Triple scale segmentation of non-equilibrium system simulated by macro-micro-atomic line model with mesoscopic transitions

The properties of the material at the different scales are distinguished although the terminologies adopted for those at lower scales leave much to be desired. Under anti-plane shear, only the shear modulus shows up. Judicious values of the ratios of μmacro/μmicro and μmicro/μdisl are selected from a knowledge of previous atomic simulation calculations. In dependent checks, however, are implemented from the positiveness requirements imposed on the stress intensity factors and the scale multipliers that connect scale sensitive quantities from one scale to another. These conditions are used to determine the range of the free parameters. Indeed, the choice is limited. In retrospect, the numerical results represent the direct consequence of the underlying physical assumptions. The objective is to achieve “consistency” in multiscaling such that the sensitivity of parameters at the atomic level for affecting macroscopic behavior can be checked. The basic idea used in the cut-and-patch procedure of line segment model can be extended to imperfections in the forms of points, areas and volumes. Patching of the segmented scales can appeal to the use of a scale invariant criterion, a topic for future considerations.