Mechanics-informed machine learning prediction of crack path in heterogeneous materials
Mechanics-informed machine learning prediction of crack path in heterogeneous materials
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Predicting crack paths in brittle porous media with geometric or material discontinuities remains a central challenge in fracture mechanics. In this work, we present a machine learning (ML) framework trained on finite element method (FEM) simulation data to predict crack propagation in a heterogeneous medium containing a random distribution of discontinuities or defects. Our findings underscore the necessity of constructing high-quality training datasets from accurate FEM results to capture crack paths reliably. To support this, we used a special boundary condition termed as the ‘variable-stiffness boundary condition’, built on the so-called surfing boundary condition, that stabilizes crack growth even in densely distributed pores or discontinuities. The framework enables consistent data extraction for model training. This targeted dataset generation approach not only improves the relevance of the training data but also reduces the computational cost of the learning process. The trained ML model demonstrates high accuracy in predicting crack trajectories across various distributions of defects and remains robust even beyond the porosity levels used during training. These results highlight the potential of integrating ML with fracture mechanics to enable efficient and precise crack path prediction in porous media, advancing the design of next-generation composite materials.
Predicting crack paths in brittle porous media with geometric or material discontinuities remains a central challenge in fracture mechanics. In this work, we present a machine learning (ML) framework trained on finite element method (FEM) simulation data to predict crack propagation in a heterogeneous medium containing a random distribution of discontinuities or defects. Our findings underscore the necessity of constructing high-quality training datasets from accurate FEM results to capture crack paths reliably. To support this, we used a special boundary condition termed as the ‘variable-stiffness boundary condition’, built on the so-called surfing boundary condition, that stabilizes crack growth even in densely distributed pores or discontinuities. The framework enables consistent data extraction for model training. This targeted dataset generation approach not only improves the relevance of the training data but also reduces the computational cost of the learning process. The trained ML model demonstrates high accuracy in predicting crack trajectories across various distributions of defects and remains robust even beyond the porosity levels used during training. These results highlight the potential of integrating ML with fracture mechanics to enable efficient and precise crack path prediction in porous media, advancing the design of next-generation composite materials.
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Diagram of the iterative machine learning methodology for predicting crack propagation in porous media. The workflow, depicted by the flowchart on the left, begins with an initial domain containing a crack. The process involves identifying and extracting a localized sub-domain around the crack tip (top right). The machine learning (ML) model then predicts the subsequent crack path segment, a core step illustrated over two consecutive timesteps, i and i+1, to show the model's autoregressive nature (middle right). The predicted path is then integrated back into the main domain (bottom right). This iterative cycle repeats until the crack reaches the domain boundary. The dotted lines explicitly link the conceptual steps in the flowchart to their visual representations.
Predicted crack paths in a 200 x 80 porous medium at three porosity levels. (a,d) 1 % porosity, (b,e) 3 % porosity, and (c,f) 5 % porosity. The initial crack, emanating from the left edge, is indicated by a cyan strip. Pore locations are denoted by cyan square dots throughout the domain. The ML predicted crack path is illustrated in yellow, while the FE predicted crack is represented in red. The intact regions of the domain are visualized in blue.
The ML predicted crack path within a porous media featuring a 5 % porosity, captured at the 13th (a1) and 14th (a2) steps. The initial crack, emanating from the left edge, is highlighted by a cyan strip, with cyan square dots denoting pore locations across the entire domain. The ML-predicted crack path is depicted in yellow against the blue visualization of intact regions. The extracted domain, represented by a red dotted rectangle, encompassing the crack tip (depicted in gray) and adjacent pores (depicted in black), is presented both before (b1) and after (b2) the prediction, with the predicted crack path highlighted in yellow. (c1-6) The ML datasets portray pore distributions that are subsets of the extracted domain's pore distribution.
The predicted crack path (yellow line) by the trained machine learning model is compared to the actual crack path (red line). The initial crack, emanating from the left edge, is indicated by a cyan strip. Pore locations are denoted by cyan square dots throughout the domain. The intact regions of the domain are visualized in blue. Notably, the trained machine learning model, despite not having encountered this specific case previously, demonstrates accurate predictions. The model has been trained using a transformer neural network architecture, which was trained through a series of finite element method (FEM) simulations.
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