Skip to main content

Tensorial Hypoplastic Models

  • Chapter
  • First Online:
Modelling of Soil Behaviour with Hypoplasticity

Part of the book series: Springer Series in Geomechanics and Geoengineering ((SSGG))

Abstract

In Chap. 3 of this book, the basic principles of hypoplastic models were described. Obviously, for the models to be applicable in numerical modelling tools, models must be formulated in full tensorial notation. To explain the mathematical structure of hypoplastic models, their historical development is traced back in this chapter, starting with the trial-and-error models based on rational mechanics and ending with approaches explicitly enabling the incorporation of the most important features of soil behaviour into the model structure.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Kolymbas, D.: A generalised hypoelastic constitutive law. In: Proceedings of the \(11^{th}\) International Conference on Soil Mechanics and Foundation Engineering, San Francisco, p. 2626 (1985)

    Google Scholar 

  2. Kolymbas, D.: Computer-aided design of constitutive laws. Int. J. Numer. Anal. Methods Geomech. 15, 593–604 (1991)

    Article  Google Scholar 

  3. Kolymbas, D.: An outline of hypoplasticity. Arch. Appl. Mech. 61, 143–151 (1991)

    MATH  Google Scholar 

  4. Truesdell, C., Noll, W.: The Non-Linear Field Theories of Mechanics, pp. 1–541. Springer, Berlin (1965)

    MATH  Google Scholar 

  5. Niemunis, A.: Extended hypoplastic models for soils. Habilitation thesis, Ruhr-University, Bochum (2003)

    Google Scholar 

  6. Wang, C.C.: A new representation theorem for isotropic tensor functions. Arch. Rat. Mech. Anal. 36, 166–223 (1970)

    Article  Google Scholar 

  7. Wu, W.: Hypoplastizität als mathematisches Modell zum mechanischen Verhalten granularer Stoffe. Publication Series of the Institute of Soil Mechanics and Rock Mechanics, No. 129, Karlsruhe University (1992)

    Google Scholar 

  8. Wu, W.: On a simple critical state model for sand. In: Pande, G.N., Pietruszczak, S. (eds.) Proceedings of the \(7^{th}\) International Symposium Numerical Models in Geomechanics, NUMOG VII, pp. 47–52. Balkema, Rotterdam (1999)

    Google Scholar 

  9. Lanier, J., Caillerie, D., Chambon, R., Viggiani, G., Bésuelle, P., Desrues, J.: A general formulation of hypoplasticity. Int. J. Numer. Anal. Methods Geomech. 28, 1461–1478 (2004)

    Article  Google Scholar 

  10. Wu, W., Bauer, E.: A simple hypoplastic constitutive model for sand. Int. J. Numer. Anal. Methods Geomech. 18, 833–862 (1994)

    Article  Google Scholar 

  11. Gudehus, G.: A comprehensive constitutive equation for granular materials. Soils Found. 36(1), 1–12 (1996)

    Article  Google Scholar 

  12. Wu, W., Bauer, E., Kolymbas, D.: Hypoplastic constitutive model with critical state for granular materials. Mech. Mater. 23, 45–69 (1996)

    Article  Google Scholar 

  13. Kolymbas, D., Herle, I., von Wolffersdorff, P.A.: Hypoplastic constitutive equation with internal variables. Int. J. Numer. Anal. Methods Geomech. 19, 415–436 (1995)

    Article  Google Scholar 

  14. Bauer, E.: Calibration of a comprehensive constitutive equation for granular materials. Soils Found. 36(1), 13–26 (1996)

    Article  Google Scholar 

  15. Herle, I., Gudehus, G.: Determination of parameters of a hypoplastic constitutive model from properties of grain assemblies. Mech. Cohesive-Frict. Mater. 4, 461–486 (1999)

    Article  Google Scholar 

  16. von Wolffersdorff, P.A.: A hypoplastic relation for granular materials with a predefined limit state surface. Mech. Cohesive-Frict. Mater. 1(3), 251–271 (1996)

    Article  Google Scholar 

  17. Matsuoka, H., Nakai, T.: Stress-deformation and strength characteristics of soil under three different principal stresses. Proc. Jpn. Soc. Civ. Eng. 232, 59–70 (1974)

    Article  Google Scholar 

  18. Niemunis, A., Nübel, K., Karcher, C.: The consistency conditions for density limits of hypoplastic constitutive law. Task Q. 4(3), 412–420 (2000)

    Google Scholar 

  19. Herle, I., Kolymbas, D.: Hypoplasticity for soils with low friction angles. Comput. Geotech. 31(5), 365–373 (2004)

    Article  Google Scholar 

  20. Mašín, D.: A hypoplastic constitutive model for clays. Int. J. Numer. Anal. Methods Geomech. 29(4), 311–336 (2005)

    Article  Google Scholar 

  21. Wu, W., Niemunis, A.: Failure criterion, flow rule and dissipation function derived from hypoplasticity. Mech. Cohesive-Frict. Mater. 1, 145–163 (1996)

    Article  Google Scholar 

  22. Wu, W., Niemunis, A.: Beyond failure in granular materials. Int. J. Numer. Anal. Methods Geomech. 21, 153–175 (1997)

    Article  Google Scholar 

  23. Butterfield, R.: A natural compression law for soils. Géotechnique 29(4), 469–480 (1979)

    Article  Google Scholar 

  24. Mašín, D., Herle, I.: State boundary surface of a hypoplastic model for clays. Comput. Geotech. 32(6), 400–410 (2005)

    Article  Google Scholar 

  25. Mašín, D.: Hypoplastic Cam-clay model. Géotechnique 62(6), 549–553 (2012)

    Article  Google Scholar 

  26. Mašín, D.: Clay hypoplasticity with explicitly defined asymptotic states. Acta Geotech. 8(5), 481–496 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to David Mašín .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Mašín, D. (2019). Tensorial Hypoplastic Models. In: Modelling of Soil Behaviour with Hypoplasticity. Springer Series in Geomechanics and Geoengineering. Springer, Cham. https://doi.org/10.1007/978-3-030-03976-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-03976-9_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03975-2

  • Online ISBN: 978-3-030-03976-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics