Extended Minimal State Cells (EMSC): Self-Consistent Recurrent Neural Networks for Rate- and Temperature Dependent Plasticity

Abstract

Minimal State Cells (MSCs) have successfully overcome the self-consistency and state space issues of standard RNNs when modeling the large deformation response of solids. However, in case of rate- and temperature-dependent materials, MSC-based stress predictions still suffer from instabilities when refining the input path discretization. To resolve this issue, we develop an extended minimal state cell (EMSC) which provides self-consistent predictions irrespective of the type of material. Similar to the original MSC model, the EMSC decouples the number of state variables from fitting parameters, allowing a minimal number of state variables for high physical interpretability without compromising expressivity. The EMSC is trained and validated using 1D and 3D random walk datasets generated with micro-mechanical models of composites, basic rheological models, advanced thermo-visco-plasticity theories, as well as rate- and temperature-dependent von Mises, Hill’48, and Yld2000-3d models. It is demonstrated that compact EMSC models with less than 25,000 parameters and the same number of state variables as their physics-based counterparts provide accurate predictions of the large deformation response of all materials. With its minimal state space, compact parameter space, high expressivity, and computational stability, the EMSC is a promising candidate for surrogate modeling, in particular for materials for which reliable micromechanical models are available to generate rich training data.