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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Bibliographic Details
Published in:Computers & structures Vol. 299; no. 1; p. 107395
Main Authors: Dorduncu, Mehmet, Ren, Huilong, Zhuang, Xiaoying, Silling, Stewart, Madenci, Erdogan, Rabczuk, Timon
Format: Journal Article
Language:English
Published: United States Elsevier Ltd 01.08.2024
Elsevier
Subjects:
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 Access:Get full text
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Summary: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.
Bibliography:NA0003525
SAND-2024-06032J
USDOE National Nuclear Security Administration (NNSA)
ISSN:0045-7949
DOI:10.1016/j.compstruc.2024.107395