DOI QR코드

DOI QR Code

Simulations of spacing of localized zones in reinforced concrete beams using elasto-plasticity and damage mechanics with non-local softening

  • Marzec, I. (Gdansk University of Technology Faculty of Civil and Environmental Engineering) ;
  • Bobinski, J. (Gdansk University of Technology Faculty of Civil and Environmental Engineering) ;
  • Tejchman, J (Gdansk University of Technology Faculty of Civil and Environmental Engineering)
  • 투고 : 2006.11.15
  • 심사 : 2007.09.07
  • 발행 : 2007.10.25

초록

The paper presents quasi-static plane strain FE-simulations of strain localization in reinforced concrete beams without stirrups. The material was modeled with two different isotropic continuum crack models: an elasto-plastic and a damage one. In case of elasto-plasticity, linear Drucker-Prager criterion with a non-associated flow rule was defined in the compressive regime and a Rankine criterion with an associated flow rule was adopted in the tensile regime. In the case of a damage model, the degradation of the material due to micro-cracking was described with a single scalar damage parameter. To ensure the mesh-independence and to capture size effects, both criteria were enhanced in a softening regime by nonlocal terms. Thus, a characteristic length of micro-structure was included. The effect of a characteristic length, reinforcement ratio, bond-slip stiffness, fracture energy and beam size on strain localization was investigated. The numerical results with reinforced concrete beams were quantitatively compared with corresponding laboratory tests by Walraven (1978).

