Explore the fundamentals of nonlocal theories for free crack propagation in brittle materials in this comprehensive lecture. Delve into the dynamic fracture of brittle solids, examining the connection between large and small length scales. Discover a new class of multi-scale models for solving free crack propagation problems using the peridynamic formulation. Learn about short-range forces between material points, mesoscopic dynamics, and the upscaling process to identify macroscopic dynamics. Investigate the relationship between nonlocal short-range forces and dynamic free crack evolution in brittle media. Examine physical and mathematical underpinnings of nonlocal fracture modeling, including concepts such as weak convergence, compactness, and Gamma-convergence. Explore computational modeling challenges, cohesive dynamics in peridynamic formulation, and the dependence of dynamics on horizon size. Gain insights into multiscale models, finite horizon models, and free process zone models for a comprehensive understanding of nonlocal theories in brittle material fracture. Read more