Journal title
Mathematical Models and Methods in Applied Sciences
DOI
10.1142/S0218202510004520
Issue
7
Volume
20
Last updated
2024-04-02T21:32:39.047+01:00
Page
1021-1048
Abstract
Existence and convergence results are proved for a regularized model of dynamic brittle fracture based on the AmbrosioTortorelli 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. © 2010 World Scientific Publishing Company.
Symplectic ID
67575
Submitted to ORA
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Publication type
Journal Article
Publication date
01 Jul 2010