Skip to main content
SpringerLink
Log in

A family of bi-potentials describing the non-associated flow rule of pressure-dependent plastic models

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

In this paper, we discuss in detail the derivation of the bi-potential function used to express the flow rule of pressure-dependent non-associated plastic models. In particular, we show that an infinity of equivalent expressions of the bi-potential can be derived for pressure-dependent models. The method consists in applying a transformation to the plastic strain rate or the stress or both to recover the normality rule. Then, the Fenchel inequality is used to derive the bi-potential function. The construction method itself indicates clearly that a class with infinite equivalent expressions of the bi-potential can be derived.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Collins I.F., Houlsby G.T.: Application of thermomechanical principles to the modelling of geotechnical materials. Proc. Roy. Soc. Ser. A. 453, 1975–2001 (1997)

    Article  MATH  Google Scholar 

  2. de Saxcé G.: Une généralisation de l’inégalité de Fenchel et ses applications aux lois constitutives. Comptes Rendus de l’Académie des Sciences de Paris, Série II 314, 125–129 (1992)

    MATH  Google Scholar 

  3. Drucker D.-C., Prager W.: Soil mechanics and plasticity analysis or limit design. Quart. Appl. Math. 10, 157–165 (1953)

    MathSciNet  Google Scholar 

  4. Eve R.A., Reddy B.D., Rockafellar R.T.: An internal variable theory of elastoplasticity based on the maximum plastic work inequality. Quart. Appl. Math. 48, 59–83 (1990)

    MATH  MathSciNet  Google Scholar 

  5. Han W., Reddy B.D.: Plasticity: Mathematical Theory and Numerical Analysis. Springer, Berlin (1999)

    MATH  Google Scholar 

  6. Moreau J.J.: La notion de sur-potentiel et les liaisons en élastostatique. Comptes Rendus de l’Académie des Sciences 267, 954–957 (1968)

    MATH  MathSciNet  Google Scholar 

  7. Moreau J.-J.: Inf-convolution des fonctions numériques sur un espace vectoriel Proximité et dualité dans un espace hilbertien. Comptes Rendus de l’Académie des Sciences de Paris 256, 125–129 (1963)

    Google Scholar 

  8. Moreau J.-J.: Proximité et dualité dans un espace hilbertien. Bulletin de la Société Mathathématique de France 93, 273–299 (1965)

    MATH  MathSciNet  Google Scholar 

  9. Mróz Z.: Mathematical Models of Inelastic Behavior. Solid Mechanics Division, University of Waterloo, Canada (1973)

    Google Scholar 

  10. Moreau J.-J.: Evolution problem associated with a moving convex set in a Hilbert space. J. Differ. Equ. 26, 347–374 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  11. Mróz Z.: Mathematical Models of Inelastic Behavior. Solid Mechanics Division, University of Waterloo, Canada (1973)

    Google Scholar 

  12. Nguyen Q.S.: Matériaux élasto-visco-plastiques à potentiel généralisé. Comptes Rendus de l’Académie des Sciences. 277, 915–918 (1973)

    MATH  Google Scholar 

  13. Halphen B., Nguyen Q.S.: Sur les matériaux standard généralisés. Journal de Mécanique 14, 39–63 (1975)

    MATH  Google Scholar 

  14. Rockafellar R.T., Wets J.B.: Variational Analysis. Springer, Berlin (1998)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. INSA de Rennes-LGCGM/Structural Engineering Research Group, Université Européenne de Bretagne, 20 avenue des Buttes de Coësmes, CS 70839, 35708, Rennes Cedex 7, France

    Mohammed Hjiaj & Duy-Lam Dao

  2. Laboratoire de Mécanique de Lille, Boulevard Paul Langevin, 59655, Villeneuve d’Ascq Cédex, France

    Géry de Saxcé

Authors
  1. Mohammed Hjiaj
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Duy-Lam Dao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Géry de Saxcé
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammed Hjiaj.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hjiaj, M., Dao, DL. & de Saxcé, G. A family of bi-potentials describing the non-associated flow rule of pressure-dependent plastic models. Acta Mech 220, 237–246 (2011). https://doi.org/10.1007/s00707-011-0477-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-011-0477-z

Keywords

Search

Navigation