Vol. 15, No. 2, 2020

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Elastic fields for a parabolic hole endowed with surface effects

Xu Wang and Peter Schiavone

Vol. 15 (2020), No. 2, 241–248

We study the contribution of surface energy to the plane strain deformations of an isotropic elastic material with a parabolic hole. A closed-form full-field solution is derived using Muskhelishvili’s complex variable formulation and the technique of conformal mapping. We also obtain the corresponding expressions for the stresses and displacements in the full-field arising solely from the influence of the surface effects. When the radius of curvature at the vertex of the parabola is reduced to the order of the square of the ratio of surface energy to the generalized stress intensity factor, the surface contribution is significant and cannot be disregarded.

surface effect, blunt crack, plane elasticity, closed-form solution, complex variable method
Received: 11 October 2019
Revised: 12 January 2020
Accepted: 29 January 2020
Published: 8 April 2020
Xu Wang
School of Mechanical and Power Engineering
East China University of Science and Technology
Peter Schiavone
Department of Mechanical Engineering
University of Alberta
10-203 Donadeo Innovation Center for Engineering
Edmonton, AB