A simple hybrid linear and nonlinear interpolation finite element for the adaptive Cracking Elements Method

The Cracking Elements Method (CEM) is a numerical tool for simulation of quasi-brittle fracture. It neither needs remeshing, nor nodal enrichment, or a complicated crack-tracking strategy. The cracking elements used in the CEM can be considered as a special type of Galerkin finite elements. A disadv...

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Published in:Finite elements in analysis and design Vol. 244; p. 104295
Main Authors: Wang, Xueya, Zhang, Yiming, Wen, Minjie, Mang, Herbert A.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.02.2025
Subjects:
Cracking Elements Method
Hanging node
Localization
Quasi-brittle fracture
Strong Discontinuity embedded Approach (SDA)
Quasi-brittle fracture
Hanging node
Cracking Elements Method
Localization
Strong Discontinuity embedded Approach (SDA)
ISSN:0168-874X
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Abstract The Cracking Elements Method (CEM) is a numerical tool for simulation of quasi-brittle fracture. It neither needs remeshing, nor nodal enrichment, or a complicated crack-tracking strategy. The cracking elements used in the CEM can be considered as a special type of Galerkin finite elements. A disadvantage of the CEM is that it uses nonlinear interpolation of the displacement field (e.g. Q8 and T6 elements for 2D problems), introducing more nodes and consequently requiring greater computing efforts than in case of elements based on linear interpolation of the displacement field. With the aim to solve this problem we propose a hybrid linear and nonlinear interpolation finite element for the adaptive CEM presented in this work. A simple strategy is proposed for treating elements with p edge nodes, where p∈0,n, with n as the edge number of the considered element. Only a few program codes are needed. Then, by just adding edge and center nodes to the elements experiencing cracking, while keeping linear interpolation of the displacement field for the elements outside the cracking domain, the number of total nodes is reduced to almost one half of the number in case of using the conventional CEM. Numerical investigations have shown that the new approach not only preserves all of the advantages of the CEM, but also results in a significantly enhanced computing efficiency. •A hybrid linear and nonlinear interpolation finite element is designed for the CEM.•A strategy (codes given) is proposed for treating elements with some edge nodes.•The number of total nodes and computing time are greatly reduced (around 50%).
AbstractList The Cracking Elements Method (CEM) is a numerical tool for simulation of quasi-brittle fracture. It neither needs remeshing, nor nodal enrichment, or a complicated crack-tracking strategy. The cracking elements used in the CEM can be considered as a special type of Galerkin finite elements. A disadvantage of the CEM is that it uses nonlinear interpolation of the displacement field (e.g. Q8 and T6 elements for 2D problems), introducing more nodes and consequently requiring greater computing efforts than in case of elements based on linear interpolation of the displacement field. With the aim to solve this problem we propose a hybrid linear and nonlinear interpolation finite element for the adaptive CEM presented in this work. A simple strategy is proposed for treating elements with p edge nodes, where p∈0,n, with n as the edge number of the considered element. Only a few program codes are needed. Then, by just adding edge and center nodes to the elements experiencing cracking, while keeping linear interpolation of the displacement field for the elements outside the cracking domain, the number of total nodes is reduced to almost one half of the number in case of using the conventional CEM. Numerical investigations have shown that the new approach not only preserves all of the advantages of the CEM, but also results in a significantly enhanced computing efficiency. •A hybrid linear and nonlinear interpolation finite element is designed for the CEM.•A strategy (codes given) is proposed for treating elements with some edge nodes.•The number of total nodes and computing time are greatly reduced (around 50%).
ArticleNumber 104295
Author Wang, Xueya
Zhang, Yiming
Wen, Minjie
Mang, Herbert A.
Author_xml – sequence: 1
  givenname: Xueya
  surname: Wang
  fullname: Wang, Xueya
  organization: Faculty of Mechanical Engineering & Mechanics, Ningbo University, Fenghua Road 818, 315211 Ningbo, Zhejiang Province, PR China
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  givenname: Yiming
  orcidid: 0000-0002-3693-8039
  surname: Zhang
  fullname: Zhang, Yiming
  email: yiming.zhang@zstu.edu.cn
  organization: School of Civil Engineering and Architecture, Zhejiang Sci-Tech University, No. 2 Street, 310018 Hangzhou, Zhejiang Province, PR China
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  givenname: Minjie
  surname: Wen
  fullname: Wen, Minjie
  organization: School of Civil Engineering and Architecture, Zhejiang Sci-Tech University, No. 2 Street, 310018 Hangzhou, Zhejiang Province, PR China
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  givenname: Herbert A.
  surname: Mang
  fullname: Mang, Herbert A.
  email: herbert.mang@tuwien.ac.at
  organization: Department of Geotechnical Engineering, Tongji University, Siping Road 1239, 200092 Shanghai, PR China
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Sat Nov 29 04:56:35 EST 2025
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Keywords Quasi-brittle fracture
Hanging node
Cracking Elements Method
Localization
Strong Discontinuity embedded Approach (SDA)
Language English
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Snippet The Cracking Elements Method (CEM) is a numerical tool for simulation of quasi-brittle fracture. It neither needs remeshing, nor nodal enrichment, or a...
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StartPage 104295
SubjectTerms Cracking Elements Method
Hanging node
Localization
Quasi-brittle fracture
Strong Discontinuity embedded Approach (SDA)
Title A simple hybrid linear and nonlinear interpolation finite element for the adaptive Cracking Elements Method
URI https://dx.doi.org/10.1016/j.finel.2024.104295
Volume 244
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