Computers and Concrete

  • 제5권4호
  • /
  • Pages.417-434
  • /
  • 2008
  • /
  • 1598-8198(pISSN)
  • /
  • 1598-818X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Anisotropic damage modelling of biaxial behaviour and rupture of concrete structures

  • Ragueneau, F. (LMT-Cachan (ENS Cachan/CNRS/Universite Paris 6/UniverSud Paris)) ;
  • Desmorat, R. (LMT-Cachan (ENS Cachan/CNRS/Universite Paris 6/UniverSud Paris)) ;
  • Gatuingt, F. (LMT-Cachan (ENS Cachan/CNRS/Universite Paris 6/UniverSud Paris))
  • 투고 : 2007.11.01
  • 심사 : 2008.04.01
  • 발행 : 2008.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper deals with damage induced anisotropy modeling for concrete-like materials. A thermodynamics based constitutive relationship is presented coupling anisotropic damage and elasticity, the main idea of the model being that damage anisotropy is responsible for the dissymmetry tension/compression. A strain written damage criterion is considered (Mazars criterion extended to anisotropy in the initial model). The biaxial behavior of a family of anisotropic damage model is analyzed through the effects of yield surface modifications by the introduction of new equivalent strains.

키워드

참고문헌

  1. Badel, P, Godard, V. and Leblond, J.-B. (2007), "Application of some anisotropic damage model to the prediction of the failure of some complex industrial concrete structures", Solids Struct., 44, 5848-5874. https://doi.org/10.1016/j.ijsolstr.2007.02.001
  2. Badel, P. B. (2001), "Contributions a la simulation mecanique de structures en beton arme", These de doctorat de l'universite Pierre et Marie Curie.
  3. Bazant, Z. P. (1976), "Instability, ductility and size effect in strain-softening concrete", J. Eng. Mech., ASCE, 114(12), 2013-2034.
  4. Bazant, Z. P., Prat, P. C. (1988), "Microplane model for brittle plastic material: I. Theory", J. Eng. Mech. ASCE, 114, pp. 1672-1688. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:10(1672)
  5. Bazant, Z. P., Carol, I. and Adley, M., Akers. (2000), "Microplane model M4 for concrete: I formulation with work-conjugate deviatoric stress", J. Eng. Mech., ASCE, 126, 944-54. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:9(944)
  6. Belytschko, T. and Black, T. (1999), "Elastic crack growth in fininite 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
  7. Carol, I., Prat, P. C. and Bazant, Z. P. (1992), "New explicit microplane model for concrete: theoretical aspects and numerical implementation", Int. J. Solids Struct., 29(9), 1173-91. https://doi.org/10.1016/0020-7683(92)90141-F
  8. Carol, I., Rizzi, E. and Willam, K. (2001), "On the formulation of anisotropic elastic degradation. Part I: Theory based on a pseudo-logarithmic damage tensor rate. Part II: Generalized pseudo-Rankine model for tensile damage", Int. J. Solids Struct., 38(4), 491-518, 519-546. https://doi.org/10.1016/S0020-7683(00)00030-5
  9. Chaboche, J. L. (1979), "Le concept de contrainte effective applique a l'elasticite et a la viscoplasticite en presence d'un endommagement anisotrope", Col. Euromech 115, Eds du CNRS 1982, Grenoble.
  10. Chow, C. L. and Wang, J. (1987), "An anisotropic theory for continuum damage mechanics", Int. J. Fract., 33, 3-16. https://doi.org/10.1007/BF00034895
  11. Cordebois, J. P. and Sidoroff, J. (1982), "Endommagement anisotrope en elasticite et plasticite", J. M. T. A., Numero special : 45-60.
  12. de Vree, J., Brekelmans, W. and van Gils, M. (1995), "Comparison of nonlocal approaches in continuum damage mechanics", Comput. Struct. 55, 581-588. https://doi.org/10.1016/0045-7949(94)00501-S
  13. Desmorat, R. (2006), "Positivite de la dissipation intrinseque d'une classe de modeles d'endommagement anisotropes non standards", Comptes-Rendus Mecanique, 334(10), pp. 587-592. https://doi.org/10.1016/j.crme.2006.07.015
