Atomic/Continuum Model Transformation and Its Application to Stress-Strain Analysis of Nanoscale Cutting

Abstract

A method by which to transform quantities of an atomic model to those of a continuum one, and vice versa has been proposed. The method is based on an idea that displacement at a point in a continuum model should be a weighted mean of those of surrounding atoms in the corresponding atomic model, while stress values should have the inverse relation so as to preserve strain energy between the two models. The continuum model is then discretized by the Finite-Element Method so that matrix equations for the transformation are derived. These equations have been applied to the results of atomic-model-based simulation of nanoscale cutting to evaluate the stress and strain distribution in nanoscale cutting. The results show that the strain distribution is not very different from that of macroscale cutting but that there is almost no concentrated shear stress in the primary shear zone in nanoscale cutting.