Simple Scalar and Vectorial Hypoplastic Models

  • David MašínEmail author
Part of the Springer Series in Geomechanics and Geoengineering book series (SSGG)


The aim of this chapter is to demonstrate the basic principles of hypoplasticity without the formalism of tensorial operations. Simple 1D scalar hypoplastic models for shear and for compression are introduced first. Subsequently, the model is defined in terms of vectors and, finally, simple tensorial models are introduced as hypoplastic equivalents of the standard elasto-plastic models (Modified Cam-clay model).


  1. 1.
    Mroz, Z., Norris, V.A., Zienkiewicz, O.C.: An anisotropic hardening model for soils and its application to cyclic loading. Int. J. Numer. Anal. Methods Geomech. 2, 203–221 (1978)CrossRefGoogle Scholar
  2. 2.
    Al-Tabbaa, A., Muir Wood, D.: An experimentally based “bubble” model for clay. In: Proceedings of 3th International Conference on Numerical Models in Geomechanics. Niagara Falls (1989)Google Scholar
  3. 3.
    Stallebrass, S.E., Taylor, R.N.: Prediction of ground movements in overconsolidated clay. Géotechnique 47(2), 235–253 (1997)CrossRefGoogle Scholar
  4. 4.
    Dafalias, Y.F., Manzari, M.T.: Simple plasticity sand model accounting for fabric change effects. J. Eng. Mech. 130(6), 622–634 (2004)CrossRefGoogle Scholar
  5. 5.
    Niemunis, A., Herle, I.: Hypoplastic model for cohesionless soils with elastic strain range. Mech. Cohesive-Frictional Mater. 2(4), 279–299 (1997)CrossRefGoogle Scholar
  6. 6.
    Butterfield, R.: A natural compression law for soils. Géotechnique 29(4), 469–480 (1979)CrossRefGoogle Scholar
  7. 7.
    Gudehus, G.: A comprehensive constitutive equation for granular materials. Soils Found. 36(1), 1–12 (1996)CrossRefGoogle Scholar
  8. 8.
    von Wolffersdorff, P.A.: A hypoplastic relation for granular materials with a predefined limit state surface. Mech. Cohesive-Frictional Mater. 1(3), 251–271 (1996)CrossRefGoogle Scholar
  9. 9.
    Mašín, D.: A hypoplastic constitutive model for clays. Int. J. Numer. Anal. Methods Geomech. 29(4), 311–336 (2005)CrossRefGoogle Scholar
  10. 10.
    Mašín, D.: Hypoplastic Cam-clay model. Géotechnique 62(6), 549–553 (2012)CrossRefGoogle Scholar
  11. 11.
    Mašín, D.: Clay hypoplasticity with explicitly defined asymptotic states. Acta Geotechnica 8(5), 481–496 (2013)CrossRefGoogle Scholar
  12. 12.
    Mašín, D.: Clay hypoplasticity model including stiffness anisotropy. Géotechnique 64(3), 232–238 (2014)CrossRefGoogle Scholar
  13. 13.
    Roscoe, K.H., Burland, J.B.: On the generalised stress-strain behaviour of wet clay. In: Heyman, J., Leckie, F.A. (eds.) Engineering Plasticity, pp. 535–609. Cambridge University Press, Cambridge (1968)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of ScienceCharles UniversityPragueCzech Republic

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