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Approximation of fracture problems via Gamma-convergence: state of art and new results

Banff International Research Station for Mathematical Innovation and Discovery

Fracture problems and damage processes have been widely studied in the last twenty years, starting from the pioneristic work of Griffith (and the later approach of Francfort - Marigò) to the more recent $Gamma$-convergence point of view developed by exploiting the Ambrosio - Tortorelli approximation for image recovery applied to the context of function of Bounded Deformation. In this talk we ill give a brief overview of the state of art of such a topic and we will end by presenting a recent approximation of fluid driven fracture based on a suitable correction of the classical energy with a lower order term that enable the introduction of several application. Some numerical experiments will also be discussed.

Mathematics; Calculus of variations and optimal control; optimization; Partial differential equations

video/mp4

Author affiliation: Carnegie Mellon University

2019-04-02

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69400

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/