A mode-III crack with variable surface effects
Xu Wang 1,   Peter Schiavone 2  
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School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai
University of Alberta, Department of Mechanical Engineering, Edmonton
Publication date: 2016-10-15
Journal of Theoretical and Applied Mechanics 2016;54(4):1319–1327
We study the contribution of variable surface effects to the antiplane deformation of a linearly elastic material with a mode-III crack. The surface elasticity is incorporated using a modified version of the continuum based surface/interface model of Gurtin and Murdoch. In our discussion, the surface moduli are not constant but vary along the crack surfaces. Using Green’s function method, the problem is reduced to a single first-order Cauchy singular integro-differential equation, which is solved numerically using Chebyshev polynomials and a collocation method. Our results indicate that the gradient of the surface shear modulus exerts a significant influence on the crack opening displacement and on the singular stress field at the crack tips.