Comptes Rendus
no. 3
Some micromechanical aspects of failure in granular materials based on second-order work
François Nicot1 ; Nejib Hadda1; Luc Sibille2; Farhang Radjai3; Pierre-Yves Hicher4; Félix Darve5
1 Irstea, domaine universitaire, 2, rue de la Papeterie, 38400 Saint-Martin-d'Hères cedex, France
2 Institut de recherche en génie civil et mécanique, Université de Nantes, ECN-CNRS, Nantes, France
3 Laboratoire de mécanique et de génie civil, Université de Montpellier, Montpellier, France
4 Institut de recherche en génie civil et mécanique, École centrale de Nantes, Nantes, France
5 UJF-INPG-CNRS, Laboratoire Sols Solides Structures Risques, Grenoble, France
Comptes Rendus. Mécanique, Volume 342 (2014) no. 3, pp. 174-188.

This paper discusses the notion of failure in a granular assembly by examining the key microstructural mechanisms which are most likely to trigger the nucleation and propagation of instabilities within a granular material. For this purpose, the key variable to predict the occurrence of failure, known as second-order work, is expressed from variables on the grain scale. The local behaviour incidents (where contacts may open or slide), compared to the global response of the assembly, are analysed by two approaches. First, numerical computations made by a discrete element model confirm the microscopic definition of the second-order work. Secondly, a micromechanical model, based on a homogenization procedure, relating the macroscopic behaviour to microscopic ingredients, namely contact planes, points to a close link between the occurrence of failure on the macroscopic scale as well as on the contact planes.

Published online:
DOI: 10.1016/j.crme.2014.01.006
Mots clés : Stress, Large deformations, Second-order work, Granular materials, Homogenization, Multiscale, Micromechanics, Microstructure

François Nicot 1; Nejib Hadda 1; Luc Sibille 2; Farhang Radjai 3; Pierre-Yves Hicher 4; Félix Darve 5

1 Irstea, domaine universitaire, 2, rue de la Papeterie, 38400 Saint-Martin-d'Hères cedex, France
2 Institut de recherche en génie civil et mécanique, Université de Nantes, ECN-CNRS, Nantes, France
3 Laboratoire de mécanique et de génie civil, Université de Montpellier, Montpellier, France
4 Institut de recherche en génie civil et mécanique, École centrale de Nantes, Nantes, France
5 UJF-INPG-CNRS, Laboratoire Sols Solides Structures Risques, Grenoble, France 
@article{CRMECA_2014__342_3_174_0,
     author = {Fran\c{c}ois Nicot and Nejib Hadda and Luc Sibille and Farhang Radjai and Pierre-Yves Hicher and F\'elix Darve},
     title = {Some micromechanical aspects of failure in granular materials based on second-order work},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {174--188},
     publisher = {Elsevier},
     volume = {342},
     number = {3},
     year = {2014},
     doi = {10.1016/j.crme.2014.01.006},
     language = {en},
}
TY  - JOUR
AU  - François Nicot
AU  - Nejib Hadda
AU  - Luc Sibille
AU  - Farhang Radjai
AU  - Pierre-Yves Hicher
AU  - Félix Darve
TI  - Some micromechanical aspects of failure in granular materials based on second-order work
JO  - Comptes Rendus. Mécanique
PY  - 2014
SP  - 174
EP  - 188
VL  - 342
IS  - 3
PB  - Elsevier
DO  - 10.1016/j.crme.2014.01.006
LA  - en
ID  - CRMECA_2014__342_3_174_0
ER  - 
%0 Journal Article
%A François Nicot
%A Nejib Hadda
%A Luc Sibille
%A Farhang Radjai
%A Pierre-Yves Hicher
%A Félix Darve
%T Some micromechanical aspects of failure in granular materials based on second-order work
%J Comptes Rendus. Mécanique
%D 2014
%P 174-188
%V 342
%N 3
%I Elsevier
%R 10.1016/j.crme.2014.01.006
%G en
%F CRMECA_2014__342_3_174_0
François Nicot; Nejib Hadda; Luc Sibille; Farhang Radjai; Pierre-Yves Hicher; Félix Darve. Some micromechanical aspects of failure in granular materials based on second-order work. Comptes Rendus. Mécanique, Volume 342 (2014) no. 3, pp. 174-188. doi : 10.1016/j.crme.2014.01.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.01.006/

