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Existence of solutions to a regularized model of dynamic fracture
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Larsen, Christopher J., Ortner, Christoph and Süli, Endre (2010) Existence of solutions to a regularized model of dynamic fracture. Mathematical Models and Methods in Applied Sciences, Volume 20 (Number 7). pp. 1021-1048. doi:10.1142/S0218202510004520 ISSN 0218-2025.
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Official URL: http://dx.doi.org/10.1142/S0218202510004520
Abstract
Existence and convergence results are proved for a regularized model of dynamic brittle fracture based on the Ambrosio–Tortorelli approximation. We show that the sequence of solutions to the time-discrete elastodynamics, proposed by Bourdin, Larsen & Richardson as a semidiscrete numerical model for dynamic fracture, converges, as the time-step approaches zero, to a solution of the natural time-continuous elastodynamics model, and that this solution satisfies an energy balance. We emphasize that these models do not specify crack paths a priori, but predict them, including such complicated behavior as kinking, crack branching, and so forth, in any spatial dimension.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Fracture mechanics | ||||
Journal or Publication Title: | Mathematical Models and Methods in Applied Sciences | ||||
Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
ISSN: | 0218-2025 | ||||
Official Date: | July 2010 | ||||
Dates: |
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Volume: | Volume 20 | ||||
Number: | Number 7 | ||||
Page Range: | pp. 1021-1048 | ||||
DOI: | 10.1142/S0218202510004520 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 20 December 2015 | ||||
Date of first compliant Open Access: | 20 December 2015 | ||||
Funder: | National Science Foundation (U.S.) (NSF), Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | DMS-0505660 (NSF), DMS-0807825 (NSF) |
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