{
  "id": "2208.04195",
  "version": "v1",
  "published": "2022-08-08T14:51:47.000Z",
  "updated": "2022-08-08T14:51:47.000Z",
  "title": "A continuum model for brittle nanowires derived from an atomistic description by $Γ$-convergence",
  "authors": [
    "Bernd Schmidt",
    "Jiří Zeman"
  ],
  "comment": "33 pages, 2 figures",
  "categories": [
    "math.AP",
    "cond-mat.mes-hall",
    "cond-mat.mtrl-sci",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Starting from a particle system with short-range interactions, we derive a continuum model for the bending, torsion, and brittle fracture of inextensible rods moving in three-dimensional space. As the number of particles tends to infinity, it is assumed that the rod's thickness is of the same order as the interatomic distance. Fracture energy in the $\\Gamma$-limit is expressed by an implicit cell formula, which covers different modes of fracture, including (complete) cracks, folds and torsional cracks. Our approach applies e.g. to atomistic systems with Lennard-Jones-type potentials and is motivated by the research of ceramic nanowires.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-08T14:51:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "74K10",
      "49J45",
      "74R10",
      "70G75"
    ],
    "keywords": [
      "continuum model",
      "atomistic description",
      "brittle nanowires",
      "convergence",
      "implicit cell formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}