An extended polygonal finite element method for large deformation fracture analysis

authored by: Hai D. Huynh, Phuong Tran, Xiaoying Zhuang, Hung Nguyen-Xuan
Abstract: The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of cracks. This paper further investigates the extended finite element method (XFEM) for the simulation of large strain fracture for hyper-elastic materials, in particular rubber ones. A crucial idea is to use a polygonal mesh to represent space of the present numerical technique in advance, and then a local refinement of structured meshes at the vicinity of the discontinuities is additionally established. Due to differences in the size and type of elements at the boundaries of those two regions, hanging nodes produced in the modified mesh are considered as normal nodes in an arbitrarily polygonal element. Conforming these special elements becomes straightforward by the flexible use of basis functions over polygonal elements. Results of this study are shown through several numerical examples to prove its efficiency and accuracy through comparison with former achievements.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Vietnam National University Ho Chi Minh City
Royal Melbourne Institute of Technology University
Sejong University
Type: Article
Journal: Engineering Fracture Mechanics
Volume: 209
Pages: 344-368
No. of pages: 25
ISSN: 0013-7944
Publication date: 15.03.2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Materials Science(all), Mechanics of Materials, Mechanical Engineering
Electronic version(s): https://arxiv.org/abs/1903.05160 (Access: Open)
https://doi.org/10.1016/j.engfracmech.2019.01.024 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{f417b61e0fc24bec81496bbecbe05d9f,
title = "An extended polygonal finite element method for large deformation fracture analysis",
abstract = "The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of cracks. This paper further investigates the extended finite element method (XFEM) for the simulation of large strain fracture for hyper-elastic materials, in particular rubber ones. A crucial idea is to use a polygonal mesh to represent space of the present numerical technique in advance, and then a local refinement of structured meshes at the vicinity of the discontinuities is additionally established. Due to differences in the size and type of elements at the boundaries of those two regions, hanging nodes produced in the modified mesh are considered as normal nodes in an arbitrarily polygonal element. Conforming these special elements becomes straightforward by the flexible use of basis functions over polygonal elements. Results of this study are shown through several numerical examples to prove its efficiency and accuracy through comparison with former achievements.",
keywords = "Hanging nodes, Large fracture deformation, Level set, Polygonal elements, XFEM",
author = "Huynh, {Hai D.} and Phuong Tran and Xiaoying Zhuang and Hung Nguyen-Xuan",
note = "Funding information: This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.01-2018.32. The support provided by RISE-project BESTOFRAC (734370)–H2020 is gratefully acknowledged.",
year = "2019",
month = mar,
day = "15",
doi = "10.1016/j.engfracmech.2019.01.024",
language = "English",
volume = "209",
pages = "344--368",
journal = "Engineering Fracture Mechanics",
issn = "0013-7944",
publisher = "Elsevier BV",
}