Switching mode of deformation in post-localization solutions with a quasi brittle material

[en] Localization in a quasi brittle material is studied using a local second gradient model. Since localization takes place in a medium assumed to be initially homogeneous, non uniqueness of the solutions of an initial boundary value problem is then also studied. Using enhanced models implies to generalize the classical localization analysis, especially it is necessary to study solutions more continuous (i.e., continuous up to the degree one) than the ones used in analysis involving classical constitutive equations. Within the assumptions done, it appears that localization is possible in the second gradient model if it is possible in the underlying classical model. Then the study of non uniqueness is conducted for the numerical problem, using different first guesses in the full Newton-Raphson procedure solving the incremental non linear equations. It turns out ¯nally that we are able thanks to this method to reproduce qualitatively the non reproducibility of usual experiment in the post peak regime.

Disciplines :

Civil engineering

Author, co-author :

Bésuelle, Pierre; Centre National de la Recherche Scientifique - CNRS > Laboratoire 3S-R

Chambon, René; Université Joseph Fourier > Laboratoire 3S-R

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

Language :

English

Title :

Switching mode of deformation in post-localization solutions with a quasi brittle material

Publication date :

2006

Journal title :

Journal of Mechanics of Material and Structures

ISSN :

1559-3959

Publisher :

Mathematical Sciences Publishers, Berkley, United States - California

Volume :

Issue :

Pages :

1115-1134

Peer reviewed :

Peer reviewed

Available on ORBi :

