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| Physics-informed neural networks coupled with hybrid phase-field modeling for rock crack propagation |
| YUE Jiahao1, WANG Guilin1, 2, 3, WANG Runqiu1, HUANG Jianming1, LIAO Mingyong1, LI Baiyi1 |
(1. School of Civil Engineering, Chongqing University, Chongqing 400045, China; 2. State Key Laboratory of Safety and Resilience of Civil Engineering in Mountain Area, Chongqing 400045, China; 3. National Joint Engineering Research Center
of Geohazards Prevention in the Reservoir Areas, Chongqing 400045, China) |
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Abstract To address the limitations of traditional fracture phase-field models—including their challenges in accurately describing tension-shear mixed-mode cracks in rock, their heavy reliance on meshes within mechanical solution frameworks, and their susceptibility to the “curse of dimensionality” in high-dimensional problems—this paper proposes a novel method that integrates Physics-Informed Neural Networks (PINNs) with a mixed-mode phase-field fracture model to simulate the tension-shear failure behavior of rock under loading. First, based on the modified fracture F-criterion, the method decomposes elastic energy into tensile and shear strain energy components through volumetric-deviatoric splitting. By combining this with the critical energy release rates for tension and shear, it derives the governing equations of the mixed-mode phase-field model for tension-shear cracks. Second, the study employs PINNs to construct an adaptive solution framework and optimizes the energy functional using the Deep Ritz Method (DRM), thereby circumventing the optimization conflicts typically associated with traditional residual-based loss functions. Validation through numerical examples—including the single-edge notched tension test, inclined crack propagation test, and parallel crack staggered propagation test—demonstrates that the calculated results align well with laboratory test data, confirming the correctness and effectiveness of the proposed method. Additionally, by varying the phase-field characteristic length, the regulatory mechanism of crack diffusion effects on fracture behavior is elucidated. This study not only provides a new theoretical framework and numerical implementation pathway for addressing rock mixed-mode failure issues but also establishes a foundation for researching real-time predictions of rock mechanical responses under varying initial conditions, including boundary conditions and material properties, by integrating PINNs with high-fidelity datasets.
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2025, Vol. 44 
