenblatt G., “ The mathematical theory of equilibrium cracks formed in brittle fracture”,
Advanced Applied Mechanics, vol. 7, p. 55-129, 1962.
Belytschko T., Liu W., Moran B., Nonlinear finite elements for continua and structures, Wiley,
Chichester, 2000.
Belytschko T., Moës N., Usui S., Parimi C., “ Arbitrary discontinuities in finite elements”,
International Journal for Numerical Methods in Engineering, vol. 50, n° 4, p. 993-1013,
Benvenuti E., “ A regularized XFEM framework for embedded cohesive interfaces”, Computer
Methods in Applied Mechanics and Engineering, vol. 197, n° 49-50, p. 4367-4378, 2008.
Black T., Belytschko T., “ Elastic crack growth in finite elements with minimal remeshing”,
International Journal for Numerical Methods in Engineering, vol. 45, p. 601-620, 1999.
Bui H., Mecanique de la rupture fragile, Masson, 1978.
Combescure A., Gravouil A., Gregoire D., Réthoré J., “ X-FEM a good candidate for energy
conservation in simulation of brittle dynamic crack propagation”, Computer Methods in
Applied Mechanics and Engineering, vol. 197, n° 5, p. 309-318, 2008.
Dolbow J., Moës N., Belytschko T., “ An extended finite element method for modeling crack
growth with frictional contact”, Computer Methods in Applied Mechanics and Engineering,
vol. 190, p. 6825-6846, 2001.
Duan Q., Song J., Menouillard T., Belytschko T., “ Element-local level set method for threedimensional
dynamic crack growth”, International Journal for Numerical Methods in Engineering,
Freund L., “ Crack Propagation in an Elastic Solid Subjected to General Loading. Pt. 1. Constant
Rate of Extension”, Journal of the Mechanics of Physics and Solids, vol. 20, n° 3, p. 129-
, 1972.
Freund L., Dynamic Fracture Mechanics, Cambridge University Press, 1990.
Freund L., Douglas A., “ Influence of inertia on elastic-plastic antiplane-shear crack growth.”,
Journal of the Mechanics of Physics and Solids, vol. 30, n° 1, p. 59-74, 1982.
Hansbo A., Hansbo P., “ A finite element method for the simulation of strong and weak discontinuities
in solid mechanics”, Computer Methods in Applied Mechanics and Engineering,
vol. 193, n° 33-35, p. 3523-3540, 2004.
Hillerborg A., Modeer M., Petersson P. et al., “ Analysis of crack formation and crack growth
in concrete by means of fracture mechanics and finite elements”, Cement and Concrete
Research, vol. 6, n° 6, p. 773-782, 1976.
Khenous H., Laborde P., Renard Y., “ On the discretization of contact problems in elastodynamics”,
Lecture Notes in Applied and Computational Mechanics, vol. 27, p. 31-38, 2006.
Melenk J., Babuška I., “ The partition of unity finite element method: Basic theory and applications”,
Computer Methods in Applied Mechanics and Engineering, vol. 139, n° 1-4,
p. 289-314, 1996.
Menouillard T., Elguedj T., Combescure A., “ Mixed-mode stress intensity factors for graded
materials”, International journal of solids and structures, vol. 43, n° 7-8, p. 1946-1959,
Menouillard T., Réthoré J., Combescure A., Bung H., “ Efficient explicit time stepping for the
eXtended Finite Element Method (X-FEM)”, International Journal for Numerical Methods
in Engineering, vol. 68, p. 911-939, 2006.
Menouillard T., Réthoré J., Moës N., Combescure A., Bung H., “ Mass lumping strategies for
X-FEM explicit dynamics: Application to crack propagation”, International Journal for
Numerical Methods in Engineering, vol. 74, n° 3, p. 447-474, 2008.
Menouillard T., Song J.-H., Duan Q., Belytschko T., “ Time Dependent Crack Tip Enrichment
for Dynamic Crack Propagation”, International Journal of Fracture, 2009.
Moës N., Belytschko T., “ Extended finite element method for cohesive crack growth”, Engineering
Fracture Mechanics, vol. 69, n° 7, 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, n° 1, p. 131-
, 1999.
Ortiz M., Pandolfi A., “ Finite-deformation irreversible cohesive elements for three-dimensional
crack-propagation analysis”, Int. J. Numer. Methods Eng, vol. 44, n° 9, p. 1267-1282, 1999.
Patzák B., Jirasek M., “ Process zone resolution by extended finite elements”, Engineering
Fracture Mechanics, vol. 70, n° 7-8, p. 957-977, 2003.
Rabczuk T., Song J., Belytschko T., “ Simulations of instability in dynamic fracture by the
cracking particles method”, Engineering Fracture Mechanics, vol. 76, p. 730-741, 2009.
Ravi-Chandar K., Dynamic fracture, Elsevier Science, 2004.
Remmers J., Borst R., Needleman A., “ A cohesive segments method for the simulation of crack
growth”, Computational Mechanics, vol. 31, n° 1, p. 69-77, 2003.
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.
Rosakis A., Freund L., “ Optical Measurement of the Plastic Strain Concentration at a Crack Tip
in a Ductile Steel Plate”, Journal of Engineering Materials and Technology (Transactions
of the ASME), vol. 104, n° 2, p. 115-120, 1982.
Song J., Areias P., Belytschko T., “ A method for dynamic crack and shear band propagation
with phantom nodes”, International Journal for Numerical Methods in Engineering, vol.
, p. 868-893, 2006.
Stolarska M., Chopp D., Moës N., Belytschko T., “ Modelling crack growth by level sets in
the extended finite element method”, International Journal for Numerical Methods in Engineering,
vol. 51, p. 943-960, 2001.
Unger J., Eckardt S., Könke C., “ Modelling of cohesive crack growth in concrete structures
with the extended finite element method”, Computer Methods in Applied Mechanics and
Engineering, vol. 196, n° 41-44, p. 4087-4100, 2007.
