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

verfasst von
Huilong Ren, Xiaoying Zhuang, Nguyen Thoi Trung, Timon Rabczuk
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.

Organisationseinheit(en)
Institut für Kontinuumsmechanik
Externe Organisation(en)
Bauhaus-Universität Weimar
Tongji University
Ton Duc Thang University
Typ
Artikel
Journal
Computer Methods in Applied Mechanics and Engineering
Band
384
ISSN
0045-7825
Publikationsdatum
01.10.2021
Publikationsstatus
Veröffentlicht
Peer-reviewed
Ja
ASJC Scopus Sachgebiete
Numerische Mechanik, Werkstoffmechanik, Maschinenbau, Physik und Astronomie (insg.), Angewandte Informatik
Elektronische Version(en)
https://doi.org/10.1016/j.cma.2021.113963 (Zugang: Geschlossen)
 

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