Stress and Displacement Intensity Factors of Cracks in Anisotropic Media

S. Kuznetsov 1  and A. Karakozova 2
  • 1 Ishlinsky Institute for Problems in Mechanics, , Bauman Moscow State Technical University, , Moscow State University of Civil Engineering, , Russia, Moscow
  • 2 Moscow State University of Civil Engineering, , Russia, Moscow

Abstract

A relation connecting stress intensity factors (SIF) with displacement intensity factors (DIF) at the crack front is derived by solving a pseudodifferential equation connecting stress and displacement discontinuity fields for a plane crack in an elastic anisotropic medium with arbitrary anisotropy. It is found that at a particular point on the crack front, the vector valued SIF is uniquely determined by the corresponding DIF evaluated at the same point.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] Zehnder A. (2012): Fracture Mechanics.− Springer.

  • [2] Tada H., Paris P.C. and Irwin G.R. (1985): The stress analysis of cracks handbook.− 2nd Ed. Paris Productions Inc., St. Louis.

  • [3] Kuznetsov S.V. (1996): On the operator of the theory of cracks.− C. R. Acad. Sci. Paris, vol.323, pp.427-432.

  • [4] Goldstein R.V. and Kuznetsov S.V. (1995): Stress intensity factors for half-plane crack in an anisotropic elastic medium.− C. R. Acad. Sci. Paris, vol.320. Ser. IIb, pp.165-170.

  • [5] BrennerA.V. and Shargorodsky E.M. (1997): Boundary value problems for elliptic pseudodifferential operators. − In: Agranovich M.S., Egorov Y.V., Shubin M.A. (eds) Partial Differential Equations IX. Encyclopaedia of Mathematical Sciences, vol.79. Springer, Berlin.

  • [6] Papadopoulos G.A. (1993): Theory of Cracks. − In: Fracture Mechanics. Springer, London.

  • [7] Duduchava R. and Wendland W.L. (1995): The Wiener-Hopf method for systems of pseudodifferential equations with an application to crack problems. − Integral Equations and Operator Theory, vol.23, pp.294-335.

  • [8] Kapanadze D. and Schulze B.W. (2003): Crack Theory and Edge Singularities.− Netherlands: Springer.

  • [9] Buchukuri T., Chkadua O. and Duduchava R. (2004): Crack-type boundary value problems of electro-elasticity. − In: Gohberg I., Wendland W., Ferreira dos Santos A., Speck FO., Teixeira F.S. (eds) Operator Theoretical Methods and Applications to Mathematical Physics. Operator Theory: Advances and Applications, vol.147. Birkhäuser, Basel.

  • [10] Treves F. (1982): Introduction to Pseudodifferential and Fourier Integral Operators. 1. Pseudodifferential Operators. − Plenum Press, N.Y. and London.

  • [11] Shubin M.A. (2001): Pseudodifferential Operators and Spectral Theory. − Berlin: Springer.

  • [12] Duduchava R. (1979): Singular Integral Equations with Fixed Singularities.− Leipzig: Teubner.

  • [13] Kupradze V., Gegelia T., Basheleisvili M. and Burchuladze T. (1979): Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity. − Amsterdam: North Holland.

  • [14] Duduchava R., Natroshvili D. and Schargorodsky E. (1989): On the continuity of generalized solutions of boundary value problems of the mathematical theory of cracks. − Bulletin of the Georgian Academy of Sciences, vol.135, pp.497-500.

  • [15] Kuznetsov S.V. (1995): Direct boundary integral equation method in the theory of elasticity. − Quart. Appl. Math., vol.53, pp.1-8.

  • [16] Kuznetsov S.V. (2005): Fundamental and singular solutions of equilibrium equations for media with arbitrary elastic anisotropy.− Quart. Appl. Math., vol.63, pp.455-467.

  • [17] Gurtin M.E. (1972): The Linear Theory of Elasticity. − In: Handbuch der Physik, Bd. VIa/2, Springer, Berlin, 1-295.

  • [18] Kuznetsov S.V. (2005): “Forbidden” planes for Rayleigh waves. − Quart. Appl. Math., vol.60, pp.87-97.

OPEN ACCESS

Journal + Issues

Search