Numerical post failure methods in multiphysical problems

[en] Rupture in geomaterials is often preceded by a localization of the deformations within thin bands. The strain localization is thus an important process, which has been studied both experimentally and theoretically. This paper summaries main observations on localized phenomena and proposes theoretical and numerical tools to characterize localization processes. To deal with interactions occurring between the different phases of porous media, a regularization technique based on the second gradient model has been extended to multiphysic couplings.

Disciplines :

Civil engineering

Author, co-author :

Collin, Frédéric ; Université de Liège - ULiège > Département Argenco : Secteur GEO3 > Géomécanique et géologie de l'ingénieur

Levasseur, Séverine ; Université de Liège - ULiège > Département Argenco : Secteur GEO3 > Géomécanique et géologie de l'ingénieur

Chambon, René; Université Joseph Fourier - Grenoble 1 - UJF > Laboratoires 3S-R

Language :

English

Title :

Numerical post failure methods in multiphysical problems

Publication date :

2009

Journal title :

European Journal of Environmental and Civil Engineering

ISSN :

1964-8189

eISSN :

2116-7214

Publisher :

Lavoisier, France

Volume :

7-8

Pages :

983-1004

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]

Available on ORBi :

since 04 December 2009

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Bibliography

Aifantis, E. C., 1984. “On the microstructural origin of certain inelastic models”. Journal of Engineering Materials and Technology, ASME, 106:326–330.
Bazant, Z. P., Belytschko, T. B., and Chang, T. P., 1984. “Continuum model for strain softening”. Journal of Engineering Mechanics, ASCE, 110:1666–1692.
Chambon, R., 1986. “Bifurcation and shear band localization an approach for incrementally non linear constitutive equations”. Journal de mécanique théorique et Appliquée, 5 (n° 2):277–298.
Chambon, R., Caillerie, D., and El Hassan, N., 1998. “One-dimensional localisation studied with a second grade model”. Eur. J. Mech. A/Solids, 17 (n° 4):637–656.
Chambon, R., Caillerie, D., and Matsushima, T., 2001. “Plastic continuum with microstructure, local second gradient theories for geomaterials:Localization studies”. International Journal of Solids and Structures, 38:8503–8527.
Chambon, R., Crochepeyre, S., and Charlier, R., 2001. “An algorithm and a method to search bifurcation points in non-linear problems”. International Journal for Numerical Methods in Engineering, 51:315–332.
Chavant, C., and Fernandes, R., March 2005. “Evaluating the reliability of hydro-mechanical simulation:A benchmark of numerical techniques carried out by Research Group of MoMas”. In 2nd International Meeting Clays in Natural & Engineered Barriers for Radioactive Waste Confinement Tours, 14–18 March, 249–250.
Collin, F., Chambon, R., and Charlier, R., 2006. “A finite element method for poro mechanical modelling of geotechnical problems using local second gradient models”. International Journal for Numerical Methods in Engineering, 65 (n° 11):1749–1772.
Collin, F., Laloui, L., and Charlier, R., 2005. “Unified approach of coupled constitutive laws”. Revue européenne de génie civil ALERT Autumn School 2005, 9 (n° 5–6):713–724.
Cosserat, E., and Cosserat, F., 1909. Théorie des corps déformables Paris Hermann
Coussy, O., 1995. Mechanics of Porous Continua London, Wiley
Desrues, J., 1984. La localisation de la déformation dans les matériaux granulaires Thèse de doctorat ès Sciences, Institut de mécanique de Grenoble
Desrues, J., 2005. “Hydro-mechanical coupling and strain localization in saturated porous media”, ALERT Autumn School 2005. Revue européenne de génie civil, 9 (n° 5–6):619–634.
Desrues, J., Chambon, R., Mokni, M., and Mazerolles, F., 1996. “Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography”. Géotechnique, 46 (n° 7):529–546.
Desrues, J., and Viggiani, G., 2004. “Strain localization in sand:an overview of the experimental results obtaines in Grenoble using stereophotogrammetry”. International Journal for Numerical and Analytical Methods in Geomechanics, 28 (n° 4):279–321.
Ehlers, W., and Volk, W., 1998. “On theoretical and numerical methods in the theory of porous media based on polar and non-polar elasto-plastic solid materials”. International Journal of Solids and Structures, 35:4597–4617.
Fernandes, R., 2009. Modélisation numérique objective des problèmes hydromécaniques couplés dans le cas des géomatériaux Thèse de doctorat, UJF Grenoble
Finno, R., Harris, W., Mooney, M., and Viggiani, G., 1996. “Strain localization and undrained steady state of sands”. Journal of Geotechnical Engineering ASCE, 122 (n° 6):462–473.
Finno, R., Harris, W., Mooney, M., and Viggiani, G., 1997. “Shear bands in plane strain compression of loose sand”. Géotechnique, 47 (n° 1):149–165.
