{
  "id": "2311.04810",
  "version": "v1",
  "published": "2023-11-08T16:33:42.000Z",
  "updated": "2023-11-08T16:33:42.000Z",
  "title": "Finite Element Methods for the Stretching and Bending of Thin Structures with Folding",
  "authors": [
    "Andrea Bonito",
    "Diane Guignard",
    "Angelique Morvant"
  ],
  "comment": "30 pages, 5 figures, 2 tables",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In [Bonito et al., J. Comput. Phys. (2022)], a local discontinous Galerkin method was proposed for approximating the large bending of prestrained plates, and in [Bonito et al., IMA J. Numer. Anal. (2023)] the numerical properties of this method were explored. These works considered deformations driven predominantly by bending. Thus, a bending energy with a metric constraint was considered. We extend these results to the case of an energy with both a bending component and a nonconvex stretching component, and we also consider folding across a crease. The proposed discretization of this energy features a continuous finite element space, as well as a discrete Hessian operator. We establish the $\\Gamma$-convergence of the discrete to the continuous energy and also present an energy-decreasing gradient flow for finding critical points of the discrete energy. Finally, we provide numerical simulations illustrating the convergence of minimizers and the capabilities of the model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-08T16:33:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N12",
      "65N30",
      "74K20"
    ],
    "keywords": [
      "finite element methods",
      "thin structures",
      "local discontinous galerkin method",
      "continuous finite element space",
      "discrete hessian operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}