Multi-scale Modeling – Bridging the Molecular Continuum Divide
any recent technological advances have been made possible through an understanding of materials and fabrication of structures at the molecular level. At this length scale, where molecular interactions dominate,
mechanical analyses are almost always performed using molecular mechanics and dynamics (MD) simulations. While they have provided important insights into the mechanical properties of material systems at the nanometer scale, MD simulations are limited to systems of at most micrometer dimensions because of the large number of molecules involved. In situations where events at the molecular level are strongly coupled to events at a much larger scale, such as the debonding of material interfaces due to far field forces, multi-scale simulation techniques to bridge molecular and continuum levels are needed to accurately describe these multi-physics problems.
Several multi-scale simulation techniques have surfaced in the past decade but none have been applied to study the mechanics of polymer deformation. Polymers are inherently more complex to model than crystalline materials due to their amorphous nature. Determining an equilibrated configuration of polymer chains is itself a challenge. Hence constructing a model of the polymer domain of interest is the first hurdle in computational simulations of polymers. The usual method to determine material properties of bulk polymers through MD simulations is to construct a parent chain of molecules (or clusters of molecules) attached to a cube known as an amorphous cell (AC), and subject the AC to deformations assuming periodic boundary conditions on all sides of the cell.
Research into multi-scale simulations at the Department of Mechanical Engineering has focused on polymer systems. In our study, the polymer domain is firstly constructed as a tessellation of ACs. For regions of small deformation, the number of degrees of freedom (DOF) is then significantly reduced by computing the displacements of only the corners of the ACs instead of molecules within the ACs. This is achieved by determining, a priori, the molecular displacements within an AC associated with judiciously selected orthogonal deformation modes of the cell.
Simulations of nanoindentation of a polymer substrate using full MD computation and our multi-scale approach were compared (Figure 1). In the multi-scale model, the number of DOF of the bottom half of the substrate is 50 times less than the full MD model. The accuracy of multi-scale simulation is demonstrated by its almost identical prediction of indentation force compared to full MD simulations. Figure 2 shows the strain contours of the polymer at various indentation depths from the multi-scale simulations. A comparison of the strain contours in Figures 2(c) and 2(d) further shows that the multi-scale model not only predicts macroscopic behavior accurately but also gives good prediction of the molecular rearrangement.
Contact person
Assoc Prof VBC Tan
Tel: 65168088,
Fax: 67791459
E-mail: mpetanbc@nus.edu.sg
