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.
Bibliographical noteFunding Information:
This work was supported in part by National Science Foundation Grants DMS-0757355 and MS-0811039, the Institute for Mathematics and Its Applications, and the University of Minnesota Supercomputing Institute. This work was also supported by the Department of Energy under Award Number DE-SC0002085.
- Finite-range interaction
- Hybrid method