A Generalized Quasi-Nonlocal Atomistic-to-Continuum Coupling Method with Finite Range Interaction

Xingjie Helen Li, Mitchell Luskin

Published 2010-07-14, updated 2010-10-13Version 2

The accurate and efficient computation of the deformation of crystalline solids requires the coupling of atomistic models near lattice defects such as cracks and dislocations with coarse-grained models away from the defects. Quasicontinuum methods utilize a strain energy density derived from the Cauchy-Born rule for the coarse-grained model. Several quasicontinuum methods have been proposed to couple the atomistic model with the Cauchy-Born strain energy density. The quasi-nonlocal coupling method is easy to implement and achieves a reasonably accurate coupling for short range interactions. In this paper, we give a new formulation of the quasi-nonlocal method in one space dimension that allows its extension to arbitrary finite range interactions. We also give an analysis of the stability and accuracy of a linearization of our generalized quasi-nonlocal method that holds for strains up to lattice instabilities.