Article (Scientific journals)
Minimum energy multiple crack propagation. Part III: XFEM computer implementation and applications.
Sutula, Danas; Bordas, Stéphane
n.d.In Engineering Fracture Mechanics
Peer Reviewed verified by ORBi
 

Files


Full Text
main-p3-implementation.pdf
Publisher postprint (3.54 MB)
Download
Full Text Parts
highlights-p3.txt
Author preprint (1.51 kB)
Download
Annexes
XFEM_Fracture2D.zip
Publisher postprint (37.61 MB)
Request a copy
competing_cracks.zip
Publisher postprint (437.55 kB)
Request a copy
all_sources.zip
Publisher postprint (25.62 MB)
Request a copy
competing_cracks-20170807.zip
Publisher postprint (1.35 MB)
Request a copy
XFEM_Fracture2D-20170807.zip
Publisher postprint (104.83 MB)
Request a copy
efm-2017-minimum_energy-p3.zip
Publisher postprint (16.71 MB)
Request a copy

All documents in ORBilu are protected by a user license.

Send to



Details



Keywords :
Griffiths crack ; energy minimisation ; variational fracture ; stability of cracks ; competing crack growth ; stiffness derivative ; comparison of crack growth criteria ; extended finite element method ; XFEM implementation ; multiple cracks ; crack intersections ; linear elastic fracture
Abstract :
[en] The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and fracture energies, which stems directly from the Griffith's theory of cracks, is applied to the problem of arbitrary crack growth in 2D. The proposed formulation enables minimisation of the total energy of the mechanical system with respect to the crack extension directions and crack extension lengths to solve for the evolution of the mechanical system over time. The three parts focus, in turn, on (I) the theory of multiple crack growth including competing cracks, (II) the discrete solution by the extended finite element method using the minimum-energy formulation, and (III) the aspects of computer implementation within the Matlab programming language. The key contributions of Part-III of the three-part paper are as follows: (1) implementation of XFEM in Matlab with emphasis on the design of the code to enable fast and efficient computational times of fracture problems involving multiple cracks and arbitrary crack intersections, (2) verification of the minimum energy criterion and comparison with the maximum tension criterion via multiple benchmark studies, and (3) we propose a numerical improvement to the crack growth direction criterion that gives significant improvements in accuracy and convergence rates of the fracture paths, especially on coarse meshes. The comparisons of the fracture paths obtained by the maximum tension (or maximum hoop-stress) criterion and the energy minimisation approach via a multitude of numerical case studies show that both criteria converge to virtually the same fracture solutions albeit from opposite directions. In other words, it is found that the converged fracture path lies in between those obtained by each criterion on coarser meshes. Thus, a modified crack growth direction criterion is proposed that assumes the average direction of the directions obtained by the maximum tension and the minimum energy criteria. The numerical results show significant improvements in accuracy (especially on coarse discretisations) and convergence rates of the fracture paths. Finally, the open-source Matlab code, documentation, benchmarks and example cases are included as supplementary material.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Sutula, Danas ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Bordas, Stéphane ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
External co-authors :
no
Language :
English
Title :
Minimum energy multiple crack propagation. Part III: XFEM computer implementation and applications.
Publication date :
n.d.
Journal title :
Engineering Fracture Mechanics
ISSN :
0013-7944
eISSN :
1873-7315
Publisher :
Pergamon Press - An Imprint of Elsevier Science
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
Available on ORBilu :
since 06 April 2017

Statistics


Number of views
2110 (148 by Unilu)
Number of downloads
575 (3 by Unilu)

Scopus citations®
 
77
Scopus citations®
without self-citations
70
OpenCitations
 
61
WoS citations
 
71

Bibliography


Similar publications



Contact ORBilu