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The Griffith formula and the Rice–Cherepanov integral for crack problems with unilateral conditions in nonsmooth domains

Published online by Cambridge University Press:  01 August 1999

A. M. KHLUDNEV
Affiliation:
Lavrentyev Institute of Hydrodynamics of the Russian Academy of Sciences, Novosibirsk 630090, Russia (e-mail: khlud@hydro.nsc.ru)
J. SOKOLOWSKI
Affiliation:
Institut Elie Cartan, Laboratoire de Mathématiques, Université Henri Poincaré Nancy I, B.P. 239, 54506 Vandoeuvre lès Nancy Cedex, France and Systems Research Institute of the Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland (e-mail: sokolows@iecn.u-nancy.fr)
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Abstract

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As a paradigm for non-interpenetrating crack models, the Poisson equation in a nonsmooth domain in R2 is considered. The geometrical domain has a cut (a crack) of variable length. At the crack faces, inequality type boundary conditions are prescribed. The behaviour of the energy functional is analysed with respect to the crack length changes. In particular, the derivative of the energy functional with respect to the crack length is obtained. The associated Griffith formula is derived, and properties of the solution are investigated. It is shown that the Rice–Cherepanov integral defined for the solutions of the unilateral problem defined in the nonsmooth domain is path-independent. Finally, a non-negative measure characterising interaction forces between the crack faces is constructed.

Type
Research Article
Copyright
1999 Cambridge University Press