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The Griffith formula and Cherepanov–Rice integral for a plate with a rigid inclusion and a crack

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We consider the model problem for a plate described by a biharmonic equation. The plate contains a rigid inclusion separated from the elastic part by a crack. We show that the target energy functional is differentiable with respect to a small perturbation of the crack length and the derivative can be represented as an invariant integral — a contour integral along a contour surrounding a crack vertex. The formula for the derivative and the invariant integral are analogues of the Griffith formula and Cherepanov–Rice integral known in the brittle fracture theory. Bibliography: 34 titles.

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Authors and Affiliations

  1. Lavrent’ev Institute of Hydrodynamics SB RAS, 15, pr. Akad. Lavrent’eva, Novosibirsk, 630090, Russia

    E. M. Rudoy

  2. Novosibirsk State University, 2, ul. Pirogova, Novosibirsk, 630090, Russia

    E. M. Rudoy

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Correspondence to E. M. Rudoy.

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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 10, No. 2, 2010, pp. 98-117.

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Rudoy, E.M. The Griffith formula and Cherepanov–Rice integral for a plate with a rigid inclusion and a crack. J Math Sci 186, 511–529 (2012). https://doi.org/10.1007/s10958-012-1004-z

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