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.
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