Abstract
Critical points of a variant of the Ambrosio-Tortorelli functional, for which non-zero Dirichlet boundary conditions replace the fidelity term, are investigated. They are shown to converge to particular critical points of the corresponding variant of the Mumford-Shah functional; those exhibit many symmetries. That Dirichlet variant is the natural functional when addressing a problem of brittle fracture in an elastic material.
Original language | English (US) |
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Pages (from-to) | 576-598 |
Number of pages | 23 |
Journal | ESAIM - Control, Optimisation and Calculus of Variations |
Volume | 15 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2009 |
Keywords
- Ambrosio-Tortorelli functional
- Brittle fracture
- Critical points
- Gamma-convergence
- Mumford-Shah functional
ASJC Scopus subject areas
- Control and Systems Engineering
- Control and Optimization
- Computational Mathematics