The development of an approximation method which could rigorously average small-scale atomistic physics, and embed them into large-scale mechanics, was considered. A general computational procedure was presented which was based upon the use of homogenization to average frozen nanoscale atomistics and couple them to the equations of continuum hyper-elasticity. It was applied to nano-patterned systems, in which complex atomic configurations were organized into a repeating periodic array. The finite element method was used to solve the equations on the large scale, but the small-scale equation represented the lattice statics. The method was based upon a quasi-static zero-temperature assumption. By using homogenization, this led to a coupled set of variational equations. The homogenization gave rise to an inner displacement term via which point defects were modelled, and their non-linear interactions with 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