Dynamic Brittle Fracture as a Well-Posed Nonlocal Initial Value Problem

Explore a 50-minute lecture on dynamic brittle fracture presented by Robert Lipton at the Hausdorff Center for Mathematics. Delve into a nonlocal model for dynamic brittle damage, consisting of elastic and inelastic phases, where evolution depends on material strength. Examine the existence and uniqueness of displacement-failure set pairs in the initial value problem, and understand how they satisfy energy balance. Investigate the concept of nonlocality length and its relation to the domain size. Learn how the evolution interpolates between volume energy for elastic behavior and surface energy for failure. Discover how the deformation energy resulting in material failure is uniformly bounded as nonlocality approaches zero. Analyze the failure energy for flat crack surfaces and its relation to Griffith fracture energy. Understand how the nonlocal field theory recovers solutions of Naiver's equation for propagating flat traction-free cracks. Explore the implications for curved or countably rectifiable cracks and the limit deformation in SBD. Finally, examine a numerical scheme introduced and its asymptotic compatibility to the zero nonlocality limit.