Đồng nhất hóa hệ thống phản ứng khuếch tán mô hình ăn mòn sulfat của bê tông trong các miền lỗ hổng định kỳ cục bộ

Hewlett PC (1998) Lea’s Chemistry of cement and concrete. Elsevier Butterworth-Heinemenn Linacre House, Oxford, pp 327–328 Beddoe RE, Dorner HW (2005) Modelling acid attack on concrete: part 1. The essential mechanisms. Cem Concr Res 35: 2333–2339 Beddoe RE (2009) Modelling the evolution of damage to concrete by acid attack. In: Franke L (eds) Simulation of time dependent degradation of porous materials: final report on priority program 1122. Cuvillier Verlag, Göttingen, pp 275–293 Song HW, Lim HJ, Saraswathy V, Kim TH (2007) A micro-mechanics based corrosion model for predicting the service life of reinforced concrete structures. Int J Electr Sci 2: 341–354 Müllauer W, Beddoe RE, Heinz D (2009) Sulfate attack on concrete-solution concentration and phase stability. In: Concrete in aggressive aqueous environments, performance, testing and modeling. Toulouse, France, pp 18–27 Marchand J, Samson E, Maltais Y, Lee RJ, Sahu S (2002) Predicting the performance of concrete structures exposed to chemically aggressive environment-field validation. Mater Struct 35: 623–631 Tixier R, Mobasher B, Asce M (2003) Modeling of damage in cement-based materials subjected to external sulfate attack. I: formulation. J Mater Civil Eng 15: 305–313 Taylor HFW (1990) Cement chemistry. Academic Press, London Böhm M, Jahani F, Devinny J, Rosen G (1998) A moving-boundary system modeling corrosion of sewer pipes. Appl Math Comput 92: 247–269 Jahani F, Devinny J, Mansfeld F, Rosen G, Sun Z, Wang C (2001) Investigations of sulfuric acid corrosion of the concrete, I: modeling and chemical observations. J Environ Eng 127(7): 572–579 Jahani F, Devinny J, Mansfeld F, Rosen G, Sun Z, Wang C (2001) Investigations of sulfuric acid corrosion of the concrete, II: electrochemical and visual observations. J Environ Eng 127(7): 580–584 Agreba-Driolett D, Diele F, Natalini R (2004) A mathematical model for the SO2 aggression to calcium carbonate stones: numerical approximation and asymptotic analysis. SIAM J Appl Math 64(5): 1636–1667 Auriault J-L (1991) Heterogeneous medium: is an equivalent macroscopic description possible?. Int J Eng Sci 29(7): 785–795 Bensoussan A, Lions JL, Papanicolau G (1978) Asymptotic analysis for periodic structures. North-Holland, Amsterdam Persson LE, Persson L, Svanstedt N, Wyller J (1993) The homogenization method. Chartwell Bratt, Lund Cioranescu D, Donato P (1999) An introduction to homogenization. Oxford University Press, New York van Duijn C, Mikelic A, Pop IS, Rosier C (2008) Effective dispersion equations for reactive flows with dominant Peclet and Damköhler numbers. In: Marin GB, West D, Yablonsky GS (eds) Mathematics in chemical kinetics and engineering. Academic Press, New York, pp 1–45 Chechkin GA, Chechkina TP (2004) On homogenization of problems in domains of the “infusorium” type. J Math Sci 120(3): 386–407 Hornung U, Jäger W (1991) Diffusion, convection, adsorption, and reaction of chemicals in porous media. J Diff Equ 92: 199–225 Marciniak-Czochra A, Ptashnyk M (2008) Derivation of a macroscopic receptor-based model using homogenization techniques. SIAM J Math Anal 40(1): 215–237 Mascarenhas ML (1995) Homogenization problems in locally periodic perforrated domains. In: Procedings of the international conference in asymptotic methods for elastic structures, Berlin, pp 141–149 Belyaev AG, Pyatnitskii AL, Chechkin GA (1998) Asymptotic behaviour of a solution to a boundary value problem in a perforated domain with oscillating boundary. Siber Math J 39(4): 621–644 Chechkin G, Pianitskii AL (1999) Homogenization of boundary-value problem in a locally periodic perforated domain. Appl Anal 71(1): 215–235 Chechkin GA, Piatnitskii AL, Shamaev AS (2007) Homogenization. Methods and applications, vol 234 of translations of mathematical monographs. AMS, Providence Eck C (2004) Homogenization of a phase field model for binary mixtures. Multiscale Model Simul 3(1): 1–27 Meier SA (2008) Two-scale models for reactive transport and evolving microstructure. PhD thesis, University of Bremen, Germany Meier SA, Muntean A (2009) A two-scale reaction-diffusion system with micro-cell reaction concentrated on a free boundary. Comp Rendus Mécan 336(6): 481–486 Meier SA, Peter MA, Muntean A, Böhm M, Kropp J (2007) A two-scale approach to concrete carbonation. In: Proceedings of the first international RILEM workshop on integral service life modeling of concrete structures, Guimaraes, Portugal, pp 3–10 Hornung U, Jäger W, Mikelic A (1994) Reactive transport through an array of cells with semi-permeable membranes. RAIRO Model Math Anal Numer 28(1): 59–94 van Noorden T (2009) Crystal precipitation and dissolution in a porous medium: effective equations and numerical experiments. Multiscale Model Simul 7(3): 1220–1236 Fatima T, Muntean A (2010) Well-posedness and two-scale convergence for a pore model describing sulfate corrosion (in preparation)