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Constitutive Equations and Instabilities of Granular Materials

  • Chapter
Modeling and Mechanics of Granular and Porous Materials

Abstract

Constitutive equations for geomaterials constitute a very intricate field. In the first part of this chapter, a synthetic view of constitutive formalism is presented. An intrinsic classification of all existing constitutive relations is deduced. Then examples of incrementally non-linear relations are given and some applications follow. A numerical study of the so-called “yield surfaces” is presented, and is followed by a discussion on the validity of the principle of superposition for incremental loading. Finally the question of bifurcations and instabilities in geomaterials is investigated. Essentially because of the non-associative character of geomaterial plastic strains, a large domain of failure with various modes of ruptures is exhibited.

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References

  1. D. Aubry, J.C. Hujeux, F. Lassoudire, Y. MEIMON: A double memory model with multiple mechanisms for cyclic soil behaviour, in: R. Dungar, G.N. Pande, J. Studer (eds.):Proc. Int. Symp. Numer. Models Geomech. 1Balkema, Rotterdam, 1982, pp. 3–13.

    Google Scholar 

  2. Z.P. bazant: Endochronic inelasticity and incremental plasticityInt. J. Solids Struct. 14pp. 691–714, 1978.

    Article  MATH  Google Scholar 

  3. R. Chambon, J. Desrues, W. Hammad, R. Charlier: CLoE, a new rate-type constitutive model for geomaterials. Theoretical basis and implementationInt. J. Num. Anal. Meth. Geomech. 18pp. 253–278, 1994.

    Article  MATH  Google Scholar 

  4. Y.F. Dafalias: Bounding surface plasticity. I: mathematical foundation and hypoelasticityJ. Eng. Mech. 112(9)pp. 966–987, 1986.

    Article  Google Scholar 

  5. Y.F. Dafalias, L.R. Hermann: A bounding surface soil plasticity model, in: G.N. Pande, O.C. Zienkiewicz (eds.):Proc. Symp. SoilsunderCyclic and Transient LoadingBalkema, Rotterdam, 1980, pp. 335–345.

    Google Scholar 

  6. F. Darve: Une loi rhéologique incrémentale non-linéaire pour les solidesMech. Res. Comm. 7(4)pp. 295–212, 1980.

    Article  Google Scholar 

  7. F. Darve: An incrementally non-linear constitutive law of second-order and its application to strain localization, in: C.S. DESAI, R.H. Gallagher (eds.):Mechanics of Engineering MaterialsJohn Wiley and Sons, London, 1984, pp. 179–196.

    Google Scholar 

  8. F. Darve: Incrementally non-linear constitutive relationships, in: F. Darve (ed.):Geomaterials Constitutive Equations and ModellingElsevier Applied Science, Amsterdam, 1990, pp. 213–238.

    Google Scholar 

  9. F. Darve: Liquefaction phenomenon of granular materials and constitutive instabilityInt. J. Eng. Comp. 7pp. 5–28, 1996.

    Google Scholar 

  10. F. Darve, B. Chau: Constitutive instabilities in incrementally nonlinear modelling, in: C.S. Desai (ed.):Constitutive Laws for Engineering MaterialsElsevier Applied Science, Amsterdam, 1987, pp. 301–310.

    Google Scholar 

  11. F. Darve, H. Dendani: An incrementally non-linear constitutive relation and its predictions, in: A.S. Saada, G.F. Bianchini (eds.):Constitutive Equations for Granular Non-Cohesive SoilsBalkema, Rotterdam, 1989, pp. 237–254.

    Google Scholar 

  12. F. Darve, S. Labanieh: Incremental constitutive law for sands and clays, simulation of monotonic and cyclic testsInt. J. Num. Anal. Meth. Geomech. 6pp. 243–273, 1982.

    Article  MATH  Google Scholar 

  13. F. Darve, F. Laouafa: Instabilities in granular materials and application to landslidesMech. Coh.-Frict. Mater. 5(8)pp. 627–652, 2000.

    Article  Google Scholar 

  14. F. Darve, X. Roguiez: Instabilities in granular materials, in: D.R.J. Owen, E. Onate, E. Hinton (eds.):Computational Plasticity - Fundamentals and ApplicationsCIMNE, Barcelona, 1997, pp. 720–727.

    Google Scholar 

  15. R.D. Davis, G. Mullenger: A rate-type constitutive model for soils with critical stateInt. J. Num. Anal. Meth. Geomech. 2pp. 255–282, 1978.

    Article  MATH  Google Scholar 

  16. H. Di Benedetto, F. Darve: Comparaison de lois rhéologique en cinématique rotationnelleJ. Mécan. Théor. Appl. 2(5)pp. 769–798, 1983.

    MATH  Google Scholar 

  17. C. Di Prisco, R. Nova: Stability problems related to static liquefaction of loose sand, in: J. Desrues, R. Chambon, I. Vardoulakis (eds.):Localisation and Bifurcation Theory for Soils and RocksBalkema, Rotterdam, 1994, pp. 59–70.

    Google Scholar 

  18. C. Di Prisco, R. Matiotti, R. Nova: Theoretical investigation of undrained stability of shallow submerged slopesGéotechnique 45pp. 479–496, 1995.

