Plasticity

Chapter

Abstract

The continuum mechanics basics for the one-dimensional bar will be compiled at the beginning of this chapter. The yield condition, the flow rule, the hardening law and the elasto-plastic modulus will be introduced for uniaxial, monotonic loading conditions. Within the scope of the hardening law, the description is limited to isotropic hardening, which occurs for example for the uniaxial tensile test with monotonic loading. For the integration of the elasto-plastic constitutive equation, the incremental predictor-corrector method is generally introduced and derived for the fully implicit and semi-implicit backward-Euler algorithm. On crucial points the difference between one- and three-dimensional descriptions will be pointed out, to guarantee a simple transfer of the derived methods to general problems. Calculated examples and supplementary problems with short solutions serve as an introduction for the theoretical description.

Keywords

Yield Surface Strain Increment Flow Rule Displacement Increment Back Projection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New YorkMATHGoogle Scholar
  2. 2.
    Drucker DC et al (1952) A more fundamental approach to plastic stress–strain relations. In: Sternberg E (ed) Proceedings of the 1st US national congress for applied mechanics. Edward Brothers Inc, Michigan, p 491Google Scholar
  3. 3.
    Betten J (2001) Kontinuumsmechanik. Springer, BerlinMATHCrossRefGoogle Scholar
  4. 4.
    de Borst R (1986) Non-linear analysis of frictional materials. Delft University of Technology, DissertationGoogle Scholar
  5. 5.
    Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, ChichesterMATHGoogle Scholar
  6. 6.
    Mang H, Hofstetter G (2008) Festigkeitslehre. Springer, WienGoogle Scholar
  7. 7.
    Altenbach H, Altenbach J, Zolochevsky A (1995) Erweiterte Deformationsmodelle und Versagenskriterien der Werkstoffmechanik. Deutscher Verlag für Grundstoffindustrie, StuttgartGoogle Scholar
  8. 8.
    Jirásek M, Bazant ZP (2002) Inelastic analysis of structures. Wiley, ChichesterGoogle Scholar
  9. 9.
    Chakrabarty J (2009) Applied plasticity. Springer, New YorkMATHGoogle Scholar
  10. 10.
    Yu M-H, Zhang Y-Q, Qiang H-F, Ma G-W (2006) Generalized plasticity. Springer, BerlinGoogle Scholar
  11. 11.
    Wriggers P (2001) Nichtlineare finite-element-methoden. Springer, BerlinMATHCrossRefGoogle Scholar
  12. 12.
    Crisfield MA (2001) Non-linear finite element analysis of solids and structures. Bd. 1: essentials. Wiley, Chichester.Google Scholar
  13. 13.
    Crisfield MA (2000) Non-linear finite element analysis of solids and structures. Bd. 2: advanced topics. Wiley, Chichester.Google Scholar
  14. 14.
    de Souza Neto EA, Perić D, Owen DRJ (2008) Computational methods for plasticity: theory and applications. Wiley, ChichesterCrossRefGoogle Scholar
  15. 15.
    Dunne F, Petrinic N (2005) Introduction to computational plasticity. Oxford University Press, OxfordMATHGoogle Scholar
  16. 16.
    Simo JC, Ortiz M (1985) A unified approach to finite deformation elastoplasticity based on the use of hyperelastic constitutive equations. Comput Method Appl M 49:221–245MATHCrossRefGoogle Scholar
  17. 17.
    Ortiz M, Popov EP (1985) Accuracy and stability of integration algorithms for elastoplastic constitutive equations. Int J Num Meth Eng 21:1561–1576MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Moran B, Ortiz M, Shih CF (1990) Formulation of implicit finite element methods for multiplicative finite deformation plasticity. Int J Num Meth Eng 29:483–514MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Betten J (1979) Über die Konvexität von Fließkörpern isotroper und anisotroper Stoffe. Acta Mech 32:233–247MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Lubliner J (1990) Plasticity theory. Macmillan Publishing Company, New YorkMATHGoogle Scholar
  21. 21.
    Balankin AS, Bugrimov AL (1992) A fractal theory of polymer plasticity. Polym Sci 34:246–248Google Scholar
  22. 22.
    Spencer AJM (1992) Plasticity theory for fibre-reinforced composites. J Eng Math 26:107–118MATHCrossRefGoogle Scholar
  23. 23.
    Chen WF, Baladi GY (1985) Soil plasticity. Elsevier, AmsterdamMATHGoogle Scholar
  24. 24.
    Chen WF, Liu XL (1990) Limit analysis in soil mechanics. Elsevier, AmsterdamGoogle Scholar
  25. 25.
    Chen WF (1982) Plasticity in reinforced concrete. McGraw-Hill, New YorkGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Faculty of Mechanical Engineering, Department of Applied MechanicsUniversity of Technology Malaysia—UTMSkudaiMalaysia
  2. 2.Department of Mechanical EngineeringAalen University of Applied SciencesAalenGermany

Personalised recommendations