Ambrosio-Tortorelli approximation of quasi-static evolution of brittle fractures
نویسندگان
چکیده
منابع مشابه
Ambrosio-tortorelli Approximation of Quasi-static Evolution of Brittle Fractures
We define a notion of quasistatic evolution for the elliptic approximation of the Mumford-Shah functional proposed by Ambrosio and Tortorelli. Then we prove that this regular evolution converges to a quasi static growth of brittle fractures in linearly elastic bodies.
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Francfort and Marigo presented in 1998 a model for quasi-static brittle fracture which requires the minimization of the Mumford-Shah functional, representing the energy of the system. The minimization of this functional represents a very challenging issue since it is non-smooth and non-convex. The numerical approximation of this problem can be issued via a Gamma-approximation on the energy func...
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We present an extension of the classical Ambrosio-Tortorelli approximation of the Mumford-Shah approach for the segmentation of images with uncertain gray values resulting from measurement errors and noise. Our approach yields a reliable precision estimate for the segmentation result, and it allows to quantify the robustness of edges in noisy images and under gray value uncertainty. We develop ...
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ژورنال
عنوان ژورنال: Calculus of Variations
سال: 2005
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-004-0269-6