A Data-Driven Method for Modeling Creep-Fatigue Stress-Strain Behavior Using Neural ODEs

TL;DR

This paper presents a novel neural ODE-based data-driven approach for modeling creep-fatigue stress-strain behavior, outperforming traditional models and providing interpretable equations from experimental data.

Contribution

Introduces neural ODE models for creep-fatigue behavior, compares with standard models, and derives interpretable equations via symbolic regression.

Findings

Neural ODE models accurately capture experimental creep-fatigue behavior.

Models outperform the standard Chaboche model in accuracy.

Interpretable models achieve comparable accuracy to complex neural models.

Abstract

In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress-strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep-fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain-stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke's Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress-strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep-fatigue mechanical behavior, exceeding the standard Chaboche model's accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep-fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.