Open Access
2016 A mode III interface crack with surface strain gradient elasticity
Xu Wang, Peter Schiavone
J. Integral Equations Applications 28(1): 123-148 (2016). DOI: 10.1216/JIE-2016-28-1-123


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.


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Xu Wang. Peter Schiavone. "A mode III interface crack with surface strain gradient elasticity." J. Integral Equations Applications 28 (1) 123 - 148, 2016.


Published: 2016
First available in Project Euclid: 15 April 2016

zbMATH: 1381.74022
MathSciNet: MR3488157
Digital Object Identifier: 10.1216/JIE-2016-28-1-123

Primary: 45E99 , 74B05

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

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

Vol.28 • No. 1 • 2016
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