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

authored by: Huilong Ren, Xiaoying Zhuang, Erkan Oterkus, Hehua Zhu, Timon Rabczuk
Abstract: 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 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.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Bauhaus-Universität Weimar
Tongji University
University of Strathclyde
Ton Duc Thang University
Type: Article
Journal: Engineering with computers
Volume: 39
Pages: 23-44
No. of pages: 22
ISSN: 0177-0667
Publication date: 02.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Software, Modelling and Simulation, General Engineering, Computer Science Applications
Electronic version(s): https://doi.org/10.48550/arXiv.2103.08696 (Access: Open)
https://doi.org/10.1007/s00366-021-01502-8 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{442747d142ee4f35bc910a6f82f35094,
title = "Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase-field fracture by nonlocal operator method",
abstract = "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 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.",
keywords = "Dual-support, Energy form, Explicit time integration, Fracture, Peridynamics, Variational principle, Weak form",
author = "Huilong Ren and Xiaoying Zhuang and Erkan Oterkus and Hehua Zhu and Timon Rabczuk",
year = "2023",
month = feb,
doi = "10.48550/arXiv.2103.08696",
language = "English",
volume = "39",
pages = "23--44",
journal = "Engineering with computers",
issn = "0177-0667",
publisher = "Springer London",
number = "1",
}