On two approaches to asymptotic analysis of subsonic rupture propagation

• Autorzy: Linkov A. M.
• Języki publikacji: EN

Abstrakty

EN

Two approaches to the asymptotic analysis of a surface wave arising under shear rupture propagation are compared. They differ in Green's functions used to derive asymptotic integral equations. One of them provides a finite stress at the rupture front while the displacement discontinuity at infinity behind the front tends to infinity; the other, quite oppositely, leads to an infinite stress at the front while the displacement discontinuity at infinity is finite. Detailed analysis of the equations of the second approach shows its advantages: the possibility of using important results of fracture mechanics and simplification of the eigenvalue problem.

Słowa kluczowe

EN

asymptotic integral equations; Green's functions; rupture propagation; contact wave

PL

równania całkowe asymptotyczne; funkcje Greena

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2006
• Tom: Vol. 28
• Strony: 93--100
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Linkov A. M.

• Institute for Problems of Mechanical Engineering 61 Bol'shoi pr. V.O., Saint-Petersburg 199178, Russia Department of Mathematics Rzeszów University of Technology ul. W. Pola 2, 35-359 Rzeszów, Poland,

Bibliografia

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• [3] L. Galin, Contact Problems of Elasticity Theory, Gostehizdat, Moscow, 1953. (In Russian).
• [4] Stress Intensity Factors Handbook 1, 2, Y. Murakami (ed.), Pergamon Press, Oxford, New York, 1990.
• [5] Y. Ida, Cohesive force. across the tip of a longitudinal shear crack and Griffith's specific surface energy, J. Geophys. Research 77 (1972), 3796-3805.
• [6] A. Linkov, On the determination of the abutment pressure and evaluation of stability of seam edges acconting for post-failure deformations, Soviet Mining Science 14 (1978), 3-7.
• [7] A. Linkov, On the size of a fracture process zone and on the velocity of displacement discontinuity propagation, Applied Mathematics and Mechanics 69 (2005), 155-160.
• [8] A. Linkov, M. Tleujanov, On evaluation of local zones of irreversible deformations at a crack tip, Proc. Kirgizian Academy of Sciences 1 (1990), 47-51. (In Russian).
• [9] N. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, 1975.
• [10] I. Petukhov, A. Linkov, The theory of post-failure deformations and the problem of stability iii rock mechanics, Int. J. Rock Mech. Mining Sci. & Geomech. Abstr. 16 (1979), 57-76.
• [11] J. Rice, Mathematical analysis in the mechanics of fracture, in: Fracture II, H. Liebowitz (ed.), Academic Press, New York, London, 1968, 191-311.