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Cracks with smoothly closing edges under plane deformation. (English. Russian original) Zbl 0653.73042

J. Appl. Math. Mech. 51, No. 1, 99-107 (1987); translation from Prikl. Mat. Mekh. 51, No. 1, 130-139 (1987).
Summary: Asymptotic methods are used to compute the stress intensity coefficients at the tips of a thin cut with smoothly closing edges, and the asymptotic form of the potential energy is determined. Amongst various mathematical models representing real cracks, the “crack-cut” model is of special interest, since it requires the simplest mathematical methods in its study. However, the model does not reflect some of the properties of actual cracks, in particular the crack does not respond, within its framework, to loading in the direction of the cut. The case of a thin cut with smoothly closing edges ensures good agreement with reality, while retaining the simplicity of the cut. The present paper deals chiefly with the explanation of how sensitive such cracks are to the loading along the cut.

MSC:

74R05 Brittle damage
74G70 Stress concentrations, singularities in solid mechanics
35C20 Asymptotic expansions of solutions to PDEs
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