(217z) Transferring The Mechanical Behavior Of Polymeric Surface Layers From Atomistic To Continuum

Contact problems study the behavior of distinguishable, solid bodies that interact with each other due to very small length scales of separation between them. In particular, we are especially interested in molecular-scale phenomena that are of purely mechanical origin.

Mechanical contact gives rise to complex effects occuring at the nanometer scale, which can be adequately described using a particle-based classical mechanical description and molecular dynamics (MD). The downside is the high computational cost of atomistic simulations. Among others, one possible approach to reduce the model order of the fully atomistic approach is to define a continuum-mechanical surrogate model. Such a latter description might be seen as favorable since the theory of continuum mechanics constitutes a unified framework that allows the incorporation of physical phenomena on the basis of continuously defined field variables. Furthermore, highly developed discretization techniques like Finite Element Methods (FEM) and solution methods are available. Therefore, we pursue the development of a procedure to establish the transition from atomistic to continuous scales, where the potentials governing interatomic interactions are known while the constitutive law remains to be constructed systematically.

We consider nanoindentation as a model problem, with an idealized indenter tip moving into a polymeric surface arranged as a self-assembled monolayer, an array of chain molecules that have one end grafted to an underlying metallic substrate and one end that is allowed to move around freely. The indentation process entails pushing the indenter, further and further down on the monolayer, thereby considerably deforming it and exerting forces on it. As alluded to above, these contact quantities can be determined precisely through MD simulations [1]. The interesting question is then how well these quantities can be reproduced when solving the surrogate model using FEM calculations. To this end, an analogous continuum-mechanical formulation of the nanoindentation problem is set up [2], based on the found constitutive law. Finally, the corresponding contact quantities (geometric deformation measures, forces) can be compared to those from the atomistic simulations.

In our studies, we were able to obtain reasonable agreement between the contact quantities that we have considered: the contact radius of the interaction between indenter and surface, the gap between these two objects, as well as the normal forces. The computational effort, on the other hand, was reduced by orders of magnitude.

REFERENCES

[1|   Chandross, M.; Lorenz, C.; Stevens, M.; Grest, G.: Simulations of Nanotribology with Realistic Probe Tip Models. In: Langmuir 24 (2008), pg. 1240-1246

[2]   Sauer, R.; Wriggers, P.: Formulation and analysis of a three-dimensional finite element implementation for adhesive contact at the nanoscale. In: Comput. Methods Appl. Mech. Engrg. 198 (2009), pg. 3871-3883