Development of a data-driven user-defined hardening model for cyclic behavior via transformer

Quantifying material response to external cyclic loading is an essential prerequisite for calculating the fatigue life of components and estimating their reliability. Conventional methods, such as experiments and physics-based simulations, used to obtain cyclic behaviour, have served us well but are time-consuming and can be expensive. In particular, the accuracy of simulations heavily relies on the accuracy of their constitutive laws and the precision with which their parameters are calibrated. An alternative approach, proposed in this research, is a deep learning-based method that efficiently predicts cyclic responses using a Transformer model with a scale factor and tailored loss function. To train the model, constant-amplitude cyclic experiments on stainless steel type 316H were conducted. Training was performed at strain ranges of 0.3% and 2.0%, and the model’s predictive performance was evaluated at an unseen strain range of 1.2%. Furthermore, a data-driven User Hardening (UHARD) model was devised, integrating the predictions of the Transformer model into a Finite Element Analysis (FEA) framework. The UHARD successfully captured the combined isotropic and kinematic hardening effects of 316H stainless steel at the 1.2% strain range, outperforming the Armstrong-Frederick model, which is a conventional approach for simulating the yield stress evolution under cyclic loading. The developed UHARD model can be used in engineering applications to predict the cyclic behaviour of engineering components with complex geometry and loading cycles. • A data-driven model captured combined hardening under cyclic loading. • The transformer-based combined hardening model predicts the cyclic behavior of 316H. • The transformer model is embedded into a FE software via a UHARD user subroutine. • The performance of the UHARD model is compared to conventional hardening models.