Journal of Integral Equations and Applications

A mode III interface crack with surface strain gradient elasticity

Xu Wang and Peter Schiavone

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Abstract

We study the contribution of surface strain gradient elasticity to the anti-plane deformations of an elastically isotropic bimaterial containing a mode~III interface crack. The surface strain gradient elasticity is incorporated using an enriched version of the continuum-based surface/interface model of Gurtin and Murdoch. We obtain a complete semi-analytic solution valid everywhere in the solid (including at the crack tips) by reducing the boundary value problem to two coupled hyper-singular integro-differential equations which are solved numerically using Chebyshev polynomials and a collocation method. Our solution demonstrates that the presence of surface strain gradient elasticity on the crack faces leads to bounded stresses at the crack tips.

Article information

Source
J. Integral Equations Applications, Volume 28, Number 1 (2016), 123-148.

Dates
First available in Project Euclid: 15 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1460727507

Digital Object Identifier
doi:10.1216/JIE-2016-28-1-123

Mathematical Reviews number (MathSciNet)
MR3488157

Zentralblatt MATH identifier
1381.74022

Subjects
Primary: 45E99: None of the above, but in this section 74B05: Classical linear elasticity

Keywords
Surface strain gradient elasticity Mode III interface crack isotropic bimaterial stress singularity bounded stresses complete solution Green's function method hyper-singular integro-differential equation

Citation

Wang, Xu; Schiavone, Peter. A mode III interface crack with surface strain gradient elasticity. J. Integral Equations Applications 28 (2016), no. 1, 123--148. doi:10.1216/JIE-2016-28-1-123. https://projecteuclid.org/euclid.jiea/1460727507


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