An efficient adaptive length scale insensitive phase-field model for three-dimensional fracture of solids using trilinear multi-node elements

authored by: Qiang Yue, Qiao Wang, Wei Zhou, Timon Rabczuk, Xiaoying Zhuang, Biao Liu, Xiaolin Chang
Abstract: As a diffused fracture theory, phase-field models can seamlessly simulate complex crack patterns such as extending, branching, and merging. Despite the success of phase-field models, there are two issues in previous methods of three-dimensional (3-D) fracture. Firstly, the nonlinear governing equations lead to the huge computational costs, which hinder the application of phase-field models in 3-D problems. Secondly, these models, which are mostly developed based on a simple quadratic degradation function, provide numerical solutions that are sensitive to a length scale. Hence, this work addresses an efficient adaptive phase-field model with the aid of trilinear multi-node elements. The order of the elements remains constant with the increase of the number of nodes. As the mesh size and length scale significantly influence the numerical precision, a robust adaptive criterion is established in which the element refinement is controlled by both internal length scale and phase-field. According to the criterion, an expected mesh density in the failure domain can be obtained even for nonuniform initial mesh. Besides, being able to extend the phase-field regularized cohesive zone model, the adaptive model provides length scale insensitive responses for both crack path and peak load. The failure of brittle and quasi-brittle materials in three-dimensional conditions, including simple and mixed-mode fracture, can be simulated by the proposed model. Several benchmark examples are analyzed to show the efficiency and accuracy of the trilinear element-based adaptive phase-field model (TAPFM), and the results are compared with the standard phase-field model as well as experimental data.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Wuhan University
Bauhaus-Universität Weimar
China Renewable Energy Engineering Institute
Type: Article
Journal: International Journal of Mechanical Sciences
Volume: 253
ISSN: 0020-7403
Publication date: 01.09.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Civil and Structural Engineering, General Materials Science, Condensed Matter Physics, Mechanics of Materials, Mechanical Engineering
Electronic version(s): https://doi.org/10.1016/j.ijmecsci.2023.108351 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{56a7f2956fe5435fa70638803f3b1d99,
title = "An efficient adaptive length scale insensitive phase-field model for three-dimensional fracture of solids using trilinear multi-node elements",
abstract = "As a diffused fracture theory, phase-field models can seamlessly simulate complex crack patterns such as extending, branching, and merging. Despite the success of phase-field models, there are two issues in previous methods of three-dimensional (3-D) fracture. Firstly, the nonlinear governing equations lead to the huge computational costs, which hinder the application of phase-field models in 3-D problems. Secondly, these models, which are mostly developed based on a simple quadratic degradation function, provide numerical solutions that are sensitive to a length scale. Hence, this work addresses an efficient adaptive phase-field model with the aid of trilinear multi-node elements. The order of the elements remains constant with the increase of the number of nodes. As the mesh size and length scale significantly influence the numerical precision, a robust adaptive criterion is established in which the element refinement is controlled by both internal length scale and phase-field. According to the criterion, an expected mesh density in the failure domain can be obtained even for nonuniform initial mesh. Besides, being able to extend the phase-field regularized cohesive zone model, the adaptive model provides length scale insensitive responses for both crack path and peak load. The failure of brittle and quasi-brittle materials in three-dimensional conditions, including simple and mixed-mode fracture, can be simulated by the proposed model. Several benchmark examples are analyzed to show the efficiency and accuracy of the trilinear element-based adaptive phase-field model (TAPFM), and the results are compared with the standard phase-field model as well as experimental data.",
keywords = "Adaptive strategy, Fracture, Phase-field model, Three-dimensional modelling, Trilinear multi-node elements",
author = "Qiang Yue and Qiao Wang and Wei Zhou and Timon Rabczuk and Xiaoying Zhuang and Biao Liu and Xiaolin Chang",
note = "Funding Information: Financial support for the project from the National Key R&D Program of China (No. 2022YFC3005504 ) and National Natural Science Foundation of China (No. 51979207 , No. U2040223 ) is acknowledged. ",
year = "2023",
month = sep,
day = "1",
doi = "10.1016/j.ijmecsci.2023.108351",
language = "English",
volume = "253",
journal = "International Journal of Mechanical Sciences",
issn = "0020-7403",
publisher = "Elsevier Ltd.",
}