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A mesh-free multiresolution deep energy method with phase-field modeling of brittle fracture

arXiv · AI, language, vision and robotics · article · Aug 25, 2026 · UTC

Phase-field modeling of brittle fracture removes the need to track cracks explicitly by recasting their evolution as the minimization of an energy functional. In return it requires a discretization dense enough to resolve a localization band whose width is set by a regularization length and whose path is not known in advance. We propose a mesh-free discretization in which a single neural network represents the displacement and phase fields and is trained by minimizing the incremental energy directly. The coordinates enter the network through a multiresolution feature encoding built from $C^1$

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