Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase-field fracture by nonlocal operator method

  • The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of nonlocal forms for elasticity, thin plate, gradient elasticity, electro-magneto-elasticity and phase-field fracture method. The nonlocal governing equationsThe derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of nonlocal forms for elasticity, thin plate, gradient elasticity, electro-magneto-elasticity and phase-field fracture method. The nonlocal governing equations are expressed as an integral form on support and dual-support. The first example shows that the nonlocal elasticity has the same form as dual-horizon non-ordinary state-based peridynamics. The derivation is simple and general and it can convert efficiently many local physical models into their corresponding nonlocal forms. In addition, a criterion based on the instability of the nonlocal gradient is proposed for the fracture modelling in linear elasticity. Several numerical examples are presented to validate nonlocal elasticity and the nonlocal thin plate.show moreshow less

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Metadaten
Document Type:Article
Author: Huilong Ren, Xiaoying Zhuang, Erkan Oterkus, Hehua Zhu, Prof. Dr.-Ing. Timon RabczukORCiDGND
DOI (Cite-Link):https://doi.org/10.1007/s00366-021-01502-8Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20211207-45388Cite-Link
URL:https://link.springer.com/article/10.1007/s00366-021-01502-8
Parent Title (English):Engineering with Computers
Language:English
Date of Publication (online):2021/12/01
Date of first Publication:2021/09/15
Release Date:2021/12/07
Publishing Institution:Bauhaus-Universität Weimar
Institutes and partner institutions:Fakultät Bauingenieurwesen / Institut für Strukturmechanik
Volume:2021
Pagenumber:1-22
First Page:1
Last Page:22
Tag:energy form; explicit time integration; peridynamics; variational principle; weak form
GND Keyword:Bruchmechanik; Elastizität; Peridynamik
Dewey Decimal Classification:600 Technik, Medizin, angewandte Wissenschaften / 620 Ingenieurwissenschaften
BKL-Classification:50 Technik allgemein / 50.38 Technische Thermodynamik
Licence (German):License Logo Creative Commons 4.0 - Namensnennung (CC BY 4.0)