키워드

참고문헌

  1. Abaqus, Theory Manual, (1998), Version 5.8, Hibbit, Karlsson & Sorensen Inc.
  2. Bazant, Z. P. and Bhat, P. D. (1976), "Endochronic theory of inelasticity and failure of concrete", J. Eng. Mech. Div. ASCE, 102, 701-722.
  3. Bazant, Z. P. and Cedolin, L. (1979), "Blunt crackband propagation in finite element analysis", J. Eng. Mech. Div. ASCE, 105, 2, 297-315.
  4. Bazant, Z. and Ozbolt, J. (1990), "Non-local microplane model for fracture, damage and size effect in structures", J. Eng. Mech. ASCE, 116, 2485-2505. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:11(2485)
  5. Bazant, Z. P. and Jirasek, M. (2002), "Nonlocal integral formulations of plasticity and damage: survey of progress", J. Eng. Mech. 128, 11, 1119-1149. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1119)
  6. Bobin'ski, J. and Tejchman, J. (2004), "Numerical simulations of localization of deformation in quasi-brittle materials within non-local softening plasticity", Comput. Concrete, 4, 433-455.
  7. Bobin' ski, J. and Tejchman, J. (2006), "Modelling of strain localization in quasi-brittle materials with a coupled elasto-plastic-damage model", Theoretical Appl. Mech., 44, 767-782.
  8. de Borst, R., Mühlhaus, H.-B, Pamin, J. and Sluys, L. (1992), "Computational modelling of localization of deformation", Proc. of the 3rd Int. Conf. Comp. Plasticity (eds.: D. R. J. Owen, H. Onate, E. Hinton), Swansea, Pineridge Press 483-508.
  9. Box, G. E. P. and Muller, M. E. (1958), "A note of the generation of random normal deviates", Annals. Math. Stat., 29, 610-611, 1958. https://doi.org/10.1214/aoms/1177706645
  10. Brinkgreve, R. B. (1994), "Geomaterial models and numerical analysis of softening", PhD thesis, Delft University of Technology, Delft.
  11. CEB-FIP Model Code 1990 for Concrete Structures (1991), 228, 1-205.
  12. Cusatis, G., Bazant, Z. P. and Cedolin, L. (2003), "Confinement-shear lattice model for concrete damage in tension and compression: I. Theory", J. Eng. Mech. ASCE, 1439-1448.
  13. D'Addetta, G. A., Kun, F. and Ramm, E. (2002), "In the application of a discrete model to the fracture process of cohesive granular materials", Granular Matter, 4, 77-90. https://doi.org/10.1007/s10035-002-0103-9
  14. Donze, F. V., Magnier, S. A., Daudeville, L., Mariotti, C. and Davenne, L. (1999), "Numerical study of compressive behaviour of concrete at high strain rates", J. Eng. Mech., 1154-1163.
  15. Dorr, K. (1980), "Ein Beitrag zur Berechnung von Stahlbetonscheiben unter besonderer Berücksichtigung des Verbundverhaltens", PhD thesis, Darmstadt University.
  16. Dragon, A. and Mroz, Z. (1979), "A continuum model for plastic-brittle behaviour of rock and concrete", Int. J. Eng. Sci., 17.
  17. Eurocode 2 (1991), "Design of Concrete Structures, part 1-1".
  18. Ferrara, I., di Prisco, M. (2001), "Mode I fracture behaviour in concrete: nonlocal damage modeling", ASCE J. Eng. Mech., 127(7), 678-692. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:7(678)
  19. Gatuingt, F., Desmorat, R. and Ragnueneau, F. (2006). "Finite element computation of rupture with induced anisotropic damage", Compu. Modelling of Concrete Structures, EURO-C 2006 (eds.: G. Meschke, R. de Borst, H. Mang and N. Bicanic), Taylor and Francis, 345-352.
  20. Geers, M., Peijs, T., Brekelmans, W. and de Borst, R. (1996), "Experimental monitoring of strain localization and failure behaviour of composite materials", Compos. Sci. Tech., 56, 1283-1290. https://doi.org/10.1016/S0266-3538(96)00088-7
  21. Groen, A. E. (1997), "Three-dimensional elasto-plastic analysis of soils", PhD Thesis, Delft University, 1-114.
  22. Hughes T. J. R. and Winget J. (1980), "Finite rotation effects in numerical integration of rate constitutive equations arising in large deformation analysis", Int. J. Numer. Methods Eng., 15, 1862-1867. https://doi.org/10.1002/nme.1620151210
  23. Jirasek, M. and Marfia, S. (2005), "Non-local damage model based on displacement averaging", Int. J. for Numer. Meths. Eng., 63, 77-102. https://doi.org/10.1002/nme.1262
  24. Kachanov, L. M. (1986), Introduction to Continuum Damage Mechanics, Dordrecht: Martimus Nijhoff.
  25. Kani, G. N. J. (1966), "Basic facts concerning shear failure", ACI-Journal Proceedings, 63, 675-692.
  26. Kozicki, J. and Tejchman, J. (2007a), "Effect of aggregate structure on fracture process in concrete using 2D lattice model", Archives of Mechanics, 2007 (in press).
  27. Kozicki, J. and Tejchman, J. (2007b), "Experimental investigations of strain localization in concrete using Digital Image Correlation (DIC) technique", Archives of Hydro-Engineering and Environmental Mechanics, 54, 1, pp.3-24.
  28. Le Bellego, C., Dube, J. F., Pijaudier-Cabot, G. and Gerard, B. (2003), "Calibration of nonlocal damage model from size effect tests", E. J. Mechanics A/Solids 22, 33-46. https://doi.org/10.1016/S0997-7538(02)01255-X
  29. Lemaitre, J. (1985), "Coupled elasto-plasticity and damage constitutive equations", Comput Methods Appl. Mech. Eng., 51, 31-49. https://doi.org/10.1016/0045-7825(85)90026-X
  30. Lorrain, M., Maurel, O. and Seffo, M. (1998), "Cracking behaviour of reinforced high-strength concrete tension ties", ACI Struct. J., 95(5), 626-635.