  14. Desmorat, R., Gatuingt, F. and Ragueneau, F. (2007), "Nonlocal anisotropic damage model and related computational aspects for quasi-brittle materials", Eng. Fract. Mech., 60, 1539-1560.
  15. Halm, D. and Dragon, A. (1998), "An anisotropic model of damage and frictional sliding for brittle materials", European J. Mech., A/Solids, 17, pp. 439-460. https://doi.org/10.1016/S0997-7538(98)80054-5
  16. Drucker, D. C. and Prager, W. (1952), "Soils mechanics and plastic analysis or limit design", Quartely of Appl. Math., 10, pp. 157-175.
  17. Feenstra, P. H. (1993), "Computational aspects of biaxial sress in plain and reinforced concrete", Doct Dissertation, Delft University of Technology, The Netherlands.
  18. Fichant, S., Laborderie, C. and Pijaudier-Cabot, G. (1999), "Isotropic and anisotropic descriptions of damage in concrete structures", Int. J. Mech. Cohesive Frictional Mater., 4, pp. 339-359. https://doi.org/10.1002/(SICI)1099-1484(199907)4:4<339::AID-CFM65>3.0.CO;2-J
  19. Gatuingt, F. and Pijaudier-Cabot, G. (2002), "Coupled damage and plasticity modelling in transient dynamic analysis of concrete", Int J. Numer. Anal. Meth. Geomech., 26, 1-24. https://doi.org/10.1002/nag.188
  20. Geers, M., de Borst, R. and Peerlings, F. H. J. (2000), "Damage and crack modelling in single-edge and doubleedge notched concrete beams", Eng. Fract. Mech. 65, 247-261. https://doi.org/10.1016/S0013-7944(99)00118-6
  21. Govindjee, S., Kay, G. J. and Simo, J. C. (1995), "Anisotropic modelling and numerical simulations of brittle damage in concrete". Int. J. Numer. Meth. Eng., 38, 3611-33. https://doi.org/10.1002/nme.1620382105
  22. Hermann, G. and Kestin, J. (1988), "On thermodynamic foundations of a damage theory in elastic solids", Proc. CNRS-NSF Workshop on Strain Localisation and Size Effect due to Damage and Cracking, ed. J. Mazars and Z. P. Bazant, Elsevier Pub., pp. 228-232.
  23. Hillerborg, A., Modeer, M. and Peterssonn, P. E. (1976), "Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements", Cement Concrete Res., 6, pp. 773-782. https://doi.org/10.1016/0008-8846(76)90007-7
  24. Jason, L., Huerta, A., Pijaudier-Cabot, G. and Ghavamian, S. H. (2006), "An elastic plastic damage formulation for concrete: Application to elementary tests and comparison with isotropic damage model", Comput. Methods Appl. Mech. Eng., to appear.
  25. Jirasek, M. (2000), "Comparative study on elements with embedded discontinuities", Comput. Methods Appl. Mech. Eng., 188, 307-330. https://doi.org/10.1016/S0045-7825(99)00154-1
  26. Ju, J. W. (1989), "On energy-based coupled elastoplastic damage theories: constitutive modelling and computational aspects", Int. J. Solids. Struct. 1989, 25(7), 803-33. https://doi.org/10.1016/0020-7683(89)90015-2
  27. Krajcinovic, D. (1985), "Continuous damage mechanics revisited: basic concepts and definitions", J. Appl. Mech., 52, pp. 829-834. https://doi.org/10.1115/1.3169154
  28. Kupfer, H. B. and Gerstle, K. H. (1973), "Behaviour of concrete under biaxial stresses", J. Eng. Mech., 99, 853-856.
  29. Laborderie, C., Berthaud, Y. and Pijaudier-Cabot, G. (1990), "Crack closure effect in continuum damage mechanics: numerical implementation", Proc. 2nd Int. Conf. on 'Computer aided analysis and design of concrete structures, Zell am See, Austria, 4-6 april, pp. 975-986.
  30. Ladeveze, P. (1983), "On an anisotropic damage theory", Proc. CNRS Int. Coll. 351 Villars-de-Lans, Failure criteria of structured media, Edited by J. P. Boehler, pp. 355-363.
  31. Leckie, F. A. and Onat, E. T. (1981), "Tensorial nature of damage measuring internal variables", J. Hult and J. Lemaitre eds, Springer Berlin, 1981, Ch. Physical Non-Linearities in Structural Analysis, pp. 140-155.
  32. Lemaitre, J., Desmorat, R. and Sauzay, M. (2000), "Anisotropic damage law of evolution", European J. Mech., A/Solids, 19, 187-208. https://doi.org/10.1016/S0997-7538(00)00161-3
