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

Xingjie Helen Li, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)373-393
Number of pages21
JournalIMA Journal of Numerical Analysis
Issue number2
StatePublished - Apr 2012

Bibliographical note

Funding 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.


  • Atomistic-to-continuum
  • Coupling
  • Finite-range interaction
  • Hybrid method
  • Quasicontinuum
  • Quasinonlocal


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