  Data-driven surrogate modeling 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. Surrogate models based on INCDE are
subsequently trained and tested for J2 and Drucker-Prager plasticity. The
surrogate models are 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.
