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

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 th...

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Veröffentlicht in:Computers & structures Jg. 299; H. 1; S. 107395
Hauptverfasser: Dorduncu, Mehmet, Ren, Huilong, Zhuang, Xiaoying, Silling, Stewart, Madenci, Erdogan, Rabczuk, Timon
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States Elsevier Ltd 01.08.2024
Elsevier
Schlagworte:
Failure analyses
MATHEMATICS AND COMPUTING
Nonlocal operator method
Numerical analyses
Peridynamic differential operator
Peridynamics
Nonlocal operator method
Failure analyses
Peridynamics
Peridynamic differential operator
Numerical analyses
ISSN:0045-7949
Online-Zugang:Volltext
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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. •Comprehensive review of current state-of-the-art peridynamics (PD).•Comprehensive review of novel methods based on PD- and nonlocal operators.•Extensive comparison of different methods.•Links to source codes and implementations.
AbstractList 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. •Comprehensive review of current state-of-the-art peridynamics (PD).•Comprehensive review of novel methods based on PD- and nonlocal operators.•Extensive comparison of different methods.•Links to source codes and implementations.
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.
ArticleNumber 107395
Author Madenci, Erdogan
Ren, Huilong
Zhuang, Xiaoying
Silling, Stewart
Rabczuk, Timon
Dorduncu, Mehmet
Author_xml – sequence: 1
  givenname: Mehmet
  surname: Dorduncu
  fullname: Dorduncu, Mehmet
  organization: Department of Mechanical Engineering, Erciyes University, Kayseri, Turkey
– sequence: 2
  givenname: Huilong
  surname: Ren
  fullname: Ren, Huilong
  organization: Institute of Photonics, Department of Mathematics and Physics, Leibniz University Hannover, Germany
– sequence: 3
  givenname: Xiaoying
  surname: Zhuang
  fullname: Zhuang, Xiaoying
  organization: Institute of Photonics, Department of Mathematics and Physics, Leibniz University Hannover, Germany
– sequence: 4
  givenname: Stewart
  surname: Silling
  fullname: Silling, Stewart
  organization: Center for Computing Research, Sandia National Laboratories, Albuquerque, NM, USA
– sequence: 5
  givenname: Erdogan
  surname: Madenci
  fullname: Madenci, Erdogan
  organization: Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ, USA
– sequence: 6
  givenname: Timon
  surname: Rabczuk
  fullname: Rabczuk, Timon
  email: timon.rabczuk@uni-weimar.de
  organization: Institute of Structural Mechanics, Bauhaus-Universitat Weimar, Germany
BackLink https://www.osti.gov/biblio/2350738$$D View this record in Osti.gov
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Issue 1
Keywords Nonlocal operator method
Failure analyses
Peridynamics
Peridynamic differential operator
Numerical analyses
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Jo (10.1016/j.compstruc.2024.107395_br1640) 2022; 269
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Jha (10.1016/j.compstruc.2024.107395_br2860) 2021; 151
Liu (10.1016/j.compstruc.2024.107395_br1390) 2023; 2023
Kulkarni (10.1016/j.compstruc.2024.107395_br1320) 2020; 233
Zhu (10.1016/j.compstruc.2024.107395_br4190) 2017; 121
Bie (10.1016/j.compstruc.2024.107395_br2760) 2023; 126
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Snippet This study presents a comprehensive exploration of Peridynamic (PD) theory, with a specific focus on its theoretical foundations and practical implementations,...
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StartPage 107395
SubjectTerms Failure analyses
MATHEMATICS AND COMPUTING
Nonlocal operator method
Numerical analyses
Peridynamic differential operator
Peridynamics
Title A review of peridynamic theory and nonlocal operators along with their computer implementations
URI https://dx.doi.org/10.1016/j.compstruc.2024.107395
https://www.osti.gov/biblio/2350738
Volume 299
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