The effect of a curvature-dependent surface tension on the singularities at the tips of a straight interface crack
AuthorsZemlyanova, A. Y.
KAUST Grant NumberKUS-C1-016-04
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AbstractA problem of an interface crack between two semi-planes made out of different materials under an action of an in-plane loading of general tensile-shear type is treated in a semi-analytical manner with the help of Dirichlet-to-Neumann mappings. The boundaries of the crack and the interface between semi-planes are subjected to a curvature-dependent surface tension. The resulting system of six singular integro-differential equations is reduced to the system of three Fredholm equations. It is shown that the introduction of the curvature-dependent surface tension eliminates both classical integrable power singularity of the order 1/2 and an oscillating singularity present in a classical linear elasticity solutions. The numerical results are obtained by solving the original system of singular integro-differential equations by approximating unknown functions with Taylor polynomials. © 2013 The Author.
CitationZemlyanova AY (2013) The effect of a curvature-dependent surface tension on the singularities at the tips of a straight interface crack. The Quarterly Journal of Mechanics and Applied Mathematics 66: 199–219. Available: http://dx.doi.org/10.1093/qjmam/hbt001.
SponsorsThe author is grateful to Prof. J. R. Walton for the suggestion of the topic and many helpful discussions. This publication is based on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
PublisherOxford University Press (OUP)