A generalized quasinonlocal atomistic-to-continuum coupling method with finite-range interaction

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 quasinonlocal (QNL) 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 QNL 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 QNL method that holds for strains up to lattice instabilities.