Fundamentals of constitutive equations for geomaterials

  • Félix Darve
  • Guillaume Servant
Part of the International Centre for Mechanical Sciences book series (CISM, volume 461)


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 relation 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 the existence of a flow rule is discussed for both axisymmetric and 3D conditions. In agreement with discrete element computations, it is shown that a flow rule can exist in 2D and not in 3D.


Constitutive Equation Constitutive Relation Yield Surface Flow Rule Incremental Loading 
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  1. Aubry D., Hujeux J. C., Lassoudire F and Meimon Y., A double memory model with multiple mechanisms for cyclic soil behaviour, In Proc. of Int. Symp. on Numerical Models in Geomechanics, R. Dungar, G. N.Pande J. Studer (eds), Balkema, Rotterdam, pages 3–13, 1991.Google Scholar
  2. Bazant Z. P., Endochronic inelasticity and incremental plasticity, In Int. J. Solids Struct., 14 pages 691–714, 1978.Google Scholar
  3. Calvetti F., Tamagnini C. and Viggiani V., On the incremental behavior of granular soils, In Numerical Models in Geomechanics, Pande and Pietruszczak (eds.), Zwets and Zeitlinger (publ.), pages 3–9, 2002.Google Scholar
  4. Chambon R., Desrues J., Hammad W. and Charlier R., CLoE, a new rate-type constitutive model for geomaterials. Theoretical basis and implementation, In Int. J. Num. Anal. Meth. Geomech., 18 pages 253–278, 1994.Google Scholar
  5. Dafalias Y. F., Bounding surface plasticity. i. mathematical foundation and hypoelasticity, In J. Eng. Mech., 112 (9) pages 966–987, 1986.Google Scholar
  6. Dafalias Y. F. and Hermann L. R, A bounding surface soil plasticity model, In Proc. Symp. on Soils under Cyckic and Transient Loading, G. N. Pande O. C. Zienkiewicz (eds), Balkema, 1 pages 335–345, 1980.Google Scholar
  7. Darve F., Une loi rhéologique incrémentale non-linéaire pour les solides,In Mech. Res. Comm, 7 (4) pages 295–212, 1980.Google Scholar
  8. Darve F., An incrementally non-linear constitutive law of second order and its application to strain localization,In Mechanics of Engineering Materials, C. S. Desai R. H. Gallagher. John Wiley, London, pages 179–196, 1984.Google Scholar
  9. Darve F., Incrementally non-linear constitutive relationships,In Geomaterials Constitutive Equations and Modelling, F. Darve ed., Elsevier Applied Science, pages 213–238, 1990.Google Scholar
  10. Darve F., Liquefaction phenomenon of granular materials and constitutive instability,In Int. Journal of Engineering Computations, 7 pages 5–28, 1996.Google Scholar
  11. Darve F. and Labanieh S., Incremental constitutive law for sands and clays, simulation of monotonic and cyclic test,In Int. J. Num. Anal. Meth. Geomech., 6 pages 243–273, 1982.Google Scholar
  12. Darve F., Flavigny E. and Meghachou M., Yield surfaces and principle of superposition revisited by incrementally non-linear constitutive relations, In Int. Journal of Plasticity, 11(8) pages 927–948, 1995.Google Scholar
  13. Darve F. and Laouafa F., Instabilities in granular materials and application to landslides,In Mech. Cohes. Frict. Mater., 5(8) pages 627–652, 2000.Google Scholar
  14. Davis R. D. and Mullenger G., A rate-type constitutive model for soils with critical state, In Int. J. Num. Anal. Meth. Geomech., 2 pages 255–282, 1978.Google Scholar
  15. Di Benedetto H. and Darve F., Comparaison de lois rhéologique en cinématique rotationnelle,In J. Mécan. Théor. Appl., 2(5) pages 769–798, 1983.Google Scholar
