(509b) Multiscale Modeling of Rod-like Structures Using Molecular Dynamics and Continuum Mechanics

Molecular structures can be adequately studied using molecular dynamics (MD), although the utility of MD is limited by the large high computational costs of atomistic simulations. One possible way to reduce these costs is to replace the atomistic description of the system under consideration with a continuum mechanical one.

In this work, we focus in particular on rod-like structures where the extension in one direction is clearly larger than in the remaining two dimensions. Well-known examples of such materials on the nanoscale include carbon nanotubes and macromolecules such as DNA and cellulose bundles. For these materials, the concept of geometrically exact beams introduced by Simo (also known as Reissner-Simo beam theory) is a promising candidate for a continuum formulation.

Using atomistic molecular simulations to parameterize a continuum model, we can obtain numerical results for a variety of geometric configurations and system conditions much more efficiently than using exclusively atomistic MD simulations. To this end, we outline a systematic procedure that estimates the necessary parameters (the initial geometry and strain-stress relationships) at finite, constant temperatures. By using benchmark problems that bridge the molecular and continuum scales, we can demonstrate the validity of the estimated parameters in finite element models of the beam model. We show how this model can be used to derive continuum representations of carbon nanotubes under various conditions.