  31. Majewski, T., Bobin' ski, J. and Tejchman, J. (2007), "FE-analysis of failure behaviour of reinforced concrete columns under eccentric compression", Eng. Struct. (in press).
  32. Mahnken, R. and Kuhl, E. (1999), "Parameter identification of gradient enhanced damage models", Eur. J. Mech. A/Solids, 18, 819-835. https://doi.org/10.1016/S0997-7538(99)00127-8
  33. Malecki, T., Marzec, I., Bobin' ski, J. and Tejchman, J. (2007), "Effect of a characteristic length on crack spacing in a reinforced concrete bar under tension", Mech. Res. Com. (in press).
  34. Menetrey, P. and Willam, K. J. (1995), "Triaxial failure criterion for concrete and its generalization", ACI Struct. J., 311-318.
  35. Mühlhaus, H.-B. (1986), "Scherfugenanalyse bei granularen material im rahmen der cosserat-theorie", Ingenieur Archiv, 56, 389-399. https://doi.org/10.1007/BF02570619
  36. Needdleman, A. (1988), "Material rate dependence and mesh sensitivity in localization problems", Comput. Methods. Appl. Mech. Eng. 67, 69-85. https://doi.org/10.1016/0045-7825(88)90069-2
  37. Ortiz, M. and Simo, I. C. (1986), "An analysis of a new class of integration algorithms for elastoplastic constitutive relation", Int. I, Num. Methods Eng., 23, 353-366. https://doi.org/10.1002/nme.1620230303
  38. Palaniswamy, R. and Shah, S. P. (1974), "Fracture and stress-strain relationship of concrete under triaxial compression", J. Struct. Div. ASCE, 100, 901-916.
  39. Pamin, J. (1994), "Gradient-dependent plasticity in numerical simulation of localization phenomena", PhD Thesis, University of Delft.
  40. Pamin, J. and de Borst, R. (1998), "Simulation of crack spacing using a reinforced concrete model with an internal length parameter", Arch. App. Mech., 68(9), 613-625. https://doi.org/10.1007/s004190050191
  41. Peerlings, R. H. J., de Borst, R., Brekelmans, W. A. M. and Geers, M. G. D. (1998), "Gradient enhanced damage modelling of concrete fracture", Mech. Cohesion.-Friction. Materials, 3, 323-342. https://doi.org/10.1002/(SICI)1099-1484(1998100)3:4<323::AID-CFM51>3.0.CO;2-Z
  42. Pijaudier-Cabot, G. and Bazant, Z. P. (1987), "Nonlocal damage theory", ASCE, J. Eng. Mech., 113, 1512-1533. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:10(1512)
  43. Pietruszczak, D., Jiang, J. and Mirza, F. A. (1988), "An elastoplastic constitutive model for concrete", Int. J. Solids Structures, 24(7), 705-722. https://doi.org/10.1016/0020-7683(88)90018-2
  44. Salari, M. R., Saeb, S., Willam, K. J., Patchet, S. J. and Carrasco, R. C. (2004), "A coupled elastoplastic damage model for geomaterials", Comput. Methods Appl. Mech. Eng., 193, 2625-2643. https://doi.org/10.1016/j.cma.2003.11.013
  45. Simo, J. C. and Ju, J. W. (1987), "Strain- and stress-based continuum damage models - I. Formulation", Int. J. Solids Struct., 23(7), 821-840. https://doi.org/10.1016/0020-7683(87)90083-7
  46. Simone, A. and Sluys, L. (2004), "The use of displacement discontinuities in a rate-dependent medium", Comput Methods Appl. Mech. Eng., 193, 3015-3033. https://doi.org/10.1016/j.cma.2003.08.006
  47. Sluys, L. (1992), "Wave propagation, localisation and dispersion in softening solids", PhD Thesis, Delft University of Technology.
  48. Sluys, L. J. and de Borst, R. (1996), "Failure in plain and reinforced concrete - an analysis of crack width and crack spacing", Int. J. Solids Struct., 33, 20-22, 3257-3276. https://doi.org/10.1016/0020-7683(95)00258-8
  49. Stromberg, L. and Ristinmaa, M. (1996), "FE-formulation of nonlocal plasticity theory", Comput. Methods Appl. Mech. Eng. 136, 127-144. https://doi.org/10.1016/0045-7825(96)00997-8
  50. Tejchman, J. and Wu, W. (1993), "Numerical study on patterning of shear bands in a cosserat continuum", Acta Mechanica, 99, 61-74. https://doi.org/10.1007/BF01177235
  51. Tejchman, J.. Herle, I. and Wehr, J. (1999), "FE-studies on the influence of initial density, pressure level and mean grain diameter on shear localisation", Int. J. Num. Analytical Methods Geomech, 23(15), 2045-2074. https://doi.org/10.1002/(SICI)1096-9853(19991225)23:15<2045::AID-NAG48>3.0.CO;2-B
  52. Tejchman, J. and Gorski, J. (2007), "Deterministic and statistical size effect during shearing of granular layer within a micro-polar hypoplasticity", Int. J. Num. Anal. Methods Geomech. (in press).
  53. den Uijl, J. A. and Bigaj, A. (1996), "A bond model for ribbed bars based on concrete confinement", Heron 41, 201-226.
  54. Walraven, J. C. (1978), "The influence of depth on the shear strength of lightweight concrete beams without shear reinforcement", TU-Delft Report 5-78-4, Delft University.
  55. Walvaren, J. and Lehwalter, N. (1994), "Size effects in short beams loaded in shear", ACI Struct. J., 585-593.
  56. Wittmann, F. H., Mihashi, H. and Nomura, N. (1992), "Size effect on fracture energy using three-point bend tests", Mater. Struct., 25, 327-334. https://doi.org/10.1007/BF02472591
  57. Vervuurt, A., van Mier, J. G. M. and Schlangen, E. (1994), "Lattice model for analyzing steel-concrete interactions", Comp. Methods and Advances in Geomechanics (eds.: Siriwardane and Zaman), 713-718, Balkema, Rotterdam.
  58. van Vliet, M. R. A. and van Mier, J. G.. M. (1996), "Experimental investigation of concrete fracture under uniaxial compression", Mechanics of Cohesive-Frictional Materials, 1, 115-12.

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