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. Simulation of Wöhler Curves Using Neural Networks The objective is to identify a neural network that represents experimental fatigue data (figure 1) while satisfying an underlying physical model. This approach is known as Physics-Informed Neural Networks (PINNs). Identifying the parameters and architecture of a PINN involves training the neural network on a dataset in order to accurately reproduce all experimental data within the identification domain. For PINNs associated with experimental data, an inverse analysis is performed to determine the neural network and the corresponding parameters that approximate the solution of the governing equation. To overcome the limitations of traditional empirical fatigue model, we propose a data-driven approach leveraging neural networks to learn the underlying structure of the S – N response directly from experimental data. 6.1. Classical dense neural network The goal is to approximate the S-N curve by a neural network with trainable parameters, trained to minimize the error between predicted and measured stress levels for a given number of cycles. This approach allows for smooth, continuous interpolation across fatigue regimes without requiring manually imposed transitions or fixed slopes. In contrast to classical fitting with fixed regime boundaries, the neural network autonomously learns transitions from low-cycle fatigue to high-cycle fatigue and potential plateaus (endurance limits). The figure 3 presents the fatigue wholer curve without imposing the fatigue limit in the 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.

Tab3. Neural Network parameters (Tensorflow / Keras)

Layer (type) Param # ============================================= dense (Dense) multiple 40 dense_1 (Dense) multiple 210 dense_2 (Dense) multiple 11 ============================================= Total params: 261, Trainable params: 261 Output Shape

Fig. 3. Fatigue tests simulation by a Neuronal network on the [+45/-45/90/0] S laminate. The fatigue limit 371 MPa is not respected.