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Acta Mechanica
Published in: Acta Mechanica 7/2020

27-05-2020 | Original Paper

Cracked elastic layer with surface elasticity under antiplane shear loading

Authors: Ying Yang, Zhen-Liang Hu, Xian-Fang Li

Published in: Acta Mechanica | Issue 7/2020

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Abstract

A mode-III crack embedded in a homogeneous isotropic elastic layer of nanoscale finite thickness is studied in this article. The classical elasticity incorporating surface elasticity is employed to reduce a nonclassical mixed boundary value problem, where the layer interior obeys the traditional constitutive relation and the surfaces of the layer and the crack are dominated by the surface constitutive relation. Using the Fourier transform, we convert the problem to a hypersingular integro-differential equation for the out-of-plane displacement on the crack faces. By expanding the out-of-plane displacement as series of Chebyshev polynomials, the Galerkin method is invoked to reduce the singular integro-differential equation with Cauchy kernel to a set of algebraic linear equations for the unknown coefficients. An approximate solution is determined, and the influences of surface elasticity on the elastic field and stress intensity factor are examined and displayed graphically. It is shown that surface elasticity decreases the bulk stress and its intensity factor near the crack tips for positive surface shear modulus and gives rise to an opposite trend for a negative surface shear modulus.
previous article Thermoelastic influence of convective and conduction interstitial conditions on the size of the contact zone in three-dimensional receding thermoelastic contact problem
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Metadata
Title
Cracked elastic layer with surface elasticity under antiplane shear loading
Authors
Ying Yang
Zhen-Liang Hu
Xian-Fang Li
Publication date
27-05-2020
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 7/2020
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-020-02695-7

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