Germain, P., 1973. “The method of virtual power in continuum mechanics. Part 2 Microstructure”. SIAM J. Appl. Math., 25:556–575.
Hadamar, J., 1903. Leçon sur la propagation des ondes et les équations de lhydrodynamique Paris Hermann
Han, C., and Vardoulakis, I., 1991. “Plane-strain compression experiments on water-saturated finegrained sand”. Géotechnique, 47 (n° 1):49–78.
Hassanizadeh, M., and Gray, W., 1979. “General conservation equations for multi-phase systems:1. Average procedure”. Advances in Water Resources, 2:131–144.
Hassanizadeh, M., and Gray, W., 1979. “General conservation equations for multi-phase systems:2. Mass, momenta, energy and entropy equations”. Advances in Water Resources, 2:191–208.
Hill, R., 1958. “A general theory of uniqueness and stability in elastic-plastic solids”. J. of Mechanics and Physics of Solids, 5:236–249.
Khoa, H. D.V., Georgopoulos, I. O., Darve, F., and Laouafa, F., 2006. “Diffuse failure in geomaterials:Experiments and modelling”. Computers and Geotechnics, 33 (n° 1):1–14.
Kotronis, P., Al Holo, S., Bésuelle, P., and Chambon, R., 2008. “Shear softening and localization. Modelling the evolution of the shear zone”. Acta Geotechnica, 3 (n° 2):85–97.
Lenoir, N., Bornert, M., Desrues, J., Besuelle, P., and Viggiani, G., 2008. “Volumetric digital image correlation applied to X-ray micro tomography images from triaxial compression tests on argillaceous rock”. STRAIN, 3 (n° 2):193–205.
Lewis, R. W., and Schrefler, B. A., 2000. The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media New York Wiley
Loret, B., and Prevost, J., 1991. “Dynamic strain localization in fluid-saturated porous media”. Journal of Engineering Mechanics, 117 (n° 4):907–922.
Mandel, J., 1968. “Condition de stabilité et postulat de Drucker”. Proc. Of IUTAM Symposium on Rheology and Soil Mechanics,:58–67. Grenoble
Mindlin, R. D., 1964. “Micro-structure in linear elasticity”. Arch. Ration. Mech. Anal., 16:51–78.
Mokni, M., and Desrues, J., 1999. “Strain localisation measurements in undrained plane-strain biaxial test on Hostun RF sand”. Mechanics of Cohesive-Frictional Materials, 4:419–441.
Nuth, M., and Laloui, L., 2008. “Effective stress concept in unsaturated soils:Clarification and validation of a unified framework”. International Journal for Numerical and Analytical Methods in Geomechanics, 32 (n° 7):771–801.
Peerlings, R. H.J., De Borst, R., Brekelmans, W. A.M., and De Vree, J. H.P., 1987. “Gradient-enhanced damage for quasi-brittle materials”. International Journal for Numerical Methods in Engineering, 39:1512–1533.
Pijaudier-Cabot, G., and Bazant, Z. P., 1987. “Non-local damage theory”. Journal of Engineering Mechanics, ASCE, 39:1512–1533.
Rice, J., 1976. “Theoretical and Applied Mechanics”, chapter ”. In The Localization of Plastic Deformation North-Holland Publishing Company 207–220.
Roger, V., Desrues, J., and Viggiani, G., 1998. “Experiments on strain localization in dense sand under isochoric conditions”. In O.F.(ed.) Localization and Bifurcation Theory for Soils and Rocks 239–248. 4th Workshop on Localization and Bifurcation Theory for soils and Rocks, Gifu (Japan) 28 septembre 2 octobre 1997, Balkema
Rudnicki, J., and Rice, J., 1975. “Conditions for the localisation of deformation in pressure sensitive dilatant materials”. JMPS, 23:371–394.
Sieffert, Y., Al Holo, S., and Chambon, R., 2009. “Loss of uniqueness of solutions of the borehole problem modelled with enhanced media”. International Journal of Solids and Structures
Toupin, R., 1962. “Elastic materials with couplestresses”. Archive for Rational Mechanics and Analysis, 11:385–414.
Vardoulakis, I., 1996a. “Deformation of water-saturated sand:I. uniform undrained deformation and shear banding”. Géotechnique, 46 (n° 3):441–456.
Vardoulakis, I., 1996b. “Deformation of water-saturated sand:II. Effect of pore water flow and shear banding”. Géotechnique, 46 (n° 3):457–472.
Vardoulakis, I., Goldscheider, M., and Gudehus, Q., 1978. “Formation of shear bands in sand bodies as a bifurcation problem”. International Journal for Numerical and Analytical Methods in Geomechanics, 2:99–128.
Wang, X. C., 1993. Modélisation numérique des problèmes avec localisation des déformations en bandes de cisaillement Thèse de doctorat, Université de Liège
Zhang, C., and Schrefler, B. A., 2004. “Particular aspects of internal length scales in strain localization analysis of multiphase porous materials”. Computer Methods in Applied Mechanics and Engineering, 193:2867–2884.
Zhang, H. W., Sanavia, L., and Schrefler, B. A., 1999. “An internal length scale in dynamic strain localization of multiphase porous media”. Mechanics of Cohesive-Frictional Materials, 4 (n° 5):443–460.
Zhang, H. W., and Schrefler, B. A., 2001. “Uniqueness and localization analysis of elasto-plastic saturated porous media”. International Journal for Numerical and Analytical Methods in Geomechanics, 25 (n° 1):29–48.