[en] The purpose of this paper is to determine, via a homogenization technique and in the framework of small strains, the macroscopic poroelastic properties of a saturated, deformable, cracked porous medium. The poroelastic matrix is assumed to be homogeneous and the cracks to be connected discontinuities, infilled with a poroelastic material. They are periodically distributed, with the size of the period being small compared to the size of the sample. The considered up-scaling method (based on asymptotic expansions) will provide two uncoupled mechanical and hydraulic problems describing the overall behavior of the material. The degradation of the mechanical properties due to damage is then introduced. Damage de- pends on cracks’ opening, thus making the problem non-linear. A numerical solution of the problem is provided using finite elements. Any stress-strain loading path can be reproduced. The numerical solution of an oedometric test and a biaxial test allows the exploration of the non-linear anisotropic behavior along with the bifurcation phenomenon.
Disciplines :
Materials science & engineering
Author, co-author :
Argilaga, Albert ; Université de Liège - ULiège > Département ArGEnCo > Géomécanique et géologie de l'ingénieur
Papachristos, Efthymios
Caillerie, Denis
Stefano, Dal Pont
Language :
English
Title :
Homogenization of a cracked saturated porous medium: Theoretical aspects and numerical implementation
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Bibliography
Arbogast, T., Douglas, J. Jr, Hornung, U., Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J. Math. Anal. 21:4 (1990), 823–836.
Auriault, J.-., Sanchez-Palencia, E., Etude du comportement macroscopique d'un milieu poreux saturé déformable. J. Mécanique 16:4 (1977), 575–603.
Auriault, J.-L., Heterogeneous medium. is an equivalent macroscopic description possible?. Int. J. Eng. Sci. 29:7 (1991), 785–795.
Auriault, J.-L., Transport in porous media: upscaling by multiscale asymptotic expansions. Applied Micromechanics of Porous Materials, 2005, Springer, 3–56.
Auriault, J.-L., Heterogeneous periodic and random media. are the equivalent macroscopic descriptions similar?. Int. J. Eng. Sci. 49:8 (2011), 806–808.
Bensoussan, A., Lions, J.-L., Papanicolaou, G., Asymptotic analysis for periodic structures. vol. 374, 2011, AMS Bookstore.
Bilbie, G., Dascalu, C., Chambon, R., Caillerie, D., Micro-fracture instabilities in granular solids. Acta Geotech. 3:1 (2008), 25–35.
Biot, M., General theory of three-dimensional consolidation. J. Appl. Phys. 12:2 (1941), 155–164.
Biot, M., Theory of elasticity and consolidation for a porous anisotropic solid. J. Appl. Phys. 26:2 (1955), 182–185.
Caillerie, D., Étude de la conduction stationnaire dans un domaine comportant une répartition périodique d'inclusions minces de grande conductivité. ESAIM: Math. Model. Numer. Anal.-Modélisation Math. Anal. Numérique 17:2 (1983), 137–159.
Caillerie, D., Thin and periodic plates. Math. Method Appl. Sci. 6 (1984), 159–191.
Caillerie, D., Homogenization of Periodic Media, Course, 2009, Grenoble INP - UJF - CNRS.
Chambon, R., Caillerie, D., Viggiani, G., Loss of uniqueness and bifurcation vs instability: Some remarks. Revue Française Génie Civil 8:5-6 (2004), 517–535.
Coussy, O., Poromechanics, 2004, Wiley.
Eshelby, J., The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. Ser. A. Math. Phys. Sci. 241:1226 (1957), 376–396.
Gray, W., Hassanizadeh, S., General conservation equations for multiphase systems: 1. averaging technique. Adv.Water.Res 2 (1979), 131–144.
Guo, N., Zhao, J., A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media. Int. J. Numer. Methods Eng. 99:11 (2014), 789–818.
Guo, N., Zhao, J., Multiscale insights into classical geomechanics problems. Int. J. Numer. Anal. Methods Geomech 40:3 (2015), 367–390.
Kanouté, P., Boso, D., Chaboche, J., Schrefler, B., Multiscale methods for composites: A review. Arch. Comput. Methods Eng. 16 (2009), 31–75.
Kouznetsova, V., Brekelmans, W., Baaijens, F., An approach to micro-macro modeling of heterogeneous materials. Comput. Mech. 27:1 (2001), 37–48.
Léné, F., Duvaut, G., Résultats d'isotropie pour des milieux homogénéisés. Comptes Rendus Ac.Sc. 293 (1981), 477–480.
Marinelli, F., Comportement couplé des géomatériaux: deus approches de módelisation numérique, 2013, Université Joseph Fourier, Grenoble Ph.D. thesis.
Miehe, C., Schröder, J., Schotte, J., Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials. Comput. Methods Appl. Mech. Eng. 171:3 (1999), 387–418.
Nguyen, T., Modélisation numérique à double échelle des matériaux granulaires cohésifs: Approche par éléments finis-éléments discrets, 2013, Université Joseph Fourier, Grenoble Ph.D. thesis.
Nguyen, T., Combe, G., Caillerie, D., Desrues, J., Fem x dem modelling of cohesive granular materials: numerical homogenisation and multi-scale simulation. Acta Geophys. 62:5 (2014), 1109–1126.
Nitka, M., Combe, G., Dascalu, C., Desrues, J., Two-scale modeling of granular materials: a dem-fem approach. Granul. Matter 13:3 (2011), 277–281.
Papanicolau, G., Bensoussan, A., Lions, J.-L., Asymptotic analysis for periodic structures. 1978, Elsevier.
Pensée, V., Kondo, D., Dormieux, L., Micromechanical analysis of anisotropic damage in brittle materials. J. Eng. Mech. 128:8 (2002), 889–897.
Pizzocolo, F., Huyghe, J., Ito, K., Mode i crack propagation in hydrogels is stepwise. Eng. Fract. Mech. 97 (2013), 72–79.
Rastiello, G., Boulay, C., Dal Pont, S., Tailhan, J., Rossi, P., Real-time water permeability evolution of a localized crack in concrete under loading. Cem.Conc.Res. 56 (2013), 20–28.
Sánchez-Palencia, E., Non-homogeneous media and vibration theory. Non-Homogeneous Media and Vibration Theory, vol. 127, 1980, Springer.
Smit, R., Brekelmans, W., Meijer, H., Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling. Comput. Methods Appl. Mech. Eng. 155:1 (1998), 181–192.
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