Problems involving coupled multiple space and time scales offer a real challenge for conventional frame-works of either particle or continuum mechanics. In this paper, four cases studies （shear band formation in bulk metallic glasses, spallation resulting from stress wave, interaction between a probe tip and sample, the simulation of nanoindentation with molecular statistical thermodynamics） are provided to illustrate the three levels of trans-scale problems （problems due to various physical mechanisms at macro-level, problems due to micro-structural evolution at macro/micro-level, problems due to the coupling of atoms/ molecules and a finite size body at micro/nano-level） and their formulations. Accordingly, non-equilibrium statistical mechanics, coupled trans-scale equations and simultaneous solutions, and trans-scale algorithms based on atomic/molecular interaction are suggested as the three possible modes of trans-scale mechanics.
Hybrid molecule/cluster statistical thermodynamics （HMCST） method is an efficient tool to simulate nano-scale systems under quasi-static loading at finite temperature. In this paper, a self-adaptive algorithm is developed for this method. Explicit refinement criterion based on the gradient of slip shear deformation and a switching criterion based on generalized Einstein approximation is proposed respectively. Results show that this self-adaptive method can accurately find clusters to be refined or transferred to molecules, and efficiently refine or trans- fer the clusters. Furthermore, compared with fully atomistic simulation, the high computational efficiency of the self-adaptive method appears very attractive.
