Dynamics of Macro–Nano Mechanical Systems; Fixed Interfacial Multiscale Method

Document Type : Research Paper


Robotic Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, I. R. Iran


The continuum based approaches don’t provide the correct physics in atomic scales. On the other hand, the molecular based approaches are limited by the length and simulated process time. As an attractive alternative, this paper proposes the Fixed Interfacial Multiscale Method (FIMM) for computationally and mathematically efficient modeling of solid structures. The approach is applicable to multi-body mechanical systems. In FIMM, a direct link between the nano field atoms and macro field nodes by the local atomic volume displacements associated with every macro field node in their common zone has been replaced with the previous methods. For a complete model of the macro section, a nine-noded Lagrange element has been developed, and for small dimensions, the Sutton-Chen potential (for problems of mechanics) has been used. In the presented model, the undesirable effects of free surfaces, common surfaces, and surfaces close to the interface with the macro field have been eliminated, and after presenting a practical and noteworthy procedure for the dynamics of systems in general, seven problems (in the form of three examples) have been offered to showcase the practicality