Archive for Rational Mechanics and Analysis

, Volume 152, Issue 2, pp 103–139

The Evolution of Stress Intensity Factors and the Propagation of Cracks in Elastic Media

  • Avner Friedman
  • Bei Hu
  • Juan J. L. Velazquez

DOI: 10.1007/s002050000072

Cite this article as:
Friedman, A., Hu, B. & Velazquez, J. Arch. Rational Mech. Anal. (2000) 152: 103. doi:10.1007/s002050000072


When a crack Γs propagates in an elastic medium the stress intensity factors evolve with the tip x(s) of Γs. In this paper we derive formulae which describe the evolution of these stress intensity factors for a homogeneous isotropic elastic medium under plane strain conditions. Denoting by ψ=ψ(x,s) the stress potential (ψ is biharmonic and has zero traction along the crack Γs) and by κ(s) the curvature of the crack at the tip x(s), we prove that the stress intensity factors A1(s), A2(s), as functions of s, satisfy:
where \(\), \(\) are stress intensity factors of the tangential derivative of \(\) in the polar coordinate system at x(s) with θ=0 in the direction of the crack at x(s). The case of antiplane shearing is also briefly considered; in this case ψ is harmonic.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Avner Friedman
    • 1
  • Bei Hu
    • 2
  • Juan J. L. Velazquez
    • 3
  1. 1.Department of Mathematics¶University of Minnesota¶Minneapolis, MN 55455US
  2. 2.Department of Mathematics¶University of Notre Dame¶Notre Dame, IN 46556US
  3. 3.Departamento de Matematica Aplicada¶Facultad de Matematicas¶Universidad Complutense¶28040 Madrid, SpainES