Elastic fields for a parabolic hole endowed with surface effects

Wang, Xu; Schiavone, Peter

doi:10.2140/jomms.2020.15.241

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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

DOI: 10.2140/jomms.2020.15.241

Abstract

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.

Keywords

surface effect, blunt crack, plane elasticity, closed-form solution, complex variable method

Milestones

Received: 11 October 2019

Revised: 12 January 2020

Accepted: 29 January 2020

Published: 8 April 2020

Authors

Xu Wang
School of Mechanical and Power Engineering East China University of Science and Technology Shanghai China

Peter Schiavone
Department of Mechanical Engineering University of Alberta 10-203 Donadeo Innovation Center for Engineering Edmonton, AB Canada

Vol. 15, No. 2, 2020

Xu Wang and Peter Schiavone

Abstract

Keywords

Milestones

Authors