The effect of a curvature-dependent surface tension on the singularities at the tips of a straight interface crack

Handle URI:
http://hdl.handle.net/10754/599897
Title:
The effect of a curvature-dependent surface tension on the singularities at the tips of a straight interface crack
Authors:
Zemlyanova, A. Y.
Abstract:
A 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.
Citation:
Zemlyanova 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.
Publisher:
Oxford University Press (OUP)
Journal:
The Quarterly Journal of Mechanics and Applied Mathematics
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
8-Mar-2013
DOI:
10.1093/qjmam/hbt001
Type:
Article
ISSN:
0033-5614; 1464-3855
Sponsors:
The 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).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorZemlyanova, A. Y.en
dc.date.accessioned2016-02-28T06:31:56Zen
dc.date.available2016-02-28T06:31:56Zen
dc.date.issued2013-03-08en
dc.identifier.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.en
dc.identifier.issn0033-5614en
dc.identifier.issn1464-3855en
dc.identifier.doi10.1093/qjmam/hbt001en
dc.identifier.urihttp://hdl.handle.net/10754/599897en
dc.description.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.en
dc.description.sponsorshipThe 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).en
dc.publisherOxford University Press (OUP)en
dc.titleThe effect of a curvature-dependent surface tension on the singularities at the tips of a straight interface cracken
dc.typeArticleen
dc.identifier.journalThe Quarterly Journal of Mechanics and Applied Mathematicsen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.