The development of an approximation method that rigorously averages small-scale atomistic physics and embeds them in large-scale mechanics was the principal aim of this work. This paper presents a general computational procedure based on homogenization to average frozen nanoscale atomistics and couple them to the equations of continuum hyper-elasticity. The proposed application was to nanopatterned systems in which complex atomic configurations were organized in a repeating periodic array. The finite element method was used to solve the equations at the large scale, but the small-scale equation was representative of lattice-statics. The method was predicated on a quasi-static zero-temperature assumption and, through homogenization, leads to a coupled set of variational equations. Homogenization naturally gives rise to an inner displacement term with which point defects were explicitly modelled and their non-linear interactions with global states of multi-axial strain were studied.

Computational Method for Atomistic Homogenization of Nanopatterned Point Defect Structures. P.W.Chung: International Journal for Numerical Methods in Engineering, 2004, 60[4], 833-59