Abstract
The Poisson equation and linear elasticity equations in two-dimensional case for a nonsmooth domain are 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 analyzed 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’s integral defined for the solutions of the unilateral problem defined in the nonsmooth domain is path independent.
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Khludnev, A.M., Sokolowski, J. (1999). Griffith Formula and Rice-Cherepanov’s Integral for Elliptic Equations with Unilateral Conditions in Nonsmooth Domains. In: Hoffmann, KH., Leugering, G., Tröltzsch, F., Caesar, S. (eds) Optimal Control of Partial Differential Equations. ISNM International Series of Numerical Mathematics, vol 133. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8691-8_18
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DOI: https://doi.org/10.1007/978-3-0348-8691-8_18
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