paper

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

arXiv:math/0303040

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.

34 pages