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

verfasst von

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.

Organisationseinheit(en)

Institut für Kontinuumsmechanik

Externe Organisation(en)

Bauhaus-Universität Weimar
Tongji University
University of Strathclyde
Ton Duc Thang University

Typ

Artikel

Journal

Engineering with computers

Band

39

Seiten

23-44

Anzahl der Seiten

22

ISSN

0177-0667

Publikationsdatum

02.2023

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Software, Modellierung und Simulation, Ingenieurwesen (insg.), Angewandte Informatik

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2103.08696 (Zugang: Offen)
https://doi.org/10.1007/s00366-021-01502-8 (Zugang: Offen)