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.
＂Off the Pacific coast of Tohoku Earthquake＂ （M9.0, on March l lth, 2011） is the greatest one in Japanese seismic record. The hypocenter is located 130 km ESE off the Pacific coast of Tohoku with the focal depth of 24 kin. The quake-triggered tsunami afterward seriously damaged the nuclear reactors and caused severe consequences to the society.