  16. Duncan J. M. and Chang C. Y., Non-linear analysee of stress and stress and strain in soils, In J. Soil. Mech. and Found. Div., ASCE, 95(5M5) pages 1629–1653, 1970.Google Scholar
  17. Darve F. and Dendani H., An incrementally non-linear constitutive relation and its predictions, In Constitutive Equations for granular non-cohesive soils, Cleveland ed. A.S. Saada Bianchini, Balkema, Rotterdam, pages 237–254, 1989.Google Scholar
  18. Fernandez E., Internal Report,3S Laboratory, 2002.Google Scholar
  19. Gudehus G., A comparison of some constitutive laws for soils under radially loading symmetric loading and unloading, In Proc. 3rd Int. Conf. Num. Meth. Geomech., W. Whittke (ed), Balkema, 4 pages 1309–1324, 1979.Google Scholar
  20. Guélin P., Note sur l’hystérisis mécanique,In J. Mécan., 19(2) pages 217–247, 1980.Google Scholar
  21. Hicher P. Y., Comportement mécanique des argiles saturées sur divers chemins de sollicitations monotones et cycliques: application à une modélisation élasto-plastique et visco-élastique, Ph D,École Centrale de Paris, 1985.Google Scholar
  22. Hill R., Eigenmodal deformations in elastic-plastic continua,In J. Mech. Phys. Solids, 15 pages 371–386, 1967.Google Scholar
  23. Kishino Y., Akaizawa H. and Kaneko K. On the plastic flow of granular materials, In Powders and Grains, Kishino (ed.), Zwets and Zeitlinger (publ.), pages 199–202, 2001.Google Scholar
  24. Kolymbas D., A rate dependent constitutive equation for soils, In Mech. Res. Comm., 4(6) pages 367–372, 1977.Google Scholar
  25. Lade P. V., Elasto-plastic stress theory for cohesionless soils with curved yield surfaces, In Int. J. Solids Struct., 13 pages 1019–1035, 1977.Google Scholar
  26. Loret B., Formulation d’une loi de comportement élasto-plastique des milieux granulaires, Thèse de D.I., Ecole Polytechnique, 1981.Google Scholar
  27. Mroz Z., On the description of anisotropic work hardening,In J. Mech. Phys. Sci., 15 pages 163–175, 1967.Google Scholar
  28. Nova R. and Wood D. M., A constitutive model for sand in triaxial compression, In Int. J. Num. Anal. Meth. Geomech., 3 pages 255–278, 1979.Google Scholar
  29. Owen D. R. and Williams W. O., On the time derivatives of equilibrated response functions, In ARMA, 33(4) pages 288–306, 1969.Google Scholar
  30. Prevost J. H., Plasticity theory for soil stress-strain behaviour, In J. Eng. Mech. Div., ASCE, 104(EM5) pages 1177–1194, 1978.Google Scholar
  31. Royis P. and Doanh T., Theoretical analysis of strain response envelopes using incrementally non-linear constitutive equations,In /nt. J. Num. Anal. Meth. Geomechanics, 22 pages 97–132, 1998.Google Scholar
  32. Truesdell C. and Noll W., The non-linear field theories of mechanics,In Handbuch Phys. II, Springer, 1965.Google Scholar
  33. Valanis K. C., A theory of viscoplasticity without a yield surface, In Archives of Mechanics, 23 pages 517–551, 1971.Google Scholar
  34. Vardoulakis I., Goldscheider M. and Gudehus G., Formation of shear bands in sand bodies as a bifurcation problem, In /nt. J. Num. Anal. Meth. Geomech., 2 pages 99–128, 1978.Google Scholar
  35. Vermeer P., A double hardening model for sand, In Geotechnique, 28(4) pages 413–433, 1978.Google Scholar

Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

  • Félix Darve
    • 1
  • Guillaume Servant
    • 1
  1. 1.Institut National Polytechnique de Grenoble Laboratoire Sols, Solides, StructuresINPG-UJF-CNRSGrenobleFrance

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