{
  "id": "1402.4514",
  "version": "v1",
  "published": "2014-02-18T22:14:43.000Z",
  "updated": "2014-02-18T22:14:43.000Z",
  "title": "General homogenization of bending-torsion theory for inextensible rods from 3D elasticity",
  "authors": [
    "Maroje Marohnic",
    "Igor Velcic"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We derive, by means of Gamma-convergence, the equations of homogenized bending rod starting from $3D$ nonlinear elasticity equations. The main assumption is that the energy behaves like h^2 (after dividing by the order h^2 of vanishing volume) where h is the thickness of the body. We do not presuppose any kind of periodicity and work in the general framework. The result shows that, on a subsequence, we always obtain the equations of bending-torsion rod and identifies, in an abstract formulation, the limiting quadratic form connected with that model. This is a generalization from periodic to non-periodic homogenization of bending-torsion rod theory already present in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-18T22:14:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "3d elasticity",
      "bending-torsion theory",
      "general homogenization",
      "inextensible rods",
      "bending-torsion rod theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.4514M"
    }
  }
}