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Ambrosio-Tortorelli Approximation of Quasi-Static Evolution of Brittle Fractures

Alessandro Giacomini
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Abstract

We define a notion of quasi-static 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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Alessandro Giacomini. 2003-03-04. Ambrosio-Tortorelli Approximation of Quasi-Static Evolution of Brittle Fractures. https://arxiv.org/abs/math/0303040

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