Deep Energy Method Models Brittle Fracture Without Meshes

Traditional phase-field modeling of brittle fracture requires dense discretizations to accurately track crack evolution, which can be computationally intensive as crack paths are unknown beforehand. This paper proposes a novel mesh-free approach that leverages a single neural network to represent both displacement and phase fields, trained by directly minimizing the incremental energy. A key innovation is the use of a multiresolution feature encoding built from C1 quadratic B-spline grids, allowing the network to represent fine-scale details without slow training. The energy is estimated using stratified Monte Carlo integration with points redrawn at each optimizer iteration, which is crucial for crack advancement. The method demonstrates high accuracy across various fracture problems, matching finite element references and outperforming deep Ritz baselines in complex multi-crack scenarios.