Virtual element method with non-matching and adaptive meshes for phase field fracture

authored by: Bing Bing Xu, Fan Peng, Philipp Junker, Peter Wriggers
Abstract: This work presents a stabilization-free virtual element method (VEM) for phase field fracture. The distinctive feature of the virtual element method is its ability to utilize elements of general shape. However, the existence of additional stabilization term in the traditional virtual element method has some drawbacks when solving complex phase field fracture models. Different from the conventional virtual element method, the approach employed in this work eliminates the need for additional stabilization terms, making it more suitable for the phase field modeling of fracture. In this work, the anisotropic phase field fracture model is considered. In order to improve the calculation efficiency, the non-matching mesh ability of VEM and adaptive technique are employed. Since the virtual element method is automatically applicable to elements with general shape, it is easy to handle an arbitrary number of nodes and thus also hanging nodes resulting from the non-matching meshes used to adapt the meshes. Several representative benchmarks show the accuracy and efficiency of the proposed method.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Chang'an University
Type: Article
Journal: Computational mechanics
Volume: 76
Pages: 1621–1634
No. of pages: 14
ISSN: 0178-7675
Publication date: 12.2025
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-025-02665-7 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{401142a6e3374057915bd1f8c15f88de,
title = "Virtual element method with non-matching and adaptive meshes for phase field fracture",
abstract = "This work presents a stabilization-free virtual element method (VEM) for phase field fracture. The distinctive feature of the virtual element method is its ability to utilize elements of general shape. However, the existence of additional stabilization term in the traditional virtual element method has some drawbacks when solving complex phase field fracture models. Different from the conventional virtual element method, the approach employed in this work eliminates the need for additional stabilization terms, making it more suitable for the phase field modeling of fracture. In this work, the anisotropic phase field fracture model is considered. In order to improve the calculation efficiency, the non-matching mesh ability of VEM and adaptive technique are employed. Since the virtual element method is automatically applicable to elements with general shape, it is easy to handle an arbitrary number of nodes and thus also hanging nodes resulting from the non-matching meshes used to adapt the meshes. Several representative benchmarks show the accuracy and efficiency of the proposed method.",
keywords = "Adaptive technique, Non-matching mesh, Stabilization free, Virtual element method",
author = "Xu, {Bing Bing} and Fan Peng and Philipp Junker and Peter Wriggers",
note = "Publisher Copyright: {\textcopyright} The Author(s) 2025.",
year = "2025",
month = dec,
doi = "10.1007/s00466-025-02665-7",
language = "English",
volume = "76",
pages = "1621–1634",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "6",
}