Molecular dynamics (MD) simulation is now orthodox numerical approaches to mechanical analysis of solid nanomaterials. MD simulations, with the ability to trace each atom’s movement during microscopic processes, pervade the work of elucidating microscopic mechanisms involved. However, with a time scale of about 10-12 s, MD is not suitable for quasi-static deformation analysis of nanomaterials as in experiments. In length scale aspect, it is hard to simulate a system larger than hundreds of nanometers using MD. Molecule/cluster statistical thermodynamics (MST/CST) multi-scale computational framework, proposed by Bai et al., permits quasi-static analysis of nanomaterials at finite temperature. This framework consists of three independent methods: the atomistic representation based MST, continuum representation based CST and the hybrid MST/CST.
The core of this group of methods is MST, which is based on the statistical thermodynamics formulation of Helmholtz free energy of atoms and its minimization.
MST has been applied to quasi-static analysis for several nanomaterials in order to examine its fidelity and efficiency. In the analysis of single FCC crystals, like nanorods under uniaxial loadings and nanoindentations (Figure 1(a), (b)), both loading responses and dislocation distributions obtained from MST simulations agree quite well with that of MD simulations. In particular, the application to ZnO nanowires indicates that MST is capable of identifying the wurtzite-to-tetragonal phase transformation originally predicted by MD and DFT simulations. Furthermore, the Young’s modulus of ZnO nanowires calculated with MST is in good agreement with experimentally measured values, this provides a useful reference for the analysis of size effect in nanomaterials (Figure 1(d)).
More importantly, MST has a big advantage of efficiency over MD in dealing with quasi-static problems. For the Lennard-Jones potential, CPU time consumptions in MST simulations show linear proportional to the size of the simulation system (Figure 1(c)) and at least 8 times lower than that of MD. For Buckingham-type potential, MST can be up to 60 times faster than MD, therefore, potentially allowing larger size systems to be analyzed. Since MST is an atomistic representation based method, it can be seamlessly coupled with the continuum representation based CST to form the hybrid MST/CST (HMCST) multi-scale method. The HMCST is expected to handle more quasi-static problems at finite temperature with even larger systems properly up to several micrometers in the future.
Figure 1. Applications and efficiency of MST
The study entitled “Molecular statistical thermodynamics – a distinct and efficient numerical approach to quasi-static analysis of nanomaterials at finite temperature” has been published in Composites: Part B, 43 (2012), 57-63.