Deformation of atomic models and their equivalent continuum counterparts using Eringen's two-phase local/nonlocal model

The aim of this contribution is to formulate equivalent continuum finite element model for two-dimensional atomic arrays under plane-stress condition, based on Eringen's two phase local/nonlocal model. The interaction between the atoms is modelled using translational and rotational linear elastic springs including both nearest and second nearest neighbor relations. Explicit relations between those set of springs and material properties of associated continuum model is looked for by means of equivalency of potential energy stored in atomic bonds and strain energy of continuum. Possibility of reducing computational burden of full atomic models by equivalent continuum models is discussed. This study may be regarded as the first step in composing a partitioned-domain multiscale model; with possibly smoother transition between coarse and fine scales due to the ability of nonlocal continuum model in incorporating long-range interactions.