Structural and Micropolar Beam Models of Nanocrystalline Materials (One-Dimensional Case)

Abstract

In the present paper, linear atomic chain is studied. It is assumed that there is a non-central force and moment interaction between the atoms of the chain. The discrete model of the chain is constructed with the main equations and Hamilton principle. Further, the limit procedure to the continual (beam) model is performed. It is shown that the continual (beam) model of the linear chain of atoms is identical to the applied beam model, which is constructed based on the moment (micropolar) theory of elasticity. Elastic constants of the micropolar beam are determined through the elastic parameters of the discrete model of the linear chain of atoms.