Summary
According to a recently proposed variational formulation of the Extended Finite Element Method for cohesive crack propagation analyses [1] the length and the direction of new crack segments are determined on a global level from minimizing the total energy of the system. The focus of this paper is laid on the influence of the numerical integration and of the cohesive interface law on the energy distribution and, consequently, on the predicted crack trajectory. These influences are investigated by means of crack propagation analyses in plane structures made of quasi-brittle materials.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
G. Meschke and P. Dumstorff. Energy-based modeling of cohesive and cohe-sionless cracks via X-FEM. Computer Methods in Applied Mechanics and Engineering, 2007. in press.
N. Moës, J.E. Dolbow, and T. Belytschko. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 46:131–150, 1999.
N. Moës and T. Belytschko. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics, 69:813–833, 2002.
G.N. Wells and L.J. Sluys. A new method for modelling cohesive cracks using finite elements. International Journal for Numerical Methods in Engineering, 50:2667–2682, 2001.
S. Mariani and U. Perego. Extended finite element method for quasi-brittle fracture. International Journal for Numerical Methods in Engineering, 58:103– 126, 2003.
J. Mergheim, E. Kuhl, and P. Steinmann. A finite element method for the computational modelling of cohesive cracks. International Journal for Numerical Methods in Engineering, 63:276–289, 2005.
J. Oliver, A.E. Huespe, E. Samaniego, and E.W.V. Chaves. On strategies for tracking strong discontinuities in computational failure mechanics. In H.A. Mang, F.G. Rammerstorfer, and J. Eberhardsteiner, editors, Fifth World Congress on Computational Mechanics (WCCM V). Online publication, 2002.
J. Oliver, A.E. Huespe, E. Samaniego, and E.W.V. Chaves. Continuum approach to the numerical simulation of material failure in concrete. International Journal for Numerical and Analytical Methods in Geomechanics, 28:609–632, 2004.
G.A. Francfort and J.J. Marigo. Revisiting brittle fracture as an energy minimization problem. Journal of Mechanics and Physics of Solids, 46(8):1319–1342, 1998.
P. Dumstorff and G. Meschke. Crack propagation criteria in the framework of X-FEM-based structural analyses. International Journal for Numerical and Analytical Methods in Geomechanics, 31, 2007. in press.
K. C. Le. Variational principles of non-linear theory of brittle fracture mechanics. Journal of Applied Mathematics and Mechanics, 54:543–549, 1990.
P. Dumstorff. Modellierung und numerische Simulation von Rissfortschritt in spröden und quasi-spröden Materialien auf Basis der Extended Finite Element Method. PhD thesis, Institute for Structural Mechanics, Ruhr University Bo-chum, 2005. in german.
G.T. Camacho and M. Ortiz. Computational modelling of impact damage in brittle materials. International Journal of Solids and Structures, 33:2899–2938, 1996.
B. J. Winkler. Traglastuntersuchungen von unbewehrten und bewehrten Beton-strukturen auf der Grundlage eines objektiven Werkstoffgesetzes f¨ur Beton. PhD thesis, Universität Innsbruck, 2001.
J. Mosler and G. Meschke. Embedded cracks vs. smeared crack models: A comparison of elementwise discontinuous crack path approaches with emphasis on mesh bias. Computer Methods in Applied Mechanics and Engineering, 193:3351– 3375, 2004. (Special issue on Computational Failure Mechanics).
C. Feist and G. Hofstetter. Mesh-insensitive strong discontinuity approach for fracture simulations of concrete. In Numerical Methods in Continuum Mechanics (NMCM 2003), 2003.
M.B. Nooru-Mohamed. Mixed-mode Fracture of Concrete: an Experimental Approach. PhD thesis, Technische Universiteit Delft, 1992.
C. Feist. A Numerical Model for Cracking of Plain Concrete Based on the Strong Discontinuity Approach. PhD thesis, University Innsbruck, 2004.
B. Shen and O. Stephansson. Modification of the g-criterion for crack propagation subjected to compression. Engineering Fracture Mechanics, 47:177–189, 1994.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this paper
Cite this paper
Meschke, G., Dumstorff, P., Fleming, W. (2007). Variational Extended Finite Element Model for Cohesive Cracks: Influence of Integration and Interface Law. In: Combescure, A., De Borst, R., Belytschko, T. (eds) IUTAM Symposium on Discretization Methods for Evolving Discontinuities. IUTAM Bookseries, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6530-9_17
Download citation
DOI: https://doi.org/10.1007/978-1-4020-6530-9_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-6529-3
Online ISBN: 978-1-4020-6530-9
eBook Packages: EngineeringEngineering (R0)