Homogenisation of a chemical degradation mechanism inducing an evolving microstructure

Malte A. Peter

doi:10.1016/j.crme.2007.09.003

Homogenisation of a chemical degradation mechanism inducing an evolving microstructure
[Homogénéisation d'un mécanisme du effritement chimique impliquant une évolution de la micro-structure]

Présenté par : Évariste Sanchez-Palencia

Malte A. Peter ¹

¹ Centre for Industrial Mathematics, FB 3, University of Bremen, Postfach 330 440, 28334 Bremen, Germany

Comptes Rendus. Mécanique, Volume 335 (2007) no. 11, pp. 679-684.

Résumé
Abstract

On considère un problème de réaction et diffusion dans un milieu poreux, où la réaction cause une augmentation ou une réduction du volume de la matrix solide. Pour l'homogénéisation du système d'équations résultants on emploie la méthode d'homogénéisation dans des domaines avec évolution de la micro-structure. Les fonctions que décrivent l'évolution de la micro-structure sont reliées au processus de réaction et diffusion.

We consider a reaction–diffusion problem in a porous medium, where the reaction causes a local increase or decrease of volume of the solid matrix. For the homogenisation of the resulting system of equations, we employ the method of homogenisation in domains with evolving microstructure. The functions describing the evolution of the microstructure are related to the reaction–diffusion process.

Reçu le : 2007-08-31
Accepté le : 2007-09-12
Publié le : 2007-10-18

DOI : 10.1016/j.crme.2007.09.003

Keywords: Porous media, Homogenization, Multiscale approach, Reaction–diffusion, Concrete carbonation
Mot clés : Milieux poreux, Homogénéisation, Approche multiéchelle, Reaction et diffusion, Carbonatation du beton

Affiliations des auteurs :

Malte A. Peter ¹

¹ Centre for Industrial Mathematics, FB 3, University of Bremen, Postfach 330 440, 28334 Bremen, Germany

@article{CRMECA_2007__335_11_679_0,
     author = {Malte A. Peter},
     title = {Homogenisation of a chemical degradation mechanism inducing an evolving microstructure},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {679--684},
     publisher = {Elsevier},
     volume = {335},
     number = {11},
     year = {2007},
     doi = {10.1016/j.crme.2007.09.003},
     language = {en},
}

TY  - JOUR
AU  - Malte A. Peter
TI  - Homogenisation of a chemical degradation mechanism inducing an evolving microstructure
JO  - Comptes Rendus. Mécanique
PY  - 2007
SP  - 679
EP  - 684
VL  - 335
IS  - 11
PB  - Elsevier
DO  - 10.1016/j.crme.2007.09.003
LA  - en
ID  - CRMECA_2007__335_11_679_0
ER  -

%0 Journal Article
%A Malte A. Peter
%T Homogenisation of a chemical degradation mechanism inducing an evolving microstructure
%J Comptes Rendus. Mécanique
%D 2007
%P 679-684
%V 335
%N 11
%I Elsevier
%R 10.1016/j.crme.2007.09.003
%G en
%F CRMECA_2007__335_11_679_0

Malte A. Peter. Homogenisation of a chemical degradation mechanism inducing an evolving microstructure. Comptes Rendus. Mécanique, Volume 335 (2007) no. 11, pp. 679-684. doi : 10.1016/j.crme.2007.09.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.09.003/

Bibliographie
Cité par

[1] J. Kropp Relations between transport characteristics and durability, performance criteria for concrete durability, RILEM Report, Volume 12 (1995), pp. 97-137

[2] T.A. Bier, Karbonatisierung und Realkalisierung von Zementstein und Beton, PhD dissertation, University of Karlsruhe, 1988

[3] A. Muntean, A moving-boundary problem: modeling, analysis and simulation of concrete carbonation, PhD dissertation, University of Bremen, Germany, 2006. Also: Cuvillier Verlag, 2006

[4] S.A. Meier; M.A. Peter; M. Böhm A two-scale modelling approach to reaction–diffusion processes in porous materials, Comp. Mat. Sci., Volume 39 (2007), pp. 29-34

[5] S.A. Meier, M.A. Peter, A. Muntean, M. Böhm, J. Kropp, A two-scale approach to concrete carbonation, in: Proc. International RILEM Workshop on Integral Service Life Modelling of Concrete Structures, 5–6 November 2007, Guimarães, Portugal, in press

[6] M.A. Peter Homogenisation in domains with evolving microstructure, C. R. Mécanique, Volume 335 (2007) no. 7, pp. 357-362

[7] A. Bensoussan; J.L. Lions; G. Papanicolaou Asymptotic Analysis for Periodic Structures, North-Holland, 1978

[8] E. Sanchez-Palencia Non-Homogeneous Media and Vibration Theory, Springer, 1980

[9] M.A. Peter, Coupled reaction–diffusion systems and evolving microstructure: mathematical modelling and homogenisation, PhD dissertation, University of Bremen, Germany, 2006. Also: Logos Verlag Berlin, 2007

[10] M.A. Peter, M. Böhm, Scalings in homogenisation of reaction, diffusion and interfacial exchange in a two-phase medium, in: M. Fila, A. Handlovicova, K. Mikula, M. Medved, P. Quittner, D. Sevcovic (Eds.), Proc. Equadiff-11, Bratislava, SK, 2005, pp. 369–376

[11] D. Cioranescu; A. Damlamian; G. Griso Periodic unfolding and homogenization, C. R. Acad. Sci. Paris, Ser. I, Volume 335 (2002), pp. 99-104

[12] R.E. Showalter Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, American Mathematical Society, 1997

[13] G. Nguetseng A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., Volume 20 (1989) no. 3, pp. 608-629

[14] G. Allaire Homogenization and two-scale convergence, SIAM J. Math. Anal., Volume 23 (1992) no. 6, pp. 1482-1518

Cité par Sources :

Commentaires - Politique