<p>Accurate prediction of the crack number (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:{N}_{cr}\)</EquationSource> </InlineEquation>) in fiber-reinforced cementitious composites (FRCCs) is essential because it captures how damage develops to ensure the safe design for structures made by FRCCs. Existing empirical and purely data-driven models often exhibit limited generalization capability due to heterogeneous material compositions and insufficient incorporation of fracture mechanics principles. This study proposes a physics-informed neural network (PINN) framework that integrates fracture-related physical constraints directly into the loss function to enhance prediction accuracy and robustness. A dataset comprising 268 experimental samples collected from published literature was used for model development and validation. By embedding known physical relationships during training, the proposed PINN improves generalization under limited data conditions and reduces physically inconsistent predictions. The PINN model achieves strong predictive performance (R² = 0.898 for training and 0.739 for testing). The PINN model exhibited 4.907% and 12.140% improvement in R<sup>2</sup> for training and testing datasets, respectively in comparison to the NN model. Moreover, partial dependence plot (PDP) analysis identifies fiber index, gauge length, and strain rate as the most influential parameters governing crack number of FRCCs.</p>

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Physics-informed neural network for estimating the crack number of fiber-reinforced cementitious composites at high strain rates

  • Thien Phuc Nguyen,
  • Tan Duy Phan

摘要

Accurate prediction of the crack number ( \(\:{N}_{cr}\) ) in fiber-reinforced cementitious composites (FRCCs) is essential because it captures how damage develops to ensure the safe design for structures made by FRCCs. Existing empirical and purely data-driven models often exhibit limited generalization capability due to heterogeneous material compositions and insufficient incorporation of fracture mechanics principles. This study proposes a physics-informed neural network (PINN) framework that integrates fracture-related physical constraints directly into the loss function to enhance prediction accuracy and robustness. A dataset comprising 268 experimental samples collected from published literature was used for model development and validation. By embedding known physical relationships during training, the proposed PINN improves generalization under limited data conditions and reduces physically inconsistent predictions. The PINN model achieves strong predictive performance (R² = 0.898 for training and 0.739 for testing). The PINN model exhibited 4.907% and 12.140% improvement in R2 for training and testing datasets, respectively in comparison to the NN model. Moreover, partial dependence plot (PDP) analysis identifies fiber index, gauge length, and strain rate as the most influential parameters governing crack number of FRCCs.