Thermodynamically consistent machine-learned internal state variable approach for data-driven modeling of path-dependent materials

TLDR

Modeling path‑dependent behaviors of complex materials is difficult because phenomenological models struggle to formulate appropriate internal state variables, and black‑box machine‑learning models lack physics, leading to unstable generalization. This study proposes a physics‑informed, data‑driven constitutive model for path‑dependent materials that infers internal state variables from measurable material states. The model uses a recurrent neural network whose hidden states represent thermodynamically consistent internal state variables, enforces the second law, incorporates stochastic training, and examines the influence of history length, state dimension, model complexity, and strain increment. The approach successfully captures soil behavior under cyclic shear loading, as demonstrated with experimental stress‑strain data.

Abstract

Characterization and modeling of path-dependent behaviors of complex materials by phenomenological models remains challenging due to difficulties in formulating mathematical expressions and internal state variables (ISVs) governing path-dependent behaviors. Data-driven machine learning models, such as deep neural networks and recurrent neural networks (RNNs), have become viable alternatives. However, pure black-box data-driven models mapping inputs to outputs without considering the underlying physics suffer from unstable and inaccurate generalization performance. This study proposes a machine-learned physics-informed data-driven constitutive modeling approach for path-dependent materials based on the measurable material states. The proposed data-driven constitutive model is designed with the consideration of universal thermodynamics principles, where the ISVs essential to the material path-dependency are inferred automatically from the hidden state of RNNs. The RNN describing the evolution of the data-driven machine-learned ISVs follows the thermodynamics second law. To enhance the robustness and accuracy of RNN models, stochasticity is introduced to model training. The effects of the number of RNN history steps, the internal state dimension, the model complexity, and the strain increment on model performances have been investigated. The effectiveness of the proposed method is evaluated by modeling soil material behaviors under cyclic shear loading using experimental stress-strain data.