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A fast Fourier transform based method for computing the effective crack energy of a heterogeneous material on a combinatorially consistent grid

Ernesti, Felix 1; Schneider, Matti 1
1 Institut für Technische Mechanik (ITM), Karlsruher Institut für Technologie (KIT)


This work is concerned with computing the effective crack energy of periodic and random media which arises in mathematical homogenization results for the Francfort–Marigo model of brittle fracture. A previous solver based on the fast Fourier transform (FFT) led to solution fields with ringing or checkerboard artifacts and was limited in terms of the achievable accuracy. As computing the effective crack energy may be recast as a continuous maximum flow problem, we suggest using the combinatorial continuous maximum flow discretization introduced by Couprie et al. The latter is devoid of artifacts, but lacks an efficient large-scale solution method. We fill this gap and introduce a novel solver which relies upon the FFT and a doubling of the local degrees of freedom which is resolved by the alternating direction method of multipliers (ADMM). Last but not least we provide an adaptive strategy for choosing the ADMM penalty parameter, further speeding up the solution procedure. We demonstrate the salient features of the proposed approach on problems of industrial scale.

Verlagsausgabe §
DOI: 10.5445/IR/1000136993
Veröffentlicht am 08.09.2021
DOI: 10.1002/nme.6792
Zitationen: 7
Web of Science
Zitationen: 5
Zitationen: 7
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Technische Mechanik (ITM)
Publikationstyp Zeitschriftenaufsatz
Publikationsdatum 15.11.2021
Sprache Englisch
Identifikator ISSN: 0029-5981, 1097-0207
KITopen-ID: 1000136993
Erschienen in International Journal for Numerical Methods in Engineering
Verlag John Wiley and Sons
Band 112
Heft 21
Seiten 6283-6307
Vorab online veröffentlicht am 19.07.2021
Nachgewiesen in Web of Science
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