A nonlocal operator method for finite deformation higher-order gradient elasticity

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Huilong Ren
  • Xiaoying Zhuang
  • Nguyen Thoi Trung
  • Timon Rabczuk

Organisationseinheiten

Externe Organisationen

  • Bauhaus-Universität Weimar
  • Tongji University
  • Ton Duc Thang University
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Details

OriginalspracheEnglisch
Aufsatznummer113963
FachzeitschriftComputer Methods in Applied Mechanics and Engineering
Jahrgang384
Frühes Online-Datum16 Juni 2021
PublikationsstatusVeröffentlicht - 1 Okt. 2021

Abstract

We present a general finite deformation higher-order gradient elasticity theory. The governing equations of the higher-order gradient solid along with boundary conditions of various orders are derived from a variational principle using integration by parts on the surface. The objectivity of the energy functional is achieved by carefully selecting the invariants under rigid-body transformation. The third-order gradient solid theory includes more than 10.000 material parameters. However, under certain simplifications, the material parameters can be greatly reduced; down to 3. With this simplified formulation, we develop a nonlocal operator method and apply it to several numerical examples. The numerical analysis shows that the high gradient solid theory exhibits a stiffer response compared to a ’conventional’ hyperelastic solid. The numerical tests also demonstrate the capability of the nonlocal operator method in solving higher-order physical problems.

ASJC Scopus Sachgebiete

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A nonlocal operator method for finite deformation higher-order gradient elasticity. / Ren, Huilong; Zhuang, Xiaoying; Trung, Nguyen Thoi et al.
in: Computer Methods in Applied Mechanics and Engineering, Jahrgang 384, 113963, 01.10.2021.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Ren H, Zhuang X, Trung NT, Rabczuk T. A nonlocal operator method for finite deformation higher-order gradient elasticity. Computer Methods in Applied Mechanics and Engineering. 2021 Okt 1;384:113963. Epub 2021 Jun 16. doi: 10.1016/j.cma.2021.113963
Ren, Huilong ; Zhuang, Xiaoying ; Trung, Nguyen Thoi et al. / A nonlocal operator method for finite deformation higher-order gradient elasticity. in: Computer Methods in Applied Mechanics and Engineering. 2021 ; Jahrgang 384.
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