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Deep Learning-Based Phase-Field Modelling of Brittle Fracture in Anisotropic Media
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DOI：10.1002/nme.70381.png)
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Abstract
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This work presents a variational physics-informed deep learning framework for phase-field modelling of brittle crack propagation in anisotropic media. Previous variational energy-based neural network (NN) approaches have focused on second-order, isotropic phase-field fracture formulations and have relied on fully connected NNs. In contrast, the present work introduces, for the first time within a variational deep learning setting, a family of higher-order anisotropic phase-field models through a generalised crack density functional. The fracture problem is solved by minimising the governing energy functional using the deep energy method (DEM). The trial space is enriched with higher-order B-spline basis functions to represent higher-order gradients accurately and stably, thereby eliminating the need for conventional automatic differentiation. A ReZero-based residual NN architecture is adopted, for the first time in fracture mechanics. It stabilises the optimisation of the non-convex energy functional and improves convergence under strong coupling between displacement and phase fields. Random Fourier feature (RFF) enrichment is also introduced, enhancing the representation of steep displacement gradients and narrow damage zones near crack tips. The methodology is assessed for isotropic behaviour and cubic and orthotropic anisotropies. Numerical examples demonstrate direction-dependent crack growth in anisotropic cases, highlighting the capability of the method to accurately capture this behaviour.
Keywords:
anisotropy
brittle fracture
deep energy method
phase-field fracture
variational physics-informed deep learning
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