{
  "id": "2410.15679",
  "version": "v1",
  "published": "2024-10-21T06:42:27.000Z",
  "updated": "2024-10-21T06:42:27.000Z",
  "title": "Commutativity and non-commutativity of limits in the nonlinear bending theory for prestrained microheterogeneous plates",
  "authors": [
    "Klaus Boehnlein",
    "Lucas Bouck",
    "Stefan Neukamm",
    "David Padilla-Garza",
    "Kai Richter"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we look at the nonlinear bending theory for thin prestrained elastic sheets with an oscillating periodic structure. We show that all limiting (in the sense of $\\Gamma-$convergence) energy functionals which formally correspond to an infinite thickness-to-period ratio are equivalent. In contrast, there are several different limit models that formally correspond to a $0$ thickness-to-period ratio.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-21T06:42:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49S05",
      "74K20",
      "74Q05"
    ],
    "keywords": [
      "nonlinear bending theory",
      "prestrained microheterogeneous plates",
      "non-commutativity",
      "thin prestrained elastic sheets",
      "formally correspond"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}