Finite element modeling for elastic nano-indentation problems incorporating surface energy effect

Nano materials have attracted considerable attention during the last two decades, due to their unusual electrical, mechanical and physical properties as compared with their macro counterparts. Mechanical properties of nano materials show strong size-dependency, which has been explained within the framework of continuum mechanics by including the effects of surface residual stresses and surface elasticity as introduced by Gurtin and Murdoch (GM) theory of surface elasticity. In the present work, a finite element model, based on the principle of minimum total potential energy, is developed to monitor the behavior of two-dimensional nano size structures, taking into account the surface effects according to the complete GM model, under elastic frictionless indentation process. Different from most of literature, the presented FE model is capable of solving a variety of problems no matter the complexity of the punch geometry or the boundary conditions. For the sake of comparison as well as validation, the developed model is used for analyzing a simple plane strain problem, and the obtained results have been compared with analytical results published in cited literature. Several problems with different surface-energy model assumptions, indenters of different geometrical shapes and different sizes of indented bodies are solved, to examine its size dependency. The non-conformal contact between the indenter and the elastic half plane is solved, in the context of contact mechanics, by the incremental convex programming (ICP) method. (C) 2014 Elsevier Ltd. All rights reserved.