Incremental Neural Controlled Differential Equations for Modeling of Path-dependent Materials

Data-driven surrogate modeling or metamodeling has emerged as a promising approach for reducing computational expenses of multiscale simulations. Recurrent Neural Network (RNN) is a common choice for modeling of path-dependent behavior. However, previous studies have shown that RNNs fail to make predictions that are consistent with perturbation in the input strain, leading to potential oscillations and lack of convergence when implemented within finite element simulations. In this work, we leverage neural differential equations which have recently emerged to model time series in a continuous manner and show their robustness in modeling elasto-plastic path-dependent material behavior. We develop a new sequential model called Incremental Neural Controlled Differential Equation (INCDE) for general time-variant dynamical systems, including path-dependent constitutive models. INCDE is formulated and analyzed in terms of stability and convergence. A surrogate model based on INCDE is subsequently trained and tested for J2 plasticity. The surrogate model is implemented for material point simulations and boundary value problems solved using the finite element method with various cyclic and monotonic loading protocols to demonstrate the robustness, consistency and accuracy of the proposed approach.