Micromechanical Analysis of Second Order Work in Granular Media

  • F. NicotEmail author
  • N. Hadda
  • F. Bourrier
  • L. Sibille
  • A. Tordesillas
  • F. Darve
Conference paper
Part of the Springer Series in Geomechanics and Geoengineering book series (SSGG)


This paper examines the evolution of instabilities in granular materials from a microscopic point of view, using the discrete element method. The relationship between the unstable loading directions that result in negative values for the macroscopic expression of the second order work and the terms in the microscopic expression of the second order work was investigated. Good agreement was found between the microscopic and macroscopic expressions of the second order work for the two three-dimensional specimens studied, in both the elastic and plastic tensorial zones. The vanishing of the microscopic and macroscopic second order work is shown to coincide in both specimens.


Contact Force Discrete Element Method Order Work Microscopic Variable Tangential Contact Stiffness 
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  1. Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Geotech 29(1):47–65CrossRefGoogle Scholar
  2. Hadda N, Nicot F, Bourrier F, Sibille L, Radjai F, Darve F (2013) Micromechanical analysis of second-order work in granular media. Granular Matter 15(2):221–235CrossRefGoogle Scholar
  3. Hill R (1958) A general theory of uniqueness and stability in elastic-plastic solids. J Mech Phys Solids 6(3):236–249CrossRefzbMATHGoogle Scholar
  4. Laouafa F, Darve F (2002) Modelling of slope failure by a material instability mechanism. Comp Geotech 29(4):301–325CrossRefGoogle Scholar
  5. Nicot F, Darve F, Koah HDV (2007) Bifurcation and second-order work in geomaterials. Int J Num Anal Meth Geomech 31(8):1007–1032CrossRefzbMATHGoogle Scholar
  6. Nicot F, Hadda N, Bourrier F, Sibille L, Darve F (2011) Failure mechanisms in granular media: a discrete element analysis. Granular Matter 13(3):255–260CrossRefGoogle Scholar
  7. Nicot F, Hadda N, Bourrier F, Sibille L, Wan R, Darve F (2012) Inertia effects as a possible missing link between micro and macro second-order work in granular media. Int J Solids Struct 49(10):1252–1258CrossRefGoogle Scholar
  8. Šmilauer V, Catalano E, Chareyre B, Dorofeenko S, Duriez J, Gladky A, Kozicki J, et al (2010) Yade documentation, The Yade Project. Retrieved from

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • F. Nicot
    • 1
    Email author
  • N. Hadda
    • 2
  • F. Bourrier
    • 3
  • L. Sibille
    • 4
  • A. Tordesillas
    • 5
  • F. Darve
    • 4
  1. 1.IRSTEA Geomechanics Group ETNAGrenobleFrance
  2. 2.Department of Civil EngineeringUniversity of CalgaryCalgaryCanada
  3. 3.Irstea—Centre de GrenobleSaint-Martin d’HèresFrance
  4. 4.UJF-INPG-CNRS, Laboratoire Sols Solides Structures RisquesGrenobleFrance
  5. 5.Department of Mathematics and StatisticsUniversity of MelbourneVictoriaAustralia

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