Bond-based nonlocal models by nonlocal operator method in symmetric support domain

authored by: Huilong Ren, Xiaoying Zhuang, Xiaolong Fu, Zhiyuan Li, Timon Rabczuk
Abstract: The present study focuses on the applications of energy decomposition in diverse nonlocal models, such as elasticity, thin plates, and gradient elasticity, with the aim of establishing bond-based nonlocal models in which the bond force is solely dependent on the deformation of a single bond. Through the adoption of an appropriate bond force form and the application of energy equivalence between local and nonlocal models, several kinds of highly succinct bond-based models are obtained. The present study involves a reexamination of nonlocal operator methods, with a particular focus on the simplified version within a symmetric support domain. A three-point bent-bond model has been proposed to characterize the curvature and bending moment. A crack criterion for normal strain of the bond based on Griffith theories is proposed. This approach is analogous to the phase field model and allows for individual application to each bond, resulting in strain localization. By implementing this rule, the path of the crack can be predicted in an automated manner through the act of cutting the bond, yielding outcomes that are akin to those obtained via the phase field method. Simultaneously, a crack rule for critical shear strains in shear fractures is presented. Moreover, an incremental version of the plasticity model associated with bond force has been formulated. The nonlocal bond-based models are further validated through several numerical examples.
Organisation(s): Institute of Photonics
External Organisation(s): Xi'an Modern Chemistry Research Institute
Hohai University
Bauhaus-Universität Weimar
Tongji University
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 418
No. of pages: 24
ISSN: 0045-7825
Publication date: 01.01.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.48550/arXiv.2301.00864 (Access: Open)
https://doi.org/10.1016/j.cma.2023.116230 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{3052702e2c0444f08e59ceeba903d079,
title = "Bond-based nonlocal models by nonlocal operator method in symmetric support domain",
abstract = "The present study focuses on the applications of energy decomposition in diverse nonlocal models, such as elasticity, thin plates, and gradient elasticity, with the aim of establishing bond-based nonlocal models in which the bond force is solely dependent on the deformation of a single bond. Through the adoption of an appropriate bond force form and the application of energy equivalence between local and nonlocal models, several kinds of highly succinct bond-based models are obtained. The present study involves a reexamination of nonlocal operator methods, with a particular focus on the simplified version within a symmetric support domain. A three-point bent-bond model has been proposed to characterize the curvature and bending moment. A crack criterion for normal strain of the bond based on Griffith theories is proposed. This approach is analogous to the phase field model and allows for individual application to each bond, resulting in strain localization. By implementing this rule, the path of the crack can be predicted in an automated manner through the act of cutting the bond, yielding outcomes that are akin to those obtained via the phase field method. Simultaneously, a crack rule for critical shear strains in shear fractures is presented. Moreover, an incremental version of the plasticity model associated with bond force has been formulated. The nonlocal bond-based models are further validated through several numerical examples.",
keywords = "Bent bond, Bond-based, Energy orthogonal decomposition, Shear damage, Tensile damage",
author = "Huilong Ren and Xiaoying Zhuang and Xiaolong Fu and Zhiyuan Li and Timon Rabczuk",
note = "Funding Information: The first author gratefully acknowledges the financial support from the EU project entitled ”Computational Modeling, Topological Optimization, and Design of Flexoelectric Nano Energy Harvesters” (ERC COTOFLEXI 802205 ). ",
year = "2024",
month = jan,
day = "1",
doi = "10.48550/arXiv.2301.00864",
language = "English",
volume = "418",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier BV",
}

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