Infinite elastic layer under axisymmetric surface loads and influence of surface stresses

Abstract

To present a complete solution of an infinite, rigid based elastic layer under the action of axisymmetric surface loads by taking the surface energy effects into account. The corresponding boundary value problem is formulated based on a classical theory of linear elasticity for the bulk layer and a complete Gurtin-Murdoch constitutive relation for modeling the surface energy effects. In the solution procedure, an analytical technique based on Love’s representation and Hankel integral transform is adopted to derive an explicit integral-form solution for both the displacement and stress fields. A selected numerical quadrature is subsequently applied to efficiently evaluate all involved integrals. To demonstrate the influence of surface free energy and size-dependency, an extensive parametric study is carried out. The surface energy effects show strong influence on responses at the region closed to the surface and also when a length scale of the problem is comparable to the intrinsic length of the surface. Such influences are more evident when the contribution of the residual surface tension is taken into account. Moreover, three fundamental solutions are constructed by specializing the axisymmetric surface loads to a unit normal concentrated load, a unit normal ring load and a unit tangential ring load. Such basic results constitute the essential basis for the development of boundary integral equations governing other related problems, e.g., nano-indentations.