This was part of Laplacian Growth Models

Visco-Energetic solutions to a rate-independent system for crack propagation

Riccarda Rossi, University of Brescia

Thursday, June 29, 2023

Abstract: Over the last twenty years, the mathematical analysis of the rate-independent propagation of cracks in solids has stimulated intensive research. The intrinsically variational nature of this evolutionary phenomenon has been handled with tools of Calculus of Variations, combined with refined techniques from Geometric Measure Theory. Furthermore, the nonsmooth character of the temporal evolution has led to the quest of an appropriate mathematical formulation of the process. In this talk, we are going to focus on the formulation provided by Visco-Energetic solutions, which have been recently advanced as a new solution concept for rate-independent systems. In the spirit of this novel concept, we revisit the analysis of the variational model proposed by Francfort and Marigo for crack growth in brittle materials, in the case of antiplane shear. 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.