    Article  Google Scholar 

  19. J.M. Duncan, C.Y. Chang: Non-linear analyses of stress and stress and strain in soilsJ. Soil. Mech. and Found. Div. ASCE 95(SM5)pp. 1629–1653, 1970.

    Google Scholar 

  20. G. Gudehus: A comparison of some constitutive laws for soils under radially loading symmetric loading and unloading, in: W. Whittke (ed.):Proc. 3rd Int. Conf. Num. Meth. Geomech.Balkema, Rotterdam, 4, pp. 1309–1324, 1979.

    Google Scholar 

  21. P. Guélin: Note sur l’hystérisis mécaniqueJ. Mécan. 19(2)pp. 217–247, 1980.

    MATH  Google Scholar 

  22. P.Y. Hicher:Comportement Mécanique des Argiles Saturées sur Divers Chemins de Sollicitations Monotones et Cycliques: Application à une Modélisation Élasto-Plastique et Visco-ÉlastiquePh.D. thesis, Ecole Centrale de Paris, 1985.

    Google Scholar 

  23. R. Hill: A general theory of uniqueness and stability in elastic-plastic solidsJ. Mech. Phys. Solids 6pp. 239–249, 1958.

    Google Scholar 

  24. S. Imposimato, R. Nova: An investigation on the uniqueness of the incremental response of elastoplastic models for virgin sandMech.Coh.-Frict. Mater. 3pp. 65–87, 1998.

    Article  Google Scholar 

  25. D. Kolymbas: A rate dependent constitutive equation for soilsMech. Res. Comm. 4(6)pp. 367–372, 1977.

    Article  Google Scholar 

  26. P.V. Lade: Elasto-plastic stress theory for cohesionless soils with curved yield surfacesInt. J. Solids Struct. 13pp. 1019–1035, 1977.

    Article  MATH  Google Scholar 

  27. F. Laouafa:Analyse et Développement de Méthodes d’Éléments Finis. Applications aux Mod¨¨les Incrémentaux de Type InterpolationPh.D. thesis, INSA, Lyon, 1996.

    Google Scholar 

  28. F. Laouafa, P. Royis: Eléments finis déplacements. Nouvelle forme du probl¨¨me algébrique et algorithmes adaptésC. R. Acad. Sc. Paris, Série IIb 325pp. 347–352, 1997.

    MATH  Google Scholar 

  29. B. Loret:Formulation d’Une Loi de Comportement Élasto-Plastique des Milieux GranulairesD.I. thesis, Ecole Polytechnique, 1981.

    Google Scholar 

  30. M. Méghachou:Stabilité des Sables Lâches. Essais et ModélisationsPh.D. thesis, Université Joseph Fourier, Grenoble, 1993.

    Google Scholar 

  31. Z. Mroz: On the description of anisotropic work hardeningJ. Mech. Phys. Sci. 15pp. 163–175, 1967.

    Article  Google Scholar 

  32. R. Nova, D.M. Wood: A constitutive model for sand in triaxial compressionInt. J. Num. Anal. Meth. Geomech. 3pp. 255–278,1979.

    Article  Google Scholar 

  33. D.R. Owen, W.O. Williams: On the time derivatives of equilibrated response functionsArch. Rat. Mech. Anal. 33(4)pp. 288–306, 1969.

    Article  MathSciNet  MATH  Google Scholar 

  34. J.H. Prevost: Plasticity theory for soil stress-strain behaviourJ. Eng. Mech. Div. ASCE 104(EM5)pp. 1177–1194, 1978.

    Google Scholar 

  35. C. Truesdell, W. Noll: The non-linear field theories of mechanics, in: S. Flügge (ed.):Handbuch der PhysikSpringer-Verlag, Berlin III/3, 1965.

    Google Scholar 

  36. K.C. Valanis: A theory of viscoplasticity without a yield surfaceArchives of Mechanics 23pp. 517–5511971.

    MathSciNet  MATH  Google Scholar 

  37. I. Vardoulakis, M. Goldscheider, G. Gudehus: Formation of shear bands in sand bodies as a bifurcation problemInt. J. Num. Anal. Meth. Geomech. 2pp. 99–128, 1978.

    Article  Google Scholar 

  38. P. Vermeer: A double hardening model for sandGeotechnique28 (4), pp. 413–433, 1978.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Institut National Polytechnique de Grenoble Laboratoire Sols Solides Structures, INPG-UJF-CNRS, Alert Geomaterials Domaine Universitaire - BP 53, Grenoble, F-38041, France

    Félix Darve & Farid Laouafa

Authors
  1. Félix Darve
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  2. Farid Laouafa
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, Pisa, I-56127, Italy

    Gianfranco Capriz

  2. Dipartimento di Meccanica e Materiali, Università “Mediterranea” di Reggio Calabria, Reggio Calabria, I-89060, Italy

    Vito N. Ghionna  & Pasquale Giovine  & 

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Darve, F., Laouafa, F. (2002). Constitutive Equations and Instabilities of Granular Materials. In: Capriz, G., Ghionna, V.N., Giovine, P. (eds) Modeling and Mechanics of Granular and Porous Materials. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0079-6_1

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  • DOI: https://doi.org/10.1007/978-1-4612-0079-6_1

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6603-7

  • Online ISBN: 978-1-4612-0079-6

  • eBook Packages: Springer Book Archive

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