Journal
INTERNATIONAL JOURNAL OF FRACTURE
Volume 168, Issue 2, Pages 133-143Publisher
SPRINGER
DOI: 10.1007/s10704-010-9562-x
Keywords
Dynamic fracture; Phase field; Griffith's criterion; Crack regularization; Variational fracture
Categories
Funding
- National Science Foundation [DMS-0605320, DMS-0505660, DMS-0807825, DMS0714945]
- Office of Naval Research [N000140310071]
- University of California [09-LR-04-116741-BERA]
- NCSA at the University of Illinois at Urbana-Champaign
- University of Texas [TG-DMS060011N]
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We propose a discrete time model for dynamic fracture based on crack regularization. The advantages of our approach are threefold: first, our regularization of the crack set has been rigorously shown to converge to the correct sharp-interface energy Ambrosio and Tortorelli (Comm. Pure Appl. Math., 43(8): 999-1036 (1990); Boll. Un. Mat. Ital. B (7), 6(1):105-123, 1992); second, our condition for crack growth, based on Griffith's criterion, matches that of quasi-static settings Bourdin (Interfaces Free Bound 9(3): 411-430, 2007) where Griffith originally stated his criterion; third, solutions to our model converge, as the time-step tends to zero, to solutions of the correct continuous time model Larsen (Math Models Methods Appl Sci 20:1021-1048, 2010). Furthermore, in implementing this model, we naturally recover several features, such as the elastic wave speed as an upper bound on crack speed, and crack branching for sufficiently rapid boundary displacements. We conclude by comparing our approach to so-called phase-field ones. In particular, we explain why phase-field approaches are good for approximating free boundaries, but not the free discontinuity sets that model fracture.
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