A nonlocal operator method for finite deformation higher-order gradient elasticity
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.
Details
- Organisationseinheit(en)
-
Numerische Mechanik und Simulationstechnik
- 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, Allgemeine Physik und Astronomie, Angewandte Informatik
- Elektronische Version(en)
-
https://doi.org/10.1016/j.cma.2021.113963 (Zugang:
Geschlossen
)
https://hal.science/hal-03127040v2 (Zugang: Offen )
