An Analytical Solution for the Spatiotemporal Anomalous Cohesion Problem in Non-Local Fracture Mechanics

This paper presents a rigorous closed-form solution for the global interaction energy in a novel spatiotemporal anomalous cohesion model. By coupling a censored fractional Laplacian of order 1/2 with a local viscoelastic memory term on a bounded domain (0, l), we model the cohesive zone ahead of a moving crack tip in non-local porous media. Using a fractional bubble ansatz, we prove a universal scaling law proportional to l^(5/2). We overcome the singular domain boundary integration by utilizing the Dynkin-Getoor identity, yielding an exact topological constant of sqrt(pi)/4.