Two-Step DeepONets with Diverse Trunk Architectures for Phase-Field Brittle Fracture
Learning the phase-field brittle-fracture solution operator with a two-step DeepONet (branch net encodes varying boundary conditions / notch sizes, trunk net encodes spatial coordinates and is pre-trained separately), evaluated across three trunk variants: a data-driven MLP trunk, a physics-informed trunk that embeds the phase-field energy functional in the loss (cutting required training data), and a Kolmogorov-Arnold Network trunk. The surrogate predicts crack nucleation, propagation and branching in 1D bars and single-edge-notched specimens accurately, with error localized near the crack, at a fraction of the cost of direct phase-field simulation.
Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with
Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merg…