Analysis of Indentation on Layered Elastic Medium with Surface Energy Effects

Abstract

This paper presents the analysis of an axisymmetric frictionless rigid punch on a layered elastic medium with the consideration of surface energy effects by adopting Gurtin-Murdoch continuum theory of surface elasticity. The indentation problem is formulated as a mixed-boundary value problem with the displacement boundary condition being imposed at the contact area. The unknown contact pressure under the indenter is then determined by employing a discretization technique with use of the displacement Green’s functions. The required Green’s functions are expressed in the form of the Hankel integral transform. The accuracy of the proposed solution scheme is verified by comparing with existing solutions. Selected numerical results on displacement and stress profiles in a layered elastic half-space are presented to demonstrate the influence of various parameters on elastic fields. It is found that the layered medium becomes stiffer and shows size-dependent behavior due to the presence of surface stresses.

SBFE analysis of layered elastic media with consideration of surface energy effect

“…Unlike the body treatment in a classical sense, the body, here, can be separated into the surface and the bulk in which the former is mathematically treated as the zerothickness material layer perfectly adhered to the bulk with its behavior governed by constitutive laws exhibiting different properties from the bulk. With the integration of the surface effect through such the material layer, an intrinsic length scale of materials is automatically introduced, and the resulting mathematical model can now capture the size-dependent behavior (Pinyochotiwong et al, 2013, Intarit et al, 2018, Tirapat and Senjuntichai, 2018, Tirapat et al, 2017, Tarntira, 2018.…”