DOI QR코드

DOI QR Code

A direct XFEM formulation for modeling of cohesive crack growth in concrete

  • Asferg, J.L. (Department of Civil Engineering, Technical University of Denmark) ;
  • Poulsen, P.N. (Department of Civil Engineering, Technical University of Denmark) ;
  • Nielsen, L.O. (Department of Civil Engineering, Technical University of Denmark)
  • Received : 2006.08.17
  • Accepted : 2007.02.05
  • Published : 2007.04.25

Abstract

Applying a direct formulation for the enrichment of the displacement field an extended finite element (XFEM) scheme for modeling of cohesive crack growth is developed. Only elements cut by the crack is enriched and the scheme fits within the framework of standard FEM code. The scheme is implemented for the 3-node constant strain triangle (CST) and the 6-node linear strain triangle (LST). Modeling of standard concrete test cases such as fracture in the notched three point beam bending test (TPBT) and in the four point shear beam test (FPSB) illustrates the performance. The XFEM results show good agreement with results obtained by applying standard interface elements in FEM and with experimental results. In conjunction with criteria for crack growth local versus nonlocal computation of the crack growth direction is discussed.

References

  1. Asferg, J. L., Poulsen, P. N. and Nielsen, L. O. (2004), "Modeling of cohesive crack applying XFEM", 5th International PhD Symposium in Civil Engineering, Walraven, J., Blaauwendraad, J., Scarpas, T. and Snijder, B. (Eds.), pages 1261-1269.
  2. Barenblatt, G. I. (1962), "The mathematical theory of equilibrium of cracks in brittle fracture", Advances in Applied Mech., 7, 55-129. https://doi.org/10.1016/S0065-2156(08)70121-2
  3. Bazant, Z. P. and Oh, B. H. (1983), "Crack band theory for fracture of concrete", Mater. Struct., RILEM, 16(93), 155-177.
  4. Belytschko, T. and Black, T. (1999), "Elastic crack growth in finite elements with minimal remeshing", Int. J. Numer. Methods Eng., 45(5), 601-620. https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S
  5. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P. (1996), "Meshless methods: an overiew and recent developments", Comput. Methods Appl. Mech. Eng., 139, 3-47. https://doi.org/10.1016/S0045-7825(96)01078-X
  6. Bouchard, P. O., Bay, F. and Chastel, Y. (2002), "Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria", Comput. Methods Appl. Mech. Eng., 192, 3887-3908.
  7. Bouchard, P. O., Bay, F., Chastel, Y. and Tovena, I. (2000), "Crack propagation modelling using an advanced remeshing technique", Comput. Methods Appl. Mech. Eng., 189, 723- 742. https://doi.org/10.1016/S0045-7825(99)00324-2
  8. Carpinteri, A., Valente, S., Ferrara, G. and Melchiorri, G. (1992), "Is mode II fracture energy a real material property?", Comput. Struct., 48(3), 397-413. https://doi.org/10.1107/S0108270191009496
  9. Daux, C., Moes, N., Dolbow, J., Sukumar, N. and Belytschko, T. (2000), "Arbitrary branched and intersecting cracks with the extended finite element method", Int. J. Numer. Methods Eng., 48, 1741-1760. https://doi.org/10.1002/1097-0207(20000830)48:12<1741::AID-NME956>3.0.CO;2-L
  10. Dugdale, D. S. (1960), "Yielding of steel sheets containing slits", J. Mech. Phys. Solids, 8, 100-104. https://doi.org/10.1016/0022-5096(60)90013-2
  11. Hillerborg, A., Modéer, M. and Peterson, P.-E (1976), "Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements", Cement Concrete Res., 6, 773-782. https://doi.org/10.1016/0008-8846(76)90007-7
  12. Jirasek, M. (2000), "Comparative study on finite elements with embedded discontinuities", Comput. Methods Appl. Mech. Eng., 188, 307-330. https://doi.org/10.1016/S0045-7825(99)00154-1
  13. Jirasek, M. and Belytschko, T. (2002), "Computational resolution of strong discontinuities", in: H. Mang, F. Rammerstorfer, J. Eberhardsteiner (Eds.), Proceedings of Fifth World Congress on Computational Mechanics, WCCM V, Vienna University of Technology, Austria.
