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Progressive fracture analysis of concrete using finite elements with embedded displacement discontinuity

  • Song, Ha-Won (Department of Civil Engineering, Yonsei University) ;
  • Shim, Byul (Department of Civil Engineering, Yonsei University) ;
  • Woo, Seung-Min (Department of Civil Engineering, Yonsei University) ;
  • Koo, Ja-Choon (Department of Civil Engineering, Yonsei University)
  • Published : 2001.06.25

Abstract

In this paper, a finite element with embedded displacement discontinuity which eliminates the need for remeshing of elements in the discrete crack approach is applied for the progressive fracture analysis of concrete structures. A finite element formulation is implemented with the extension of the principle of virtual work to a continuum which contains internal displacement discontinuity. By introducing a discontinuous displacement shape function into the finite element formulation, the displacement discontinuity is obtained within an element. By applying either a nonlinear or an idealized linear softening curve representing the fracture process zone (FPZ) of concrete as a constitutive equation to the displacement discontinuity, progressive fracture analysis of concrete structures is performed. In this analysis, localized progressive fracture simultaneous with crack closure in concrete structures under mixed mode loading is simulated by adopting the unloading path in the softening curve. Several examples demonstrate the capability of the analytical technique for the progressive fracture analysis of concrete structures.

Keywords

References

  1. Ali, A. (1995), "FEM analysis of tensile fracture phenomena in concrete structures", Fracture Mech. of Concrete Struct., Proc. FRAMCOS-2, Wittmann, F. H., eds., Zurich, Switzerland, July, 1565-1574.
  2. Bazant, Z.P., and Gettu, R. (1992), "Rate effect and load relaxation in static fracture concrete", ACI Mater. J., 89(5), 456-468.
  3. Bocca, P., Carpinteri, A., and Valente, S. (1991), "Mixed mode fracture of concrete", Int. J. Solids Struct., 27, 1139-1153. https://doi.org/10.1016/0020-7683(91)90115-V
  4. Cervenka, V. (1970), "Inelastic finite element analysis of reinforced concrete panels", Ph.D. Dissertation, University of Boulder.
  5. Cope, R.J., Rao, P.V., Clark, L.A., and Norris, P. (1980), "Modelling of reinforced concrete behaviour for finite element analysis of bridge slabs", Numerical Methods for Non-linear Problems, Taylor et al., eds., Pineridge Press, Swansea, 457-470.
  6. de Borst, R., and Nauta, P. (1985), "Non-orthogonal cracks in a smeared finite element model", Eng. Comput., 2, 35-46. https://doi.org/10.1108/eb023599
  7. Dvorkin, E.N., and Assanelli, A.P. (1991), "2D finite elements with displacement interpolated embedded localization lines: the analysis of fracture in frictional materials", Comput. Meth. in Appl. Mech. and Eng., 90, 829-844. https://doi.org/10.1016/0045-7825(91)90186-A
  8. Horii, H. (1993), "Micromechanics and localization in concrete and rock", Fracture and Damage of Concrete and Rock - FDCR-2, Rossmanith, H. P., eds., E & FN Spon, 54-65.
  9. Kitsutaka, Y., and Mihashi, H. (1998), Quantitative Evaluation Methods for Toughness and Softening Properties of Concrete, FRAMCOS-3 Pre-Conference Workshop, Gifu, Japan, Oct. 11-12.
  10. Lofti, H.R., and Shing, P.B. (1995), "Embedded representation of fracture in concrete with mixed finite elements", Int. J. Numer. Meth. Eng., 38, 1307-1325. https://doi.org/10.1002/nme.1620380805
  11. Malvern, L.E. (1969), Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, New Jersey, 242- 243.
  12. Matsuoka, S., Masuda, A., Takeda, Y., and Doi, S. (1999), "Analytical model for concrete structures influenced by crack initiation and propagation", J. of Mater. Concrete Struct., Pavements, JSCE, 620, 1-13 (In Japanese).
  13. Ohlsson, U., and Elfgren, L. (1991), "Anchor bolts in concrete structures: Two-dimensional modeling", Analysis of Concrete Structures by Fracture Mechanics, Proc. of the RILEM, Elfgren, L., and Shah, S. P., eds., Chapman and Hall, London, 281-301.
  14. Okamura, H., and Maekawa, K. (1991), Nonlinear Analysis and Constitutive Models of Reinforced Concrete, Gihodo-Shuppan Co., Tokyo.
  15. Ngo, D., and Scordelis, A.C. (1967), "Finite element analysis of reinforced concrete beams", J. American Concrete Inst., 64(3), 152-163.
  16. Rashid, Y.R. (1968), "Analysis of prestressed concrete pressure vessels", Nucl. Eng. Design, 6, 334-344.
  17. Reinhardt, H.W. (1984), "Fracture mechanics of an elastic softening material like concrete", Heron, Delft, 29(2), 159-170.
  18. Uchida, Y., Rokuko, K., and Koyanagi, W. (1993), "Cracking behavior of concrete under mixed mode loading", Proc. of 48th Annual Conference of JSCE, 342, 710-711 (In Japanese).
  19. Wan, R.G. (1990), "Finite element simulation of shear band development in geological media", Ph.D. Dissertation, University of Alberta, Canada.
  20. Wan, R.G., Chan, D.H., and Morgenstern, N.R. (1990), "A Finite element method for the analysis of shear bands in geomaterials", Finite Elements in Analysis and Design, Elsevier, 7, 129-143. https://doi.org/10.1016/0168-874X(90)90005-Y
  21. Wu, Z., Machida, A., and Gao, D. (1998), "Development of mixed finite element method for composite discontinuous analysis", J. of Mater. Concrete Struct., Pavements, JSCE, 598, 149-159.