Journal
ENGINEERING FRACTURE MECHANICS
Volume 184, Issue -, Pages 307-318Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.engfracmech.2017.09.013
Keywords
Phase-field model; Fracture; Damage; Gamma convergence
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Funding
- Deutsche Forschungsgemeinschaft in the Priority Program 1748 Reliable simulation techniques in solid mechanics. Development of non-standard discretisation methods, mechanical and mathematical analysis [KA3309/3-1]
- European Research Council (ERC Advanced Grant) [664734]
- European Research Council (ERC) [664734] Funding Source: European Research Council (ERC)
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A crucial issue in phase-field models for brittle fracture is whether the functional that describes the distributed crack converges to the functional of the discrete crack when the internal length scale introduced in the distribution function goes to zero. Theoretical proofs exist for the original theory. However, for continuous media as well as for discretised media, significant errors have been reported in numerical solutions regarding the approximated crack surface, and hence for the dissipated energy. We show that for a practical setting, where the internal length scale and the spacing of the discretisation are small but finite, the observed discrepancy partially stems from the fact that numerical studies consider specimens of a finite length, and partially relates to the irreversibility introduced when casting the variational theory for brittle fracture in a damage-like format. While some form of irreversibility may be required in numerical implementations, the precise form significantly influences the accuracy and convergence towards the discrete crack. (C) 2017 Elsevier Ltd. All rights reserved.
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