{
  "id": "1011.3783",
  "version": "v3",
  "published": "2010-11-16T18:33:49.000Z",
  "updated": "2011-05-16T12:14:57.000Z",
  "title": "On the commutability of homogenization and linearization in finite elasticity",
  "authors": [
    "Stefan Müller",
    "Stefan Neukamm"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study non-convex elastic energy functionals associated to (spatially) periodic, frame indifferent energy densities with a single non-degenerate energy well at SO(n). Under the assumption that the energy density admits a quadratic Taylor expansion at identity, we prove that the Gamma-limits associated to homogenization and linearization commute. Moreover, we show that the homogenized energy density, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the quadratic term associated to the linearization of the initial energy density.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-05-16T12:14:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B27",
      "49J45",
      "74E30",
      "74Q05",
      "74Q20"
    ],
    "keywords": [
      "energy density",
      "finite elasticity",
      "homogenization",
      "quadratic taylor expansion",
      "elastic energy functionals"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00205-011-0438-7",
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2011,
      "month": "Aug",
      "volume": 201,
      "number": 2,
      "pages": 465
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011ArRMA.201..465M"
    }
  }
}