  33. Lemaitre, J. and Desmorat, R. (2005), Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures, Springer.
  34. Lemaitre, J. (1992), A Course on Damage Mechanics, Springer-Verlag.
  35. Lubarda, V. A, Mastilovic, S. and Knap, J. (1996), "Brittle-Ductile transition in porous rock by Cap model", J Eng. Mech. ASCE; 122.
  36. Marigo, J. (1981), "Formulation d'une loi d'endommagement d'un materiau elastique", C. R. Acad. Sci. Paris, serie IIb 292, 1309-1312.
  37. Mazars, J. (1984), "Application de la mecanique de l'endommagement au comportement non lineaire et a la rupture du beton de structure", These d'etat Universite Paris 6.
  38. Meschke, G., Lackner, R. and Mang H. A. (1998), "An anisotropic elastoplastic-damage model for plain concrete", Int. J. Numer. Meth. Eng., 42, 703-27. https://doi.org/10.1002/(SICI)1097-0207(19980630)42:4<703::AID-NME384>3.0.CO;2-B
  39. Murakami, S. and Ohno, N. (1978), "A constitutive equation of creep damage in pollicristalline metals", in: IUTAM Colloquium Euromech 111, Marienbad.
  40. Nooru-Mohamed, M. (1992), "Mixed-mode fracture of concrete: An experimental approach", Ph.D. thesis, Delft University of Technology, The Netherlands.
  41. Ortiz, M. (1985), "A constitutive theory for the inelastic behavior of concrete", Mech. Mater., 4, 67-93. https://doi.org/10.1016/0167-6636(85)90007-9
  42. Papa, E. and Taliercio, A. (1996), "Anisotropic damage model for the multi-axial static and fatigue behaviour of plain concrete", Eng. Fract. Mech., 55(2), pp. 163-179. https://doi.org/10.1016/0013-7944(96)00004-5
  43. Peerlings, R. H. J. (1996), "Continuum damage modelling of fatigue crack initiation", Internal report MT 97.037, Faculty of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.
  44. Pijaudier-Cabot, G. and Bazant, Z. P. (1987), "Nonlocal damage theory", J. Eng. Mech., ASCE, 113(10), pp. 1512-1533. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:10(1512)
  45. Ragueneau, F., Laborderie, Ch. and Mazars, J. (2000), "Damage model for concrete like materials coupling cracking and friction, contribution towards structural damping: first uniaxial application", Mech. Cohesive Frictional Mater., 5, 607-625. https://doi.org/10.1002/1099-1484(200011)5:8<607::AID-CFM108>3.0.CO;2-K
  46. Ramtani, S. (1990), "Contribution a la modelisation du comportement multiaxial du beton endommage avec description du caractere unilateral", PhD thesis Universite Paris 6.
  47. Ramtani, S. Berthaud, Y. and J. Mazars, J. (1992), "Orthotropic behavior of concrete with directional aspects: modelling and experiments", Nucl. Eng. Des., 133(1), February 1992, pp. 97-111. https://doi.org/10.1016/0029-5493(92)90094-C
  48. Simo, J. C. and Ju, J. W. (1987), "Strain and stress based continuum damage models-I formulation", Int. J. Solids. Struct., 23, 821-40. https://doi.org/10.1016/0020-7683(87)90083-7
  49. Van Mier, J. G. M. (1984), "Strain-softening of concrete under multiaxial loading conditions", Ph. Dissertation, Eindhoven University of Technology.
  50. Voyiadjis, G. Z. and Abu-Lebdeh, T. M. (1994), "Plasticity model for concrete using the bouding surface model", Int. J. Plasticity, 10, pp. 1-21. https://doi.org/10.1016/0749-6419(94)90051-5
  51. Willam, K. J. and Warnke, K. W. E. (1975), "Constitutive model for triaxial behaviour of concrete", Proc. Concrete Struc. Subjected to Triaxial Stresses, Int. Ass. for Bridge and Structural Engineering, Zurich, 1975, pp. 1-30.
  52. Willam, K., Pramono, E. and Sture, S. (1987), "Fundamental issues of smeared crack models", In: Shah, S.P., Swartz, S.E. (Eds.), SEMRILEM Int. Conf. on Fracture of Concrete and Rock, Bethel, Connecticut. Society of Engineering Mechanics, pp. 192-207.
  53. Yazdani, S. and Schreyer, L. (1990), "Combined plasticity and damage Mechanics model for plain concrete", J. Eng. Mech., 116(7), pp. 1435-1451. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:7(1435)

