Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2008-3pp.347-359

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S.A. Nazarov, "Scenarios for the quasistatic growth of a slightly curved and kinked crack," J. Appl. Math. Mech. 72 (3), 347-359 (2008)
Year 2008 Volume 72 Issue 3 Pages 347-359
Title Scenarios for the quasistatic growth of a slightly curved and kinked crack
Author(s) S.A. Nazarov (St Petersburg, Russia, srgnazarov@yahoo.co.uk)
Abstract A variational-asymptotic model of the Griffith criterion for the development of a crack is constructed for a complex stress-strain state. It is assumed that the shear loads are much smaller than the breaking loads but the longitudinal loading of the crack is taken into account. Using asymptotic analysis, the problem of finding the minimum of the total energy of a body with a crack reduces to a sequence of algebraic equations, the solutions of which determine the form of the branch of the crack and its length as a function of a time-like dimensionless parameter. The absence of solutions is treated as a conversion of the fracture process to a dynamic stage and the impossibility of a quasistatic formulation of the problem. In particular, the application of shear and longitudinal loads just leads to an avalanche-type growth of the crack.
Received 15 March 2007
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