Numerical Analysis of Frictionless Nano-Contact Problems Based on Surface Elasticity

A nonlinear finite element model is developed to predict the response of frictionless contact of isotropic, elastic nano-bodies incorporating the effect of surface energy. The boundary value problem is formulated based on the classical theory of linear elasticity of the bulk material, while the complete Gurtin-Murdoch constitutive relation is adopted to accommodate the effect of surface energy. The Lagrange multiplier approach is employed to enforce inequality contact constraints without any need of an appropriate value for the penalty parameter, where the contact forces are treated as independent variables. The proposed finite element model accounts for both advancing and receding contact problems. The output results are compared favorably with those published analytical solutions. The influence of surface energy and its size-dependency on the behavior of conformal and nonconformal conformal/nonconformal nano-contact systems is demonstrated by carrying out by analyzing three different contact problems.