Skip to main content
SpringerLink
Log in

On path-independent integrals within the linear theory of elasticity

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

Conservation laws and associated path-independent integrals play a dominant role in field theories ranging from theoretical physics to applied engineering. Especially, material conservation laws are widely used to assess structural components with flaws like defects or cracks. Within the linear theory of elasticity, a complete set of conservation laws are derived by employing the so-called Neutral-Action method. An illustrative application is discussed.

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

  • Bessel-Hagen E (1921) Über die erhaltungssätze der elektrodynamik. Math Ann 84: 256–276

    Article  MathSciNet  Google Scholar 

  • Budiansky B, Rice JR (1973) Conservation laws and energy-release rates. J Appl Mech 40: 201–203

    MATH  Google Scholar 

  • Honein T, Chien N, Herrmann G (1991) On conservation laws for dissipative systems. Phys lett A 155: 223–224

    Article  MathSciNet  ADS  Google Scholar 

  • Kienzler R (1993) Konzepte der bruchmechanik. Vieweg, Braunschweig

    Google Scholar 

  • Kienzler R, Herrmann G (2000) Mechanics in material space. Springer, Berlin

    MATH  Google Scholar 

  • Murakami Y (1987) Stress intensity factors handbook. Pergamon, Oxford

    Google Scholar 

  • Noether E (1918) Invariante variationsprobleme. Nachrichten der königlichen gesellschaft der wissenschaften. Göttingen 2: 235–257

    Google Scholar 

  • Olver PJ (1984) Conservation laws in elasticity. II. Linear homogeneous isotropic elasticity. Arch Ration Mech Anal 85: 131–160

    Article  MATH  MathSciNet  Google Scholar 

  • Olver PJ (1998) Applications of lie groups to differential equations, 2nd edn. Springer, New York

    Google Scholar 

  • Rice JR (1968) A path independent integral and the approximate analysis of strain concentrations by notches and cracks. J Appl Mech 35: 379–386

    Google Scholar 

  • Tada H, Paris PC, Irwin GR (1973) The stress analysis of cracks handbook. Hellertown, Pennsylvania

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Production Engineering, Bremer Institute of Mechanical Engineering, University of Bremen, Bremen, Germany

    R. Kienzler, L. Rohde & R. Schröder

Authors
  1. R. Kienzler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Rohde
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Schröder
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Kienzler.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kienzler, R., Rohde, L. & Schröder, R. On path-independent integrals within the linear theory of elasticity. Int J Fract 166, 53–60 (2010). https://doi.org/10.1007/s10704-010-9482-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-010-9482-9

Keywords

Search

Navigation