[1] R. Hill A general theory of uniqueness and stability in elastic–plastic solids, J. Mech. Phys. Solids, Volume 6 (1958), pp. 236-249

[2] P.V. Lade Static instability and liquefaction of loose fine sandy slopes, J. Geotech. Eng., Volume 118 (1992), pp. 51-71

[3] M.R. Kuhn; S.C. Chang Stability, bifurcation, and softening in discrete systems: a conceptual approach for granular materials, Int. J. Solids Struct., Volume 43 (2006), pp. 6026-6051

[4] A. Tordesillas; M. Muthuswamy On the modeling of confined buckling of force chains, J. Mech. Phys. Solids, Volume 57 (2009) no. 4, pp. 706-727

[5] F. Nicot; L. Sibille; F. Darve Bifurcation in granular materials: an attempt at a unified framework, Int. J. Solids Struct., Volume 46 (2009), pp. 3938-3947

[6] F. Nicot; L. Sibille; F. Darve Failure as a bifurcation toward a dynamic regime, Int. J. Plast., Volume 29 (2012), pp. 136-154

[7] F. Nicot; F. Darve A micro-mechanical investigation of bifurcation in granular materials, Int. J. Solids Struct., Volume 44 (2007), pp. 6630-6652

[8] F. Nicot; N. Hadda; F. Bourrier; L. Sibille; R. Wan; F. Darve Inertia effects as a possible missing link between micro and macro second-order work in granular media, Int. J. Solids Struct., Volume 49 (2012), pp. 1252-1258

[9] F. Nicot; F. Darve Micro-mechanical investigation of material instability in granular assemblies, Int. J. Solids Struct., Volume 43 (2006), pp. 3569-3595

[10] R.G. Wan; M. Pinheiro; P.J. Guo Elastoplastic modelling of diffuse instability response of geomaterials, Int. J. Numer. Anal. Methods Geomech., Volume 35 (2010), pp. 140-160

[11] C. Chang; P.Y. Hicher; A. Daouadji Investigating instability in granular materials by means of a microstructural model, Eur. J. Environ. Civ. Eng., Volume 13 (2009) no. 2, pp. 167-186

[12] L. Sibille; F. Donzé; F. Nicot; B. Chareyre; F. Darve Bifurcation detection and catastrophic failure, Acta Geotech., Volume 3 (2008) no. 1, pp. 14-24

[13] L. Sibille; F. Nicot; F. Donzé; F. Darve Analysis of failure occurrence from direct simulations, Eur. J. Environ. Civ. Eng., Volume 13 (2009) no. 2, pp. 187-202

[14] F. Darve; L. Sibille; A. Daouadji; F. Nicot Bifurcations in granular media, macro- and micro-mechanics, C. R., Méc., Volume 335 (2007), pp. 496-515

[15] A. Daouadji; H. AlGali; F. Darve; A. Zeghloul Instability in granular materials: an experimental evidence of diffuse mode of failure for loose sands, J. Eng. Mech., Volume 136 (2010) no. 5, pp. 575-588

[16] F. Darve; G. Servant; F. Laouafa; H.D.V. Khoa Failure in geomaterials, continuous and discrete analyses, Comput. Methods Appl. Mech. Eng., Volume 193 (2004) no. 27–29, pp. 3057-3085

[17] L. Sibille; F. Nicot; F. Donze; F. Darve Material instability in granular assemblies from fundamentally different models, Int. J. Numer. Anal. Methods Geomech., Volume 31 (2007), pp. 457-481

[18] C. Chang; Z. Yin; P.Y. Hicher Micromechanical analysis for inter-particle and assembly instability of sand, J. Eng. Mech., Volume 137 (2011) no. 3, pp. 155-169

[19] A.E.H. Love A Treatise of Mathematical Theory of Elasticity, Cambridge University Press, Cambridge, 1927

[20] J. Weber Recherches concernant les contraintes intergranulaires dans les milieux pulvérulents, Bull. Liais. Ponts Chauss. (1966) no. 20, pp. 1-20

[21] J. Christofferson; M.M. Mehrabadi; S. Nemat-Nassar A micromechanical description on granular material behaviour, J. Appl. Mech., Volume 48 (1981), pp. 339-344

