Calculus of Variations and Geometric Measure Theory

G. Dal Maso - R. Rossi - G. Savaré - R. Toader

Visco-energetic solutions for a model of crack growth in brittle materials

created by rossi on 05 May 2021
modified by dalmaso on 11 Jul 2023


Accepted Paper

Inserted: 5 may 2021
Last Updated: 11 jul 2023

Journal: Ann. Scuola Norm. Sup. Pisa Cl. Sci.
Year: 2021


Visco-energetic solutions have been recently advanced as a new solution concept for rate-independent systems, alternative to 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.