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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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

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

First available in Project Euclid: 15 April 2016

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Zentralblatt MATH identifier

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

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


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.

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