[22] M.M. Mehrabadi; M. Oda; S. Nemat-Nasser On statistical description of stress and fabric in granular materials, Int. J. Numer. Anal. Methods Geomech., Volume 6 (1982), pp. 95-108

[23] R. Hill The essential structure of constitutive laws for metal composites and polycrystals, J. Mech. Phys. Solids, Volume 15 (1967) no. 2, pp. 79-95

[24] V. Šmilauer; E. Catalano; B. Chareyre; S. Dorofeenko; J. Duriez; A. Gladky; J. Kozicki; C. Modenese; L. Scholtès; L. Sibille; J. Stránský; K. Thoeni Yade reference documentation. Yade documentation (V. Šmilauer, ed.), The Yade Project, 2010 http://yade-dem.org/doc/

[25] P.A. Cundall; O.D.L. Strack A discrete numerical model for granular assemblies, Geotechnique, Volume 29 (1979), pp. 47-65

[26] P.A. Cundall Distinct element models for rock and soil structure (E.T. Brown, ed.), Analytical and Computational Methods in Engineering Rock Mechanics, George Allen and Unwin, London, 1987, pp. 129-163

[27] G. Gudehus A comparison of some constitutive laws for soils under radially symmetric loading and unloading, Aachen (W. Wittke, ed.) (3rd Int. Conf. Numerical Methods in Geomechanics), Volume vol. 4, Balkema Publisher (1979), pp. 1309-1324

[28] F. Darve; F. Laouafa Instabilities in granular materials and application to landslides, Mech. Cohes.-Frict. Mater., Volume 5 (2000) no. 8, pp. 627-652

[29] K. Wallton The effective elastic moduli of a random packing of spheres, J. Mech. Phys. Solids, Volume 35 (1987), pp. 213-226

[30] C.S. Chang Micromechanical modeling of constructive relations for granular material (M. Satake; J.T. Jenkins, eds.), Micromechanics of Granular Materials, 1988, pp. 271-279

[31] C.S. Chang; S.S. Sundaram; A. Misra Initial moduli of particulate mass with frictional contacts, Int. J. Numer. Anal. Methods Geomech., Volume 13 (1989) no. 6, pp. 626-641

[32] F. Emeriault; B. Cambou Micromechanical modelling of anisotropic non-linear elasticity of granular medium, Int. J. Solids Struct., Volume 33 (1996) no. 18, pp. 2591-2607

[33] C.L. Liao; T.C. Chan; A.S.J. Suiker; C.S. Chang Pressure-dependent elastic moduli of granular assemblies, Int. J. Numer. Anal. Methods Geomech., Volume 24 (2000), pp. 265-279

[34] P.Y. Hicher; C.S. Chang Anisotropic non linear elastic model for particulate materials, J. Geotech. Geoenviron. Eng., Volume 132 (2006) no. 8, pp. 1052-1061

[35] J.T. Jenkins; O.D.L. Strack Mean-field inelastic behavior of random arrays of identical spheres, Mech. Mater., Volume 16 (1993), pp. 25-33

[36] S. Nemat-Nasser; J. Zhang Constitutive relations for cohesionless frictional granular material, Int. J. Plast., Volume 18 (2002), pp. 531-547

[37] F. Nicot; F. Darve A multi-scale approach to granular materials, Mech. Mater., Volume 37 (2005), pp. 980-1006

[38] C. Chang; P.-Y. Hicher An elastoplastic model for granular materials with microstructural consideration, Int. J. Solids Struct., Volume 42 (2005) no. 14, pp. 4258-4277

[39] C.L. Liao; T.P. Chang; D. Young; C.S. Chang Stress–strain relationship for granular materials bases on hypothesis of best fit, Int. J. Solids Struct., Volume 34 (1997) no. 31–32, pp. 4087-4100

[40] R.D. Mindlin Microstructure in linear elasticity, Arch. Ration. Mech. Anal., Volume 16 (1969), pp. 51-78

[41] J. Biarez; P.Y. Hicher Elementary Mechanics of Soil Behaviour, Balkema, The Netherlands, 1994 (208 pages)

[42] P.-Y. Hicher Elastic properties of soils, J. Geotech. Eng., Volume 122 (1996) no. 8, pp. 641-648

[43] P.-Y. Hicher Experimental behavior of granular materials (B. Cambou, ed.), Behavior of Granular Materials, Springer, Wien, New York, 1998, pp. 1-97

Cited by Sources:

Comments - Politique