In this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [S.Nicaise, A.M.Sandig - \textit{J. Math. Anal. Appl.} 2007] valid for straight fractures.
@article{arxiv.1905.02498,
title = {Energy-dissipation balance of a smooth moving crack},
author = {Maicol Caponi and Ilaria Lucardesi and Emanuele Tasso},
journal= {arXiv preprint arXiv:1905.02498},
year = {2025}
}