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IssuesArchive of Issues2007-6pp.935-946

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E. M. Rudoi, "Differentiation of energy functionals in the problem on a curvilinear crack with possible contact between the shores," Mech. Solids. 42 (6), 935-946 (2007)
Year 2007 Volume 42 Number 6 Pages 935-946
Title Differentiation of energy functionals in the problem on a curvilinear crack with possible contact between the shores
Author(s) E. M. Rudoi (Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, pr-t akad. Lavrentyeva 15, Novosibirsk, 630090, Russia, rem@hydro.nsc.ru)
Abstract We consider the N-dimensional (N=2 or 3) model of a one-dimensional anisotropic elastic body containing a curvilinear or surface crack. On the crack shores, the nonpenetration conditions in the form of inequalities (Signorini type conditions) are posed. For the general form of a sufficiently smooth perturbation of the domain, we obtain the derivative of the energy functional with respect to the perturbation parameter. We derive sufficient conditions for the existence of invariant integrals over an arbitrary closed contour. In particular, we obtain an invariant Cherepanov-Rice integral for curvilinear cracks.
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19.  V. A. Kovtunenko, "Invariant Energy Integrals for the Non-Linear Crack Problem with Possible Contact of the Crack Surfaces," Prikl. Mat. Mekh. 67 (1), 109-123 (2003) [J. Appl. Math. Mech. (Engl. Transl.) 67 (1), 99-110 (2003)].
20.  J. Sokolowski and A. M. Khludnev, "On the Differentiation of Energy Functionals in Crack Theory with Possible Contact of the Crack Faces," Dokl. Ross. Akad. Nauk 374 (6), 776-779 (2000) [Russian Acad. Sci. Dokl. Math. (Engl. Transl.)].
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Received 25 April 2005
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