Quasi-static and dynamic fracture modeling by the nonlocal operator method

authored by: Yongzheng Zhang, Huilong Ren, Pedro Areias, Xiaoying Zhuang, Timon Rabczuk
Abstract: In this paper, a phase field model is developed and applied to the simulation of quasi-static and dynamic fracture using the nonlocal operator method (NOM). The phase field's nonlocal weak and associated strong forms are derived by a variational principle. The NOM requires only the definition of the energy. Its differential operators replace the shape functions in methods such as FEM which drastically simplifies the implementation. We present both a nonlocal implicit phase field model and a nonlocal explicit phase field model for fracture; the first approach is better suited for quasi-static fracture problems while the key application of the latter one is dynamic fracture. To demonstrate the performance of the underlying approach, several benchmark examples for quasi-static and dynamic fracture are solved.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Bauhaus-Universität Weimar
Universidade de Lisboa
Ton Duc Thang University
Type: Article
Journal: Engineering Analysis with Boundary Elements
Volume: 133
Pages: 120-137
No. of pages: 18
ISSN: 0955-7997
Publication date: 01.12.2021
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Analysis, General Engineering, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.enganabound.2021.08.020 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{e9fb7dd6d3ef414bbee712f4904e1e5d,
title = "Quasi-static and dynamic fracture modeling by the nonlocal operator method",
abstract = "In this paper, a phase field model is developed and applied to the simulation of quasi-static and dynamic fracture using the nonlocal operator method (NOM). The phase field's nonlocal weak and associated strong forms are derived by a variational principle. The NOM requires only the definition of the energy. Its differential operators replace the shape functions in methods such as FEM which drastically simplifies the implementation. We present both a nonlocal implicit phase field model and a nonlocal explicit phase field model for fracture; the first approach is better suited for quasi-static fracture problems while the key application of the latter one is dynamic fracture. To demonstrate the performance of the underlying approach, several benchmark examples for quasi-static and dynamic fracture are solved.",
keywords = "Crack propagation, Explicit time integration, Nonlocal operator method, Nonlocal operators, Operator energy functional, Phase field method",
author = "Yongzheng Zhang and Huilong Ren and Pedro Areias and Xiaoying Zhuang and Timon Rabczuk",
note = "Funding Information: The authors acknowledge the supports provided by China Scholarship Council and NSFC ( 11772234 ). ",
year = "2021",
month = dec,
day = "1",
doi = "10.1016/j.enganabound.2021.08.020",
language = "English",
volume = "133",
pages = "120--137",
journal = "Engineering Analysis with Boundary Elements",
issn = "0955-7997",
publisher = "Elsevier Ltd.",
}