A deep learning framework for constitutive modeling based on temporal convolutional network

Abstract

A novel and efficient deep learning framework adopting the Temporal Convolutional Network (TCN) model is proposed to simulate the ultra-long-history-dependent stress-strain constitutive model. First, the practical requirements for the constitutive models of stress-strain relationship with ultra-long-history-memory are summarized, which is favorable for adopting the TCN model in sequence modeling. The traditional Recurrent Neural Networks (RNNs) for sequence modeling are compared with the TCN model and the advantages of the TCN model for constitutive modeling are illustrated. Subsequently, the architecture of the TCN model for the constitutive modeling of steel and concrete material is illustrated in detail. In the TCN model, multiple dilated convolutional layers achieve long-term history dependence, while the causal convolution guarantees the stress is only updated based on historical strain history instead of the whole loading process. Third, a one-dimensional (1D) concrete stress-strain relationship dataset is established with significant stiffness degradation, strength degradation, and pinching effect. Two 1D reinforced concrete (RC) stress-strain datasets are established with steel content ratios of 1% and 10%. A two-dimensional (2D) low-yield-point steel dataset is also established. Fourth, the performance of the TCN model is evaluated for 1D concrete, steel, and RC datasets and 2D steel dataset. The TCN model achieves higher prediction accuracy and efficiency compared to the traditional RNN model for constitutive modeling. The influence of kernel size, hidden dimension of convolutional filter, and the number of convolutional layers on the test set performance are reported in detail. Finally, three prospective implementations of the proposed TCN model in solid mechanics are proposed, including the physics-informed machine learning, the multi-scale transfer learning framework, and the finite element force method.