Abstract:
Visco-energetic solutions have been recently advanced as a new solution concept for rate-indepen dent systems, alternative to energetic solutions/quasistatic evolutions and balanced viscosity solutions. In the
spirit of this novel concept, we revisit the analysis of the variational model proposed by Francfort and Marigo
for the quasi-static crack growth in brittle materials, in the case of antiplane shear. In this context, visco energetic solutions can be constructed by perturbing the time incremental scheme for quasistatic evolutions by
means of a viscous correction inspired by the term introduced by Almgren, Taylor, and Wang in the study of
mean curvature flows. With our main result we prove the existence of a visco-energetic solution with a given
initial crack. We also show that, if the cracks have a finite number of tips evolving smoothly on a given time
interval, visco-energetic solutions comply with Griffith’s criterion.
