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Characterization and modeling of path-dependent behaviors of complexmaterials by phenomenological models remains challenging due to difficulties informulating mathematical expressions and internal state variables (ISVs)governing path-dependent behaviors. Data-driven machine learning models, suchas deep neural networks and recurrent neural networks (RNNs), have becomeviable alternatives. However, pure black-box data-driven models mapping inputsto outputs without considering the underlying physics suffer from unstable andinaccurate generalization performance. This study proposes a machine-learnedphysics-informed data-driven constitutive modeling approach for path-dependentmaterials based on the measurable material states. The proposed data-drivenconstitutive model is designed with the consideration of universalthermodynamics principles, where the ISVs essential to the materialpath-dependency are inferred automatically from the hidden state of RNNs. TheRNN describing the evolution of the data-driven machine-learned ISVs followsthe thermodynamics second law. To enhance the robustness and accuracy of RNNmodels, stochasticity is introduced to model training. The effects of thenumber of RNN history steps, the internal state dimension, the modelcomplexity, and the strain increment on model performances have beeninvestigated. The effectiveness of the proposed method is evaluated by modelingsoil material behaviors under cyclic shear loading using experimentalstress-strain data.

Thermodynamically Consistent Machine-Learned Internal State Variable Approach for Data-Driven Modeling of Path-Dependent Materials