A review of peridynamic theory and nonlocal operators along with their computer implementations

verfasst von: Mehmet Dorduncu, Huilong Ren, Xiaoying Zhuang, Stewart Silling, Erdogan Madenci, Timon Rabczuk
Abstract: This study presents a comprehensive exploration of Peridynamic (PD) theory, with a specific focus on its theoretical foundations and practical implementations, including various PD formulations and PD operators. The objective is to highlight the unique attributes of each PD formulation and assess their suitability in the framework of material failure simulations by providing an extensive literature review. The research focuses on the bond-based (BB), ordinary state-based (OSB), and non-ordinary state-based (NOSB) PD formulations, offering a thorough understanding of their distinctive characteristics. Moreover, this study presents the importance of the PD operators on the solution of the differential equations. Numerical implementation is a central aspect of this research, providing a detailed flow chart of the computer codes for PD and PD operator models. In order to demonstrate the robustness of the PD formulations, this study presents numerical results, showcasing predictions generated by computer codes that can be accessed online.
Organisationseinheit(en): Institut für Photonik
Externe Organisation(en): Erciyes University
Sandia National Laboratories NM
University of Arizona
Bauhaus-Universität Weimar
Typ: Übersichtsarbeit
Journal: Computers and Structures
Band: 299
Anzahl der Seiten: 39
ISSN: 0045-7949
Publikationsdatum: 01.08.2024
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Tief- und Ingenieurbau, Modellierung und Simulation, Allgemeine Materialwissenschaften, Maschinenbau, Angewandte Informatik
Elektronische Version(en): https://doi.org/10.1016/j.compstruc.2024.107395 (Zugang: Offen)

BibTeX

@article{eb8cb9193e36441b9e7daf14e48076fb,
title = "A review of peridynamic theory and nonlocal operators along with their computer implementations",
abstract = "This study presents a comprehensive exploration of Peridynamic (PD) theory, with a specific focus on its theoretical foundations and practical implementations, including various PD formulations and PD operators. The objective is to highlight the unique attributes of each PD formulation and assess their suitability in the framework of material failure simulations by providing an extensive literature review. The research focuses on the bond-based (BB), ordinary state-based (OSB), and non-ordinary state-based (NOSB) PD formulations, offering a thorough understanding of their distinctive characteristics. Moreover, this study presents the importance of the PD operators on the solution of the differential equations. Numerical implementation is a central aspect of this research, providing a detailed flow chart of the computer codes for PD and PD operator models. In order to demonstrate the robustness of the PD formulations, this study presents numerical results, showcasing predictions generated by computer codes that can be accessed online.",
keywords = "Failure analyses, Nonlocal operator method, Numerical analyses, Peridynamic differential operator, Peridynamics",
author = "Mehmet Dorduncu and Huilong Ren and Xiaoying Zhuang and Stewart Silling and Erdogan Madenci and Timon Rabczuk",
note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",
year = "2024",
month = aug,
day = "1",
doi = "10.1016/j.compstruc.2024.107395",
language = "English",
volume = "299",
journal = "Computers and Structures",
issn = "0045-7949",
publisher = "Elsevier Ltd.",
}