{
  "id": "1007.2336",
  "version": "v2",
  "published": "2010-07-14T14:02:18.000Z",
  "updated": "2010-10-13T22:50:42.000Z",
  "title": "A Generalized Quasi-Nonlocal Atomistic-to-Continuum Coupling Method with Finite Range Interaction",
  "authors": [
    "Xingjie Helen Li",
    "Mitchell Luskin"
  ],
  "comment": "18 pages, improved notation and exposition",
  "categories": [
    "math.NA"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-13T22:50:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized quasi-nonlocal atomistic-to-continuum coupling method",
      "finite range interaction",
      "quasi-nonlocal method",
      "cauchy-born strain energy density",
      "atomistic model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.2336L"
    }
  }
}