Analysis of Rigid Frictionless Indentation on Half--Space with Surface Elasticity

Abstract

The formulation of a boundary value problem of an axisymmetric, rigid, frictionless indentation acting on an elastic half-space is presented. The novel feature of this formulation is associated with the treatment of surface energy effects by employing a complete Gurtin-Murdoch continuum model for surface elasticity. With use of standard Love's representation and Hankel integral transform, such boundary value problem can be reduced innto a set of dual integral equations associated with the mixed boundary conditions on the surface of the half-space. Once these dual integral equations are transformed into a Fredholm integral equation of the second kind, selected numerical procedures based upon Galerkin approximation and a collocation technique are proposed to construct its solution numerically. The complete elastic fields are to be obtained for punches of different profiles and with smooth and non-smooth contact. The insight into the influence of surface free energy and size-dependency on material properties, gained in this particular study, should indicate and shed some lights on the implications related to soft elastic solids and nanotechnology.