  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 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.
