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Abstract.

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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Correspondence to Alessandro Giacomini.

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Received: 1 January 2003, Accepted: 29 January 2004, Published online: 12 May 2004

Mathematics Subject Classification (2000):

35R35, 74R10, 35J25

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Giacomini, A. Ambrosio-Tortorelli approximation of quasi-static evolution of brittle fractures. Cal Var 22, 129–172 (2005). https://doi.org/10.1007/s00526-004-0269-6

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  • DOI: https://doi.org/10.1007/s00526-004-0269-6

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