PSI - Issue 75

Laurent Gornet et al. / Procedia Structural Integrity 75 (2025) 129–139 Author name / Structural Integrity Procedia (2025)

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6.2. Physics-Informed Neural Networks We proposed a PINN’s model by imposing the fatigue limit in neural network. It consists of a fully connected feed-forward neural network comprising two hidden layers with 20 and 10 neurons respectively, using hyperbolic tangent activation functions. The input is the normalized value of cycles, and the output is the predicted stress amplitude S in MPa. Normalization ensures training stability and faster convergence. The figure 4 presents the fatigue Wöhler curve with the fatigue limit imposed in neural network. The code of PINN’s m odel is presented in appendix 2. To model an S-N fatigue curve using a physics-informed neural network (PINN), an architecture composed of three hidden layers with decreasing sizes (for example, 20, 15, and 10 neurons) is often effective. Using smooth activation functions such as the hyperbolic tangent (tanh) allows the model to capture the complex nonlinear relationship between stress and the number of cycles while facilitating gradient stability. This structure offers a good balance between expressiveness and simplicity, limiting overfitting while enabling the integration of important physical constraints, such as the fatigue limit or horizontal tangents at the start and end of the curve. The Python code is presented in appendix B.

Fig. 4. Fatigue tests simulation by a Physics- Informed Neural Networks (PINN’s model) on the [+45/-45/90/0] S laminate. The fatigue limit of 371 MPa obtained by the self-heating test is imposed in the PINN model. 7. Conclusion This work introduced a physics-informed neural network framework to simulate Wöhler curves by coupling a neural network with a limit of fatigue and static failure, enabling the identification of fatigue parameters from sparse experimental data while ensuring physical consistency across the entire range of lifetimes from low to high cycles. The PINN model successfully reconstructs the overall shape of the S – N response by enforcing smooth transitions between the different fatigue regimes and simultaneously fitting experimental observations, thereby combining the interpretability of classical models with the flexibility of data-driven techniques. This approach paves the way for improved characterization of fatigue behavior in composite materials under limited data conditions and opens perspectives for extensions to multiaxial fatigue, environmental effects, or probabilistic fatigue life modeling through uncertainty-aware neural architectures. The limit of fatigue obtain by the self-heating method proves to be a valuable tool for engineers and researchers aiming to rapidly assess the fatigue performance of materials, while saving both time and resources. Furthermore, the use of Physics-Informed Neural Networks (PINNs) marks a significant advancement in the modelling and prediction of fatigue Wöhler curve of composite structures. The introduction of the self-heating fatigue limit in PINN considerably reduces the time required to obtain a reliable Wöhler fatigue curve.