The mechanical response of history-dependent materials depends on loading paths and thermomechanical histories, rendering neural network-based constitutive modeling challenging. Existing methods typically establish global memory based on historical sequences, requiring large model scales and extensive training data. Targeting materials whose states can be fully described by finite-dimensional internal variables, this paper proposes a Local Decoupling Evolution Operator Network (LDEONet) grounded in the Markovian property. The proposed framework explicitly decomposes the internal variable evolution model into evolution direction and evolution intensity. Using the thermomechanical cycle of shape memory polymers as a case study, eight models are trained, and a series of experiments are designed, including path generalization tests, discretization generalization tests, and decoupling ablation studies. Experimental results demonstrate that the model contains 242 trainable parameters and requires only about 1/175 of the training curves compared to sequence-based models, while making predictions without needing historical memory. The model maintains accurate predictions across various unseen loading paths and unseen step sizes, and the decoupling architecture is shown to provide structural guarantees for generalization. The Local Decoupling Evolution Operator Network thus offers a lightweight modeling approach with both path generalization and discretization generalization capabilities for history-dependent materials that possess explicit internal variable models.

Chen Wang, Fengfeng Li, Dou Zhang, Hanxing Zhao, Xianyi Li, Yanju Liu, Jinsong Leng

Local evolution decoupling paradigm for neural network constitutive models of history-dependent materials Theory, architecture, and applications to shape memory polymers.pdf