Anti-plane strain under post-critical deformation in the problem on equilibrium semi-infinite crack. Part I

  • A. I. Chanyshev


The paper analyzes formulations of mathematical problems on anti-plane strains in materials under post-critical deformation. Depending on a decline modulus, the system of equilibrium equations and strain compatibility conditions has one or two characteristics. Given the two characteristics, finding stress-strain state of a medium needs Cauchy stress vector and displacement vector to be set at one and the same boundary. The author shows that the post-critical deformation, if included in the problem on an equilibrium semi-infinite crack, results in the infinite growth of stresses at the crack tip under unalterable deformation. Based on this, it is necessary to account for the by now disintegrated and fractured material area that is more rigid and higher modulus under the further deformation as compared with the initial state material.


Anti-plane strain post-critical deformation problem formulation crack stress and strain distribution in the vicinity of crack tip 


  1. 1.
    F. A. McClintock and A. S. Argon, Mechanical Behavior of Materials, Reading, Mass., Addison Wesley (1966).Google Scholar
  2. 2.
    Yu. N. Rabotnov, Deformable Solid Mechanics [in Russian], Nauka, Moscow (1972).Google Scholar
  3. 3.
    G. P. Cherepanov, Brittle Fracture Mechanics [in Russian], Nauka, Moscow (1974).Google Scholar
  4. 4.
    J. A. Hult and F. A. McClintock, “Elastic-plastic stress and strain distribution around sharp notches under repeated shear,” in: Proceedings of the 9th International Congress of Applied Mechanics, 8, Brussels (1956).Google Scholar
  5. 5.
    E. I. Shemyakin, “Stress-strain state at a cut tip in elastic-plastic bodies under anti-plane deformation,” Prikl. Mekh. Tekh. Fiz., No. 2 (1974).Google Scholar
  6. 6.
    J. Rice, “Mathematical methods in failure mechanics,” in: Failure [Russian translation], 2, Mir, Moscow (1975).Google Scholar
  7. 7.
    V. V. Novozhilov, “Types of connection of stresses and strains in primary isotropic inelastic bodies (geometrical aspect),” Prikl. Mat. Mekh., 27 (1963).Google Scholar
  8. 8.
    A. A. Ilyushin, Plasticity. Basics of the General Mathematical Theory [in Russian], AN SSSR, Moscow (1963).Google Scholar
  9. 9.
    N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity [in Russian], AN SSSR, Moscow (1949).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Institute of Mining, Siberian BranchRussian Academy of SciencesNovosibirskRussia

Personalised recommendations