Visco-energetic solutions for a model of crack growth in brittle materials
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.
Keywords
Cite
@article{arxiv.2105.00046,
title = {Visco-energetic solutions for a model of crack growth in brittle materials},
author = {Gianni Dal Maso and Riccarda Rossi and Giuseppe Savaré and Rodica Toader},
journal= {arXiv preprint arXiv:2105.00046},
year = {2022}
}