Homogenization-based Analysis of Quasicontinuum Method for Complex Crystals

Abstract

Among the efficient numerical methods based on atomistic models, the quasicontinuum (QC) method, introduced by Tadmor, Ortiz, and Phillips (1996), has attracted growing interest in recent years. Originally, the QC method was developed for materials with simple crystalline lattice (simple crystals) and later was extended to complex lattice (Tadmor et al, 1999). In the present paper we formulate the QC method for complex lattices in a homogenization framework and perform analysis of such a method in a 1D setting. We also present numerical examples showing that the convergence results are valid in a more general setting.