Fully Discrete Approximation Schemes for Rate-Independent Crack Propagation

Explore fully discrete approximation schemes for rate-independent crack propagation in this 41-minute conference talk from the Workshop on "Between Regularity and Defects: Variational and Geometrical Methods in Materials Science" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the convergence analysis of space-time discrete approximation schemes for modeling crack propagation in an ideally brittle elastic body. Examine the single crack propagation along a prescribed path using the Griffith fracture criterion. Learn about the evolution of cracks defined by local minimizers of total energy, following the ideas of Efendiev, Mielke, Knees, and Shcherbakov. Discover the set of discretization parameters, including mesh size, crack increment, locality parameter, and regularization parameter. Understand the sufficient conditions for these parameters to ensure convergence of discrete interpolants to parametrized balanced viscosity solutions. Gain insights from numerical experiments demonstrating the convergence properties of the approximation schemes. This talk presents collaborative work with Dorothee Knees from the University of Kassel and Andreas Schröder from the University of Salzburg.