ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE
Abstract
Visco-energetic solutions have been recently advanced as a new solution concept for rate-independent 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
