Combining FEM and MD to simulate C₆₀/PA-12 nanocomposites

The purpose of this paper is the computation of the elastic mechanical behaviour of the fullerene C₆₀ reinforced polyamide-12 (PA-12) via a two-stage numerical technique which combines the molecular dynamics (MD) method and the finite element method (FEM).

At the first stage, the proposed numerical scheme utilizes MD to characterize the pure PA-12 as well as a very small cubic unit cell containing a C₆₀ molecule, centrally positioned and surrounded by PA-12 molecular chains. At the second stage, a classical continuum mechanics (CM) analysis based on the FEM is adopted to approximate the elastic mechanical performance of the nanocomposite with significantly lower C₆₀ mass concentrations. According to the computed elastic properties arisen by the MD simulations, an equivalent solid element with the same size as the unit cell is developed. Then, a CM micromechanical representative volume element (RVE) of the C₆₀ reinforced PA-12 is modelled via FEM. The matrix phase of the RVE is discretized by using solid finite elements which represent the PA-12 mechanical behaviour predicted by MD, while the C₆₀ neighbouring location is meshed with the equivalent solid element.

Several multiscale simulations are performed to study the effect of the nanofiller mass fraction on the mechanical properties of the C₆₀ reinforced PA-12 composite. Comparisons with other corresponding experimental results are attempted, where possible, to test the performance of the proposed method.

The proposed numerical scheme allows accurate representation of atomistic interfacial effects between C₆₀ and PA-12 and simultaneously offers a significantly lower computational cost compared with the MD-only method.