1. bookVolume 25 (2020): Issue 3 (September 2020)
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Stress and Displacement Intensity Factors of Cracks in Anisotropic Media

Published Online: 17 Aug 2020
Page range: 212 - 218
Received: 24 Dec 2019
Accepted: 21 Apr 2020
Journal Details
License
Format
Journal
First Published
19 Apr 2013
Publication timeframe
4 times per year
Languages
English
Copyright
© 2020 Sciendo

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.

Keywords

[1] Zehnder A. (2012): Fracture Mechanics.− Springer.Search in Google Scholar

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

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

[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.Search in Google Scholar

[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.Search in Google Scholar

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

[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.Search in Google Scholar

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

[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.Search in Google Scholar

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

[11] Shubin M.A. (2001): Pseudodifferential Operators and Spectral Theory. − Berlin: Springer.Search in Google Scholar

[12] Duduchava R. (1979): Singular Integral Equations with Fixed Singularities.− Leipzig: Teubner.Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

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

[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.Search in Google Scholar

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

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

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