피인용 문헌

  1. From diffuse damage to strain localization from an Eikonal Non-Local (ENL) Continuum Damage model with evolving internal length vol.331, 2018, https://doi.org/10.1016/j.cma.2017.12.006
  2. Localization properties of Desmorat’s anisotropic damage model vol.174, 2016, https://doi.org/10.1016/j.compstruc.2015.08.011
  3. Delay-active damage versus non-local enhancement for anisotropic damage dynamics computations with alternated loading vol.77, pp.12, 2010, https://doi.org/10.1016/j.engfracmech.2010.04.006
  4. Micromechanics based framework with second-order damage tensors vol.69, 2018, https://doi.org/10.1016/j.euromechsol.2017.11.014
  5. High temperature damage model for carbon–carbon composites vol.30, pp.3, 2011, https://doi.org/10.1016/j.euromechsol.2010.12.014
  6. Anisotropic damage modeling of concrete materials vol.25, pp.6, 2016, https://doi.org/10.1177/1056789515606509
  7. A practical method to estimate crack openings in concrete structures 2010, https://doi.org/10.1002/nag.876
  8. Orthotropic damage coupled with localized crack reclosure processing. Part I: Constitutive laws vol.97, 2013, https://doi.org/10.1016/j.engfracmech.2012.10.012
  9. On the introduction of a mean stress in kinetic damage evolution laws for fatigue vol.77, 2015, https://doi.org/10.1016/j.ijfatigue.2015.03.006
  10. Influence of the aircraft crash induced local nonlinearities on the overall dynamic response of a RC structure through a parametric study vol.298, 2016, https://doi.org/10.1016/j.nucengdes.2015.12.032
  11. Effects of load histories on dynamic biaxial compressive damage behaviours of concrete vol.64, pp.5, 2012, https://doi.org/10.1680/macr.11.00054
  12. Development for twin shear damage constitutive model of concrete vol.19, pp.sup6, 2015, https://doi.org/10.1179/1432891715Z.0000000001447
  13. Experimental study of biaxial compressive damage behaviour of concrete at different strain rates vol.15, pp.sup1, 2011, https://doi.org/10.1179/143307511X12858957673914
  14. A thermodynamically consistent nonlocal damage model for concrete materials with unilateral effects vol.297, 2015, https://doi.org/10.1016/j.cma.2015.09.010
  15. A macroscopic gradient-enhanced damage model for deformation behavior of concrete under cyclic loadings vol.90, pp.5, 2020, https://doi.org/10.1007/s00419-020-01669-4