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On the path of a quasistatic crack in Mode III
We present an approach to study the path of a crack growing in a quasistatic regime in a brittle body. The propagation process is modelled by a sequence of discrete steps optimizing the elastic energy released. A detailed study of the Mode III case is presented. We obtain an explicit relationship between the optimal growing direction and the parameters defining the local elastic field around the tip. This allows to describe a simple algorithm to compute the crack configuration. A comparison with other models proposed for the same problem is provided as well.