Skip to main content
SpringerLink
Log in

Isotropic rate-dependent finite plasticity using the theory of material evolution

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

An alternative formulation for isotropic rate-dependent finite plasticity is developed using the theory of material evolution. In this approach, the plastic-like evolution is assumed to be volume preserving and be driven by the thermodynamically dual Mandel stress, which is also known as material or configurational stress. Restrictions on the evolution laws and the yield criteria are established based on the second law of thermodynamics and rational. A simple isotropic plastic-like evolution law and yield criteria are proposed to complete the model. It is demonstrated that these simple laws render perfect, hardening or softening plastic-like responses and are rate dependent.

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. Taylor G.I.: The mechanism of plastic deformation of crystals. Part I: Theoretical. Proc. R. Soc. Lond. 145, 362–404 (1934)

    Article  MATH  Google Scholar 

  2. Kuhlmann-Wilsdorf D.: Theory of plastic deformation: properties of low energy dislocation structures. Mater. Sci. Eng. 113, 1–41 (1989)

    Article  Google Scholar 

  3. Kosevich A.: Dynamical theory of dislocations. Sov. Phys. 7, 837 (1965)

    Article  MathSciNet  Google Scholar 

  4. Lubliner J.: Plasticity Theory. Dover, New York (2008)

    MATH  Google Scholar 

  5. Kachanov L.: Fundamentals of Theory of Plasticity. Dover, New York (2004)

    Google Scholar 

  6. Hill R.: The Mathematical Theory of Plasticity. Oxford University Press, London (1950)

    MATH  Google Scholar 

  7. Khan A., Huang S.: Continuum Theory of Plasticity. Wiley, New York (1995)

    MATH  Google Scholar 

  8. Prager W.: An Introduction to Plasticity. Addison-Wesley, Reading (1959)

    MATH  Google Scholar 

  9. Epstein M., Elzanowski M.: Material Inhomogeneities and Their Evolution. Springer, Berlin (2007)

    MATH  Google Scholar 

  10. Maugin G.A.: Eshelby stress in elastoplasticity and ductile fracture. Int. J. Plast. 55, 1853–1878 (1994)

    Google Scholar 

  11. Epstein M.: Self-driven continuous dislocations and growth. In: Steinmann, P., Maugin, G.A. (eds.) Mechanics of Material Forces., pp. 129–139. Springer, Berlin (2005)

    Chapter  Google Scholar 

  12. Cleja-Tigoiu S., Maugin G.A.: Eshelby’s stress tensor in finite elastoplasticity. Acta Mech. 139, 231–249 (2000)

    Article  MATH  Google Scholar 

  13. Anurag G., Steigmann D.J., Stóken J.S.: On the evolution of plasticity and incompatibility. Math. Mech. Solids 12, 583–610 (2007)

    MathSciNet  MATH  Google Scholar 

  14. Lardner R.: Mathematical Theory of Dislocations and Fracture. University of Toronto Press, Toronto (1974)

    MATH  Google Scholar 

  15. Kröner E.: Continuum theory of defects. In: Balian, R., Kléman, M., Poirieret, J. (eds.) Les Houches, Session 35, 1980-Physique des defauts., pp. 282–315. North-Holland, New York (1981)

    Google Scholar 

  16. Teodosiu C.: Elastic Models of Crystal Defects. Springer, Berlin (1984)

    Google Scholar 

  17. Gurtin M.: Configurational Forces as Basic Concepts of Continuum Physics. Springer, New York (2000)

    Google Scholar 

  18. Gurtin M., Fried E., Anand L.: The Mechanics and Thermodynamics of Continua. Cambridge, New York (2009)

    Google Scholar 

  19. Henann D.L., Anand L.: A large deformation theory for rate-dependent elastic-plastic materials with combined isotropic and kinematic hardening. Int. J. Plast. 25, 1833–1878 (2009)

    Article  Google Scholar 

  20. Lee M.-G., Kim S.-J., Han H.N.: Crystal plasticity finite element modelling of mechanically induced martensitic transformation (mimt) in metastable austenite. Int. J. Plast. 26, 688–710 (2010)

    Article  MATH  Google Scholar 

  21. Thamburaja P., Pan H., Chau F.: The evolution of microstructure during twinning: constitutive equations, finite-element simulations and verification. Int. J. Plast. 25, 2141–2168 (2009)

    Article  Google Scholar 

  22. Li H., Yang H., Sun Z.: A robust integration algorithm for implementing rate dependent crystal plasticity into explicit finite element method. Int. J. Plast. 24, 267–288 (2008)

    Article  Google Scholar 

  23. Rossiter J., Brahme A., Simha M., Inal K., Mishra R.: A new crystal plasticity scheme for explicit time integration codes to simulate deformation in 3d microstructures: effects of strain path, strain rate and thermal softening on localized deformation in the aluminum alloy 5754 during simple shear. Int. J. Plast. 26, 1702–1725 (2010)

    Article  MATH  Google Scholar 

  24. Nadler B., Epstein M.: Slip-plane plasticity using the theory of material evolution. Math. Mech. Solids 16, 381–392 (2011)

    Article  MathSciNet  Google Scholar 

  25. Mandel J.: Equations constitutives et directors dans les milieux plastiques. Int. J. Sol. Struct. 9, 725–740 (1973)

    Article  MATH  Google Scholar 

  26. Ogden R.: Non-linear Elastic Deformations. Dover, New York (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Victoria, Victoria, BC, V8W 3P6, Canada

    Ben Nadler

Authors
  1. Ben Nadler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ben Nadler.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nadler, B. Isotropic rate-dependent finite plasticity using the theory of material evolution. Acta Mech 223, 2425–2436 (2012). https://doi.org/10.1007/s00707-012-0717-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-012-0717-x

Keywords

Search

Navigation