  14. Karihaloo, B. L. (1995), Fracture Mechanics and Structural Concrete. Longman Scientific and Technial.
  15. Karihaloo, B. L. and Xiao, Q. Z. (2002), "Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review", Comput. Struct., 81, 119-129.
  16. Krenk, S. (1995), "An orthogonal residual procedure for nonlinear finite element equations", Int. J. Numer. Methods Eng., 38, 823-839. https://doi.org/10.1002/nme.1620380508
  17. Melenk, J. M. and Babu ka, I. (1996), "The partition of unity finite element method: basic theory and application", Comput. Methods Appl. Mech. Eng., 139, 289-314. https://doi.org/10.1016/S0045-7825(96)01087-0
  18. Mergheim, J., Kuhl, E. and Steinmann, P. (2005) "A finite element method for the computational modeling of cohesive cracks", Int. J. Numer. Methods Eng., 63, 276-289. https://doi.org/10.1002/nme.1286
  19. Moes, N. and Belytschko, T. (2002), "Extended finite element method for cohesive crack growth", Eng. Fract. Mech., 69, 813-833. https://doi.org/10.1016/S0013-7944(01)00128-X
  20. Moes, N., Dolbow, J. and Belytschko, T. (1999), "A finite element method for crack growth without remeshing", Int. J. Numer. Methods Eng., 46, 131-150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
  21. Nielsen, M. P. (1999), Limit Analysis and Concrete Plasticity. CRC Press, second editon.
  22. Patzak, B. and Jirasek, M. (2004), "Adaptive resolution of localized damage in quasi-brittle materials", J. Eng. Mech., 130, 720-732. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:6(720)
  23. Stang, H., Olesen, J. F., Poulsen, P. N. and Dick-Nielsen, L. (2006), "Application of the cohesive crack in cementitious materials modelling", In Meschke, G. de Borst, R. Mang, H. and Bicanic, N., Editors, Computational Modeling of Concrete Structures, 443-449, Taylor & Francis.
  24. Stolarska, M., Chopp, D. L, Moes, N. and Belytschko, T. (2001), "Modeling crack growth by level sets in the extended finite element method", Int. J. Numer. Methods Eng., 51, 943-960. https://doi.org/10.1002/nme.201
  25. Sukumar, N., Moes, N., Moran, B. and Belytschko, T. (2000), "Extended finite element method for three dimensional crack modeling", Int. J. Numer. Methods Eng., 48, 1549-1570. https://doi.org/10.1002/1097-0207(20000820)48:11<1549::AID-NME955>3.0.CO;2-A
  26. Vandewalle, L. (2000), "Test and design methods for steel fiber reinforced concret. Recommendations for bending test", Mater. Struct., 33, 3-5. https://doi.org/10.1007/BF02481689
  27. Wells, G. and Sluys, L. (2001), "A new method for modeling of cohesive cracks using finite elements", Int. J. Numer. Methods Eng., 50(12), 2667-2682. https://doi.org/10.1002/nme.143
  28. Zi, G. and Belytschko, T. (2003), "New crack-tip elements for XFEM and applications to cohesive cracks", Int. J. Numer. Methods Eng., 57, 2221-2240. https://doi.org/10.1002/nme.849

Cited by

  1. Arch-dam crack deformation monitoring hybrid model based on XFEM vol.54, pp.10, 2011, https://doi.org/10.1007/s11431-011-4550-6
  2. Three dimensional fragmentation simulation of concrete structures with a nodally regularized meshfree method vol.72, 2014, https://doi.org/10.1016/j.tafmec.2014.04.006
  3. Complete Tangent Stiffness for eXtended Finite Element Method by including crack growth parameters vol.95, pp.1, 2013, https://doi.org/10.1002/nme.4497
  4. Numerical modeling tensile failure behavior of concrete at mesoscale using extended finite element method vol.23, pp.7, 2014, https://doi.org/10.1177/1056789513516028
  5. A partly and fully cracked triangular XFEM element for modeling cohesive fracture vol.85, pp.13, 2011, https://doi.org/10.1002/nme.3040
  6. An embedded crack in a constant strain triangle utilizing extended finite element concepts vol.117, 2013, https://doi.org/10.1016/j.compstruc.2012.11.006