A crack as a diffuse field
Phase-field fracture replaces a sharp surface with a continuous damage field d ∈ [0, 1]. Intact material is d = 0; a fully broken band is d = 1. A material length ℓ sets the band width. As ℓ → 0 the regularized Griffith energy converges to a discrete crack surface of energy Gc per unit area — without tracking topology or remeshing.