Robust deep learning framework for constitutive relations modeling

Modeling the full-range deformation behaviors of materials under complex loading and materials conditions is a significant challenge for constitutive relations (CRs) modeling. We propose a general encoder-decoder deep learning framework that can model high-dimensional stress-strain data and complex loading histories with robustness and universal capability. The framework employs an encoder to project high-dimensional input information (e.g., loading history, loading conditions, and materials information) to a lower-dimensional hidden space and a decoder to map the hidden representation to the stress of interest. We evaluated various encoder architectures, including gated recurrent unit (GRU), GRU with attention, temporal convolutional network (TCN), and the Transformer encoder, on two complex stress-strain datasets that were designed to include a wide range of complex loading histories and loading conditions. All architectures achieved excellent test results with an root-mean-square error (RMSE) below 1 MPa. Additionally, we analyzed the capability of the different architectures to make predictions on out-of-domain applications, with an uncertainty estimation based on deep ensembles. The proposed approach provides a robust alternative to empirical/semi-empirical models for CRs modeling, offering the potential for more accurate and efficient materials design and optimization.