Coarse‐to‐Fine vs. Fine‐to‐Coarse Graded Media Through a Micro‐Mechanics–Based Strain‐Gradient Approach to Brittle Fracture

This paper investigates how grain‐size gradients affect dynamic fracture nucleation and propagation in brittle materials through a second‐gradient hemivariational continuum framework employing strain‐gradient regularization. The constitutive parameters, including the Mindlin coefficients and a spatially varying characteristic length representing the mean intergranular distance, are analytically derived from a granular micromechanics upscaling, so that carries a definite physical meaning rather than a purely numerical one. Damage evolution is governed by Karush–Kuhn–Tucker conditions enforcing irreversibility. A systematic campaign is conducted on compact tension specimens with Coarse‐to‐Fine and Fine‐to‐Coarse gradings, across velocities from quasi‐static to highly dynamic, complemented by mesh‐convergence and reference‐case analyses. By monitoring kink and branching angles, dynamic increase factors, reaction forces, and strain invariants, the study reveals that the grain‐size gradient direction is a primary driver of fracture stability, rate sensitivity, and crack‐path selection, governed by the microstructural transition traversed by the crack rather than the local grain size alone.