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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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 399; p. 115402
Main Authors: Li, D.M., Liu, Jia-Hui, Nie, Feng-Hua, Featherston, Carol A., Wu, Zhangming
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.09.2022
Elsevier BV
Subjects:
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
Complex variable element-free Galerkin (CVEFG) method
Stress intensity factor
Complex variable moving least-squares (CVMLS) approximation
Computational fracture mechanics
Crack growth/propagation
ISSN:0045-7825, 1879-2138
Online Access:Get full text
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Summary: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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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2022.115402