Physics-informed neural networks for local and nonlocal modeling in continuum damage mechanics

In Continuum Damage Mechanics (CDM), numerical algorithms are widely used to predict material degradation in engineering applications. However, these methods typically require iterative computations at each time step, which creates significant challenges for complex geometries. This study presents a Physics-Informed Neural Network (PINN) model based on the Lemaitre damage model, a well-established framework in CDM, for predicting damage evolution in ductile materials. Training data for the PINN were generated from 2,000 random strain paths, with stress and damage values computed using a numerical Lemaitre model implemented in an Abaqus UMAT. The numerical model was validated with benchmark tests to ensure accuracy. The PINN architecture integrates Gated Recurrent Units (GRUs), enabling it to capture strain path dependency and history effects. Results show that the PINN closely matches the numerical solution in benchmark evaluations. Furthermore, incorporating damage growth equations into the loss function significantly improves predictions, especially for data outside the training region, and enhances physical consistency compared to standard neural networks. The application of PINNs in nonlocal damage mechanics was also investigated. A key challenge in local damage mechanics is the mesh dependency of numerical solutions, which can lead to unrealistic localization effects. While nonlocal damage models mitigate this issue by introducing a characteristic length to smooth damage field, this study demonstrates that the trained PINN, despite being trained on local data, successfully predicts nonlocal damage behavior, highlighting its potential as a data-driven tool for both local and nonlocal damage modeling.