On tracking arbitrary crack path with complex variable meshless methods
This study presents a numerical modelling framework based on complex variable meshless methods, which can accurately and efficiently track arbitrary crack paths in two-dimensional linear elastic solids. The key novelty of this work is that the proposed meshless modelling scheme enables a direct elem...
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| Published in: | Computer methods in applied mechanics and engineering Vol. 399; p. 115402 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Amsterdam
Elsevier B.V
01.09.2022
Elsevier BV |
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| ISSN: | 0045-7825, 1879-2138 |
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| Abstract | This study presents a numerical modelling framework based on complex variable meshless methods, which can accurately and efficiently track arbitrary crack paths in two-dimensional linear elastic solids. The key novelty of this work is that the proposed meshless modelling scheme enables a direct element-free approximation for the solutions of linear elastic fracture mechanics problems. The complex variable moving least-squares approximation with a group of simple complex polynomial basis is applied to implement this meshless model, with which the fracture problems with both stationary or progressive cracks are considered and studied. The effects of choosing different definitions of weighted complex variable error norm and different forms of complex polynomial basis on the computational accuracy of crack tip fields and crack paths prediction are analysed and discussed. Five benchmark numerical examples were studied to demonstrate the superiority of the present complex variable meshless framework over a standard element-free Galerkin method in tracking arbitrary crack paths in two-dimensional elastic solids. |
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| AbstractList | This study presents a numerical modelling framework based on complex variable meshless methods, which can accurately and efficiently track arbitrary crack paths in two-dimensional linear elastic solids. The key novelty of this work is that the proposed meshless modelling scheme enables a direct element-free approximation for the solutions of linear elastic fracture mechanics problems. The complex variable moving least-squares approximation with a group of simple complex polynomial basis is applied to implement this meshless model, with which the fracture problems with both stationary or progressive cracks are considered and studied. The effects of choosing different definitions of weighted complex variable error norm and different forms of complex polynomial basis on the computational accuracy of crack tip fields and crack paths prediction are analysed and discussed. Five benchmark numerical examples were studied to demonstrate the superiority of the present complex variable meshless framework over a standard element-free Galerkin method in tracking arbitrary crack paths in two-dimensional elastic solids. |
| ArticleNumber | 115402 |
| Author | Wu, Zhangming Li, D.M. Nie, Feng-Hua Featherston, Carol A. Liu, Jia-Hui |
| Author_xml | – sequence: 1 givenname: D.M. surname: Li fullname: Li, D.M. email: dongmli2-c@my.cityu.edu.hk organization: College of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan, 430070, China – sequence: 2 givenname: Jia-Hui surname: Liu fullname: Liu, Jia-Hui organization: College of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan, 430070, China – sequence: 3 givenname: Feng-Hua surname: Nie fullname: Nie, Feng-Hua organization: College of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan, 430070, China – sequence: 4 givenname: Carol A. surname: Featherston fullname: Featherston, Carol A. organization: School of Engineering, Cardiff University, Wales, CF24 3AA, UK – sequence: 5 givenname: Zhangming orcidid: 0000-0001-7100-3282 surname: Wu fullname: Wu, Zhangming email: wuz12@cardiff.ac.uk organization: School of Engineering, Cardiff University, Wales, CF24 3AA, UK |
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| Keywords | Complex variable element-free Galerkin (CVEFG) method Stress intensity factor Complex variable moving least-squares (CVMLS) approximation Computational fracture mechanics Crack growth/propagation |
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| SubjectTerms | Approximation Complex variable element-free Galerkin (CVEFG) method Complex variable moving least-squares (CVMLS) approximation Complex variables Computational fracture mechanics Crack growth/propagation Crack tips Finite element method Fracture mechanics Galerkin method Linear elastic fracture mechanics Mathematical models Meshless methods Polynomials Stress intensity factor Tracking |
| Title | On tracking arbitrary crack path with complex variable meshless methods |
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