Acta Mechanica

, Volume 218, Issue 3–4, pp 349–355 | Cite as

Conservation laws and prediction methods for stress concentration fields

  • H. Altenbach
  • V. A. Eremeyev
  • A. Kutschke
  • K. Naumenko
Article

Abstract

Starting with the Eshelby-type conservation law, path-independent line and surface integrals that allow the comparison of averaged strain-energy densities in the notch area for linear elastic and non-linear elastic material behaviors are derived. The analysis shows that a point (two-dimensional problems) and a curve (three-dimensional problems) exist on the notch boundary, where the values of the strain-energy densities are almost the same. The conditions are discussed, for which the equality of the strain energies is guaranteed. The theoretical results are illustrated by two finite-element examples.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chaboche J.L.: A review of some plasticity and viscoplasticity constitutive equations. Int. J. Plast. 24, 1642–1693 (2008)CrossRefMATHGoogle Scholar
  2. 2.
    Naumenko K., Altenbach H.: Modelling of Creep for Structural Analysis. Springer, Berlin (2007)CrossRefGoogle Scholar
  3. 3.
    Naumenko, K., Altenbach, H., Kutschke, A.: A combined model for hardening, softening and damage processes in advanced heat resistant steels at elevated temperature. Int. J. Damage Mech. (2010), doi:10.1177/10567895103868511-21
  4. 4.
    Neuber H.: Theory of stress concentration for shear-strained prismatic bodies with arbitrary nonlinear stress-strain law. Trans. ASME. J. Appl. Mech. 28, 544–550 (1961)MATHMathSciNetGoogle Scholar
  5. 5.
    Glinka G.: Energy density approach to calculation of inelastic strain–stress near notches and cracks. Engng. Fract. Mech. 22, 485–508 (1985)CrossRefGoogle Scholar
  6. 6.
    Hyde T.H., Sabesan R., Leen B.S.: Approximate prediction methods for multiaxial notch stress and strains under elastic–plastic and creep conditions. J. Strain Anal. 40, 535–548 (2005)CrossRefGoogle Scholar
  7. 7.
    Desmorat R.: Fast estimation of localized plasticity and damage by energetic methods. J. Solids Struct. 39, 3289–3310 (2002)CrossRefMATHGoogle Scholar
  8. 8.
    Kienzler R., Herrmann G.: Mechanics in Material Space with Applications to Defect and Fracture Mechanics. Springer, Berlin (2000)MATHGoogle Scholar
  9. 9.
    Gurtin M.E.: Configurational Forces as Basic Concepts of Continuum Physics. Springer, Berlin (2000)Google Scholar
  10. 10.
    Maugin G.A.: Material Inhomogeneities in Elasticity. Chapman Hall, London (1993)MATHGoogle Scholar
  11. 11.
    Cherepanov G.P.: Mechanics of Brittle Fracture. McGraw-Hill, New York (1979)MATHGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • H. Altenbach
    • 1
  • V. A. Eremeyev
    • 1
  • A. Kutschke
    • 1
  • K. Naumenko
    • 1
  1. 1.Center of Engineering SciencesMartin-Luther-Universität Halle-WittenbergHalle (Saale)Germany

Personalised recommendations