Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A method of global-local analyses of structures involving local heterogeneities and propagating cracks

  • Kurumatani, Mao (Department of Urban and Civil Engineering, Ibaraki University) ;
  • Terada, Kenjiro (Department of Civil and Environmental Engineering, Tohoku University)
  • Received : 2010.04.29
  • Accepted : 2011.04.14
  • Published : 2011.05.25
⟨ Previous Next ⟩

Abstract

This paper presents the global-local finite cover method (GL-FCM) that is capable of analyzing structures involving local heterogeneities and propagating cracks. The suggested method is composed of two techniques. One of them is the FCM, which is one of the PU-based generalized finite element methods, for the analysis of local cohesive crack growth. The mechanical behavior evaluated in local heterogeneous structures by the FCM is transferred to the overall (global) structure by the so-called mortar method. The other is a method of mesh superposition for hierarchical modeling, which enables us to evaluate the average stiffness by the analysis of local heterogeneous structures not subjected to crack propagation. Several numerical experiments are conducted to validate the accuracy of the proposed method. The capability and applicability of the proposed method is demonstrated in an illustrative numerical example, in which we predict the mechanical deterioration of a reinforced concrete (RC) structure, whose local regions are subjected to propagating cracks induced by reinforcement corrosion.

Keywords

References

  1. Asferg, J.L., Poulsen, P.N. and Nielsen, L.O. (2007), "A direct XFEM formulation for modeling of cohesive crack growth in concrete", Comput. Concrete, 4(2), 83-100. https://doi.org/10.12989/cac.2007.4.2.083
  2. Bhargava, K. and Ghosh, A.K. (2003), "Analytical model of corrosion-induced cracking of concrete considering the stiffness of reinforcement", Struct. Eng. Mech., 16(6), 749-769. https://doi.org/10.12989/sem.2003.16.6.749
  3. Chen, D. and Mahadevan, S. (2008), "Chloride-induced reinforcement corrosion and concrete cracking simulation", Cement Concrete Compos., 30(3), 227-238. https://doi.org/10.1016/j.cemconcomp.2006.10.007
  4. Daux, C., Moës, N., Dolbow, J., Sukumar, N. and Belytschko, T. (2000), "Arbitrary branched and intersecting cracks with the extended finite element method", Int. J. Numer. Meth. Eng., 48(12), 1741-1760. https://doi.org/10.1002/1097-0207(20000830)48:12<1741::AID-NME956>3.0.CO;2-L
  5. Du, Y.G., Chan, A.H.C. and Clark, L.A. (2006), "Finite element analysis of the effects of radial expansion of corroded reinforcement", Comput. Struct., 84(13-14), 917-929. https://doi.org/10.1016/j.compstruc.2006.02.012
  6. Duarte, C.A., Hamzeh, O.N., Liszka, T.J. and Tworzydlo, W.W. (2001), "A generalized finite element method for the simulation of three-dimensional dynamic crack propagation", Comput. Meth. Appl. Mech. Eng., 190(15-17), 2227-2262. https://doi.org/10.1016/S0045-7825(00)00233-4
  7. Duarte, C.A. and Kim, D.J. (2008), "Analysis and applications of a generalized finite element method with global-local enrichment functions", Comput. Meth. Appl. Mech. Eng., 197(6-8), 487-504. https://doi.org/10.1016/j.cma.2007.08.017
  8. Dumstorff, P. and Meschke, G. (2007), "Crack propagation criteria in the framework of X-FEM-based structural analyses", Int. J. Numer. Anal. Meth. Geomech., 31(2), 239-259. https://doi.org/10.1002/nag.560
  9. Farid Uddin, A.K.M., Numata, K., Shimasaki, J., Shigeishi, M. and Ohtsu, M. (2004), "Mechanisms of crack propagation due to corrosion of reinforcement in concrete by AE-SiGMA and BEM", Construct. Build. Mater., 18(3), 181-188. https://doi.org/10.1016/j.conbuildmat.2003.10.007
  10. Fish, J. (1992), "The s-version of the finite element method", Comput. Struct., 43(3), 539-547. https://doi.org/10.1016/0045-7949(92)90287-A
