Multiscale treatment of mechanical contact problems involving thin polymeric layers

Abstract

We propose a strategy to obtain a hyperelastic constitutive law for film-like systems from molecular dynamics (MD) simulations. The aim is to furnish a computationally efficient continuum model with this description of the material. In particular, two different methods are suggested, both of which consist of virtual experiments that are performed on the material to sample systematically the stress–strain relation. The latter is then fitted to a suitable functional form. We use a polymeric self-assembled monolayer, which spans a height of only a few nanometers, as a test case. Having determined the response function, we then apply it within a finite-element simulation of a continuum mechanical nanoindentation problem. Several contact quantities such as normal reaction forces and the contact geometry are extracted from these calculations and are compared to those from an analogous, fully atomistic nanoindentation simulation. We find that the considered benchmark quantities as obtained from the continuum surrogate model reproduce well the corresponding values of the MD simulation.