Computers and Concrete

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A computational setting of calcium leaching in concrete and its coupling with continuum damage mechanics

  • Nguyen, V.H. (Laboratoire d Analyse des Materiaux et Identification, Institut Navier) ;
  • Nedjar, B. (Laboratoire d Analyse des Materiaux et Identification, Institut Navier) ;
  • Torrenti, J.M. (IRSN/DIR/Pg)
  • Received : 2003.09.17
  • Accepted : 2004.03.23
  • Published : 2004.05.25
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Abstract

We present in this work a coupled phenomenological chemo-mechanical model that represents the degradation of concrete-like materials. The chemical behaviour is described by the nowadays well known simplified calcium leaching approach. And the mechanical damage behaviour is described by a continuum damage model which involves the gradient of the damage quantity. The coupled nonlinear problem at hand is addressed within the context of the finite element method. For the equation governing the calcium dissolution-diffusion part of the problem, special care is taken to treat the highly nonlinear calcium conductivity and solid calcium functions. The algorithmic design is based on a Newton-type iterative scheme where use is made of a recently proposed relaxed linearization procedure. And for the equation governing the damage part of the problem, an augmented Lagrangian formulation is used to take into account the damage irreversibility constraint. Finally, numerical simulations are compared with experimental results on cement paste.

Keywords

References

  1. Bangert, F., Kuhl, D. and Meschke, G. (2001), "Finite element simulation of chemo-mechanical damageunder cyclic loading conditions", Fracture Mechanics of Concrete and Structures, (R. de Borst, et al., eds.), Swets and Zeitlinger, Lisse, 145-152.
  2. Carde, C. (1996). "Caracterisation et modelisation de lalteration des proprietes mecaniques due a la lixiviation des materiaux cimentaires", Ph. D. thesis, INSA Toulouse.
  3. Carde, C., Francois, R. and Torrenti, J. M. (1996), "Leaching of both calcium hydroxyde and C-S-H from cement paste: modeling the mechanical behaviour", Cement Concrete Res., 28(6), 1257-1268.
  4. Coleman, B. D. and Gurtin, M. E. (1967), "Thermodynamics with internal variables", J. Chem. Phys. 47, 597-613. https://doi.org/10.1063/1.1711937
  5. Fleck, N. A. and Hutchinson, J. W. (1993), "A phenomenological theory for strain gradient effects in plasticity", J. Mech. Phys. Solids, 41 (12), 1825-1857. https://doi.org/10.1016/0022-5096(93)90072-N
  6. Fremond, M. and Nedjar, B. (1993), "Endommagement et principe des puissances virtuelles", C. R. Acad. Sci. Paris serie II 317, 857-864.
  7. Fremond, M. and Nedjar, B. (1996), "Damage, gradient of damage and principle of virtual power", Int. J. Solids Struct., 33 (8), 1083-1103. https://doi.org/10.1016/0020-7683(95)00074-7
  8. Gerard, B. (1996), "Contribution des couplages mecaniques-chimie-transfert dans la tenue a long terme des ouvrages de stockage de dechets radioactifs", Ph. D. thesis, ENS Cachan.
  9. Humbert, P. (1989), CESAR-LCPC, un code general de calcul par elements finis. Bull. Liais. Labo. des Ponts et Chaussees, 119, 112-116.
  10. Le Bellego, C., Gerard, B. and Pijaudier-Cabot, G. (2001), "Mechanical analysis of concrete structures submitted to an aggressive water", R. de Borst et al. (Ed.), Fracture Mechanics of Concrete Structures, 239-246. Swets and Zeitlinger, Lisse.
  11. Mainguy M., Tognazzi, C., Torrenti, J. M. and Adenot, F. (2000), "Modelling of leaching in pure cement paste and mortar", Cement Concrete Res., 30, 83-90. https://doi.org/10.1016/S0008-8846(99)00208-2
  12. Menzel, A. and Steinmann, P. (2000), "On the continuum formulation of gradient plasticity for single and polycrystals", J. Mech. Phys. Solids, 48, 1777-1796. https://doi.org/10.1016/S0022-5096(99)00024-1
  13. Muhlhaus, H. B. and Aifantis, E. C. (1991), "A variational principle for gradient plasticity", Int. J. Solids Struct. 28, 845-857. https://doi.org/10.1016/0020-7683(91)90004-Y
  14. Nedjar, B. (2001), "Elastoplastic-damage modelling including the gradient of damage: formulation and computational aspects", Int. J. Solids Struct., 38, 5421-5451. https://doi.org/10.1016/S0020-7683(00)00358-9
  15. Nedjar, B. (2002a), "A theoretical and computational setting for a geometrically nonlinear gradient damage modelling framework", Comput. Mech., 30, 65-80. https://doi.org/10.1007/s00466-002-0368-1
  16. Nedjar, B. (2002b), "An enthalpy-based finite element method for nonlinear heat problems involving phase change", Comput. Struct., 80, 921.
  17. Polizzoto, C. and Borino, G. (1998), "A thermodynamics-based formulation of gradient dependent plasticity", Eur. J. Mech., A/Solids, 17, 741-761. https://doi.org/10.1016/S0997-7538(98)80003-X
  18. Simo, J. C. and Laursen, T. A. (1992), "An augmented lagrangian treatment of contact problems involving friction", Comput. Struct., 42(1), 97-116. https://doi.org/10.1016/0045-7949(92)90540-G
  19. Tognazzi, C. (1998), "Couplage fissuration degradation chimique dans des materiaux cimentaire: caracterisation et modelisation", Ph. D. thesis, INSA Toulouse.
  20. Torrenti, J. M., Adenot, F., Tognazzi, C., Danese, S. and Poyet, S. (1998a), "Application du modele de degradation du beton au cas des milieux fissures et au couplage avec la mecanique", Concrete: from Material to Structure Proceedings of the International RILEM Conf. Arles.
  21. Torrenti, J. M., Didry, O., Ollivier, J. P. and Plas, F. (1999), La degradation des betons couplage fissurationdegradation chimique, Hermes.
  22. Torrenti, J. M., Mainguy, M., Adenot, F. and Tognazzi, C. (1998b), "Modelling of leaching in concrete", In R. de Borst, N. Bicanic, H. Mang, and G. Meschke (Eds.), Proc. Euro-C 98, Computational Modelling of Concrete Struct., 531-538. Balkema, Rotterdam, The Netherland.
  23. Ulm, F. J., Lemarchand, E. and Heukamp, F. H. (2002), "Elements of chemomechanics of leaching of cementbased materials at different scales", Eng. Frac. Mechanics in press.
  24. Ulm, F. J., Torrenti, J. M. and Adenot, F. (1999), "Chemoporoplasticity of calcium leaching in concrete", Eng. Mech., ASCE, 125(10), 1200-1211. https://doi.org/10.1061/(ASCE)0733-9399(1999)125:10(1200)

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