  11. Gasser, T.C. and Holzapfel, G.A. (2005), "Modeling 3D crack propagation in unreinforced concrete using PUFEM", Comput. Meth. Appl. Mech. Eng., 194(25-26), 2859-2896. https://doi.org/10.1016/j.cma.2004.07.025
  12. Hansbo, A. and Hansbo, P. (2004), "A finite element method for the simulation of strong and weak discontinuities in solid mechanics", Comput. Meth. Appl. Mech. Eng., 193(33-35), 3523-3540. https://doi.org/10.1016/j.cma.2003.12.041
  13. Hillerborg, A., Modeer, A. and Petersson, P.E. (1976), "Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements", Cement Concrete Res., 6(6), 773-782. https://doi.org/10.1016/0008-8846(76)90007-7
  14. Kurumatani, M. and Terada, K. (2005), "Finite cover method with mortar elements for elastoplasticity problems", Comput. Mech., 36(1), 45-61. https://doi.org/10.1007/s00466-004-0641-6
  15. Kurumatani, M. and Terada, K. (2009), "Finite cover method with multi-cover-layers for the analysis of evolving discontinuities in heterogeneous media", Int. J. Numer. Meth. Eng., 79(1), 1-24. https://doi.org/10.1002/nme.2545
  16. Lee, S.H., Song, J.H., Yoon, Y.C., Zi, G. and Belytschko, T. (2004), "Combined extended and superimposed finite element method for cracks", Int. J. Numer. Meth. Eng., 59(8), 1119-1136. https://doi.org/10.1002/nme.908
  17. Loehnert, S. and Belytschko, T. (2007), "A multiscale projection method for macro/microcrack simulations", Int. J. Numer. Meth. Eng., 71(12), 1466-1482. https://doi.org/10.1002/nme.2001
  18. Maekawa, K., Ishida, T. and Kishi, T. (2003), "Multi-scale modeling of concrete performance - Integrated material and structural mechanics", J. Adv. Concrete Technol., 1(2), 91-126. https://doi.org/10.3151/jact.1.91
  19. Marsavina, L., Audenaert, K., De Schutter, G., Faur, N. and Marsavina, D. (2007), "Modeling of chloride diffusion in hetero-structured concretes by finite element method", Cement Concrete Compos., 29(7), 559-565. https://doi.org/10.1016/j.cemconcomp.2007.04.003
  20. Melenk, J.M. and Babuska, I. (1996), "The partition of unity finite element method: Basic theory and applications", Comput. Meth. Appl. Mech. Eng., 139(1-4), 289-314. https://doi.org/10.1016/S0045-7825(96)01087-0
  21. Mergheim, J., Kuhl, E. and Steinmann, P. (2005), "A finite element method for the computational modelling of cohesive cracks", Int. J. Numer. Meth. Eng., 63(2), 276-289. https://doi.org/10.1002/nme.1286
  22. Pivonkaa, P., Hellmichb, C. and Smith, D. (2004), "Microscopic effects on chloride diffusivity of cement pastes - a scale-transition analysis", Cement Concrete Res., 34(12), 2251-2260. https://doi.org/10.1016/j.cemconres.2004.04.010
  23. Strouboulis, T., Copps, K. and Babuska, I. (2001), "The generalized finite element method", Comput. Meth. Appl. Mech. Eng., 190(32-33), 4081-4193. https://doi.org/10.1016/S0045-7825(01)00188-8
  24. Suda, K., Misra, S. and Motohashi, K. (1993), "Corrosion products of reinforcing bars embedded in concrete", Corrosion Sci., 35(5-8), 1543-1549. https://doi.org/10.1016/0010-938X(93)90382-Q
  25. Terada, K., Asai, M. and Yamagishi, M. (2003), "Finite cover method for linear and nonlinear analyses of heterogeneous solids", Int. J. Numer. Meth. Eng., 58(9), 1321-1346. https://doi.org/10.1002/nme.820
  26. Wells, G.N. and Sluys, L.J. (2001), "A new method for modelling cohesive cracks using finite elements", Int. J. Numer. Meth. Eng., 50(12), 2667- 2682. https://doi.org/10.1002/nme.143
  27. Zhang, J. and Lounis, Z. (2006), "Sensitivity analysis of simplified diffusion-based corrosion initiation model of concrete structures exposed to chlorides", Cement Concrete Res., 36(7), 1312-1323. https://doi.org/10.1016/j.cemconres.2006.01.015
  28. Zhang, T. and Gjorv, O.E. (1996), "Diffusion behavior of chloride ions in concrete", Cement Concrete Res., 26(6), 907-917. https://doi.org/10.1016/0008-8846(96)00069-5
  29. Zuo, X.B., Sun, W., Yu, C. and Wan, X.R. (2010), "Modeling of ion diffusion coefficient in saturated concrete", Comput. Concrete, 7(5), 421-435. https://doi.org/10.12989/cac.2010.7.5.421