since 20 August 2008

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Bibliography

S. Al Holo, Etude numérique de la localisation à l'aide d'un modèle de second gradient: Perte d'unicité et évolution de la zone localisée, Ph.D. thesis, University of Grenoble, France, 2005.
P. Bésuelle, "Implémentation d'un nouveau type d'élément fini dans le code Lagamine pour une classe de lois à longueur interne", Internal report, FNRS (Belgium), 2005. 1-17.
P. Bésuelle and R. Chambon, "Modelling the post-localization regime with local second gradient models: non uniqueness of solutions and non persistent shear bands", pp. 209-221 in Modern trends in geomechanics, edited by W. Wu and H. S. Yu, Springer, Berlin, 2006.
P. Bésuelle and J. W. Rudnicki, "Localization: shear bands and compaction bands", pp. 219-321 in Mechanics of fluid-saturated rocks, edited by Y. Guéguen and M. Boutéca, International Geophysics Series 89, Elsevier, 2004.
R. I. Borja, "Bifurcation of elastoplastic solids to shear band mode at finite strain", Comput. Methods Appl. Mech. Eng. 191:46 (2002), 5287-5314.
R. de Borst, Non linear analysis of frictional materials, Ph.D. thesis, University of Delft, Netherlands, 1986.
N. Challamel and M. Hijaj, "Non-local behavior of plastic softening beams", Acta Mech. 178:3-4 (2005), 125-146.
R. Chambon and S. Al Holo, "The borehole stability problem revisited", 2006. in preparation.
R. Chambon and J. C. Moullet, "Uniqueness studies in boundary value problems involving some second gradient models", Comput. Methods Appl. Mech. Eng. 193:27-29 (2004), 2771-2796.
R. Chambon, D. Caillerie, and N. El Hassan, "One dimensional localisation studied with a second grade model", Eur J. Mech. A: Solids 17:4 (1998), 637-656.
R. Chambon, S. Crochepeyre, and J. Desrues, "Localization criteria for non-linear constitutive equations of geomaterials", Mech. Cohes. Frict. Mater. 5:1 (2000), 61-82.
R. Chambon, D. Caillerie, and T. Matsushima, "Plastic continuum with microstructure, local second gradient theories for geomaterials: localization studies", Int. J. Solids Struct. 38:46-47 (2001), 8503-8527.
R. Chambon, S. Crochepeyre, and R. Charlier, "An algorithm and a method to search bifurcation point in non linear problems", Int. J. Numer Methods Eng. 51:3 (2001), 315-332.
R. Chambon, D. Caillerie, and C. Tamagnini, "A strain space gradient plasticity theory for finite strain", Comput. Methods Appl. Mech. Eng. 193:27-29 (2004), 2797-2826.
R. Charlier, Approche unifiée de quelques problèmes non linéaires de mécanique des milieux continus par la méthode des éléments finis, Ph.D. thesis, University of Liège, Belgium, 1987.
F. Collin, R. Chambon, and R. Charlier, "A finite element method for poro mechanical modelling of geotechnical problems using local second gradient models", Int. J. Numer. Methods Eng. 65:11 (2006), 1749-1772.
E. Cosserat and F Cosserat, Théorie des corps déformables, Hermann, Paris, 1909.
J. Desrues, La localisation de la déformation dans les matériaux granulaires, Ph.D. thesis, University of Grenoble, France, 1984.
J. Desrues and W. Hammad, "Shear banding dependency on mean stress level in sand", pp. 57-68 in Proceedings of the 2nd International Workshop on Localisation and Bifurcation, edited by E. Dembicki et al., Techn. Univ. Gdansk, Poland, 1985.
J. Desrues and G. Viggiani, "Strain localization in sand: An overview of the experimental results obtained in Grenoble using stereophotogrammetry", Int. J. Numer. Anal. Methods Geomech. 28:4 (2004), 279-321.
N. El Hassan, Modélisation théorique et numérique de la localisation de la déformation dans les géomatériaux, Ph.D. thesis, University of Grenoble, France, 1997.
N. A. Fleck and J. W. Hutchinson, "Strain gradient plasticity", pp. 295-361 in Solid mechanics, edited by J. W. Hutchinson and T. Y. Wu, Advances in Applied Mechanics 33, Academic Press, San Diego, CA, 1997.
P. Germain, "La méthode des puissances virtuelles en mécanique des milieux continus, I: Théorie du second gradient", J. Mécanique 12:2 (1973), 235-274.
R. Hill, "A general theory of uniqueness and stability in elastic-plastic solids", J. Mech. Phys. Solids 6:3 (1958), 236-249.
W. Huang, M. Hijaj, and S. C. Sloan, "Bifurcation analysis for shear localization in non-polar and micropolar hypoplastic continua", J. Eng. Math. 52:1 (2005), 167-184.
K. Ikeda and K. Murota, Imperfect bifurcation in structures and materials, Springer, Berlin, 2002.
K. Ikeda, K. Murota, Y. Yamakawa, and E. Yanagisawa, "Modes switching and recursive bifurcation in granular materials", J. Mech. Phys. Solids 45:11-12 (1997), 1929-1953.
K. Ikeda, Y. Yamakawa, and S. Tsutumi, "Simulation and interpretation of diffuse mode bifurcation of elastoplastic solids", J. Mech. Phys. Solids 51:9 (2003), 1649-1673.
M. M. Iordache and K. Willam, "Localized failure analysis in elastoplastic Cosserat continua", Comput. Methods Appl. Mech. Eng. 151:3-4 (1998), 559-586.
T. Matsushima, R. Chambon, and D. Caillerie, "Large strain finite element analysis of a local second gradient model: application to localization", Int. J. Numer Methods Eng. 54:4 (2002), 499-521.
R. D. Mindlin, "Micro-structure in linear elasticity", Arch. Ration. Mech. An. 16:1 (1964), 51-78.
K. Nübel and W. Huang, "A study of localized deformation pattern in granular media", Comput. Methods Appl. Mech. Eng. 193:27-29 (2004), 2719-2743.
G. Pijaudier-Cabot and Z. Bažant, "Nonlocal damage theory", J. Eng. Mech. 113 (1987), 1512-1533.
J. R. Rice, "The localization of plastic deformation", pp. 207-220 in 14th International Congress on Theoretical and Applied Mechanics (Delft), edited by W. T. Koiter, North-Holland, Amsterdam, 1976.
J. W. Rudnicki and J. R. Rice, "Conditions for the localization of deformation in pressure-sensitive dilatant materials", J. Mech. Phys. Solids 23:6 (1975), 371-394.
P. Steinmann, R. Larsson, and K. Runesson, "On the localization properties of multiplicative hyperelasto-plastic continua with strong discontinuities", Int. J. Solids Struct. 34:8 (1997), 969-990.
C. Tamagnini, R. Chambon, and D. Caillerie, "A second gradient elastoplastic cohesive frictional model for geomaterials", C. R. Acad. Sci. IIB Mec. 329:10 (2001), 735-739.
R. A. Toupin, "Elastic materials with couple-stresses", Arch. Ration. Mech. An. 11:1 (1962), 385-414.
G. Viggiani, M. Küntz, and J. Desrues, "An experimental investigation of the relationships between grain size distribution and shear banding in sand", pp. 111-127 in Continuous and discontinuous modelling of cohesive-frictional materials, edited by P A. Vermeer et al., Springer, Berlin, 2001.