Accelerating multiscale finite element simulations of history-dependent materials using a recurrent neural network

FE² multiscale simulations of history-dependent materials are accelerated by means of a recurrent neural network (RNN) surrogate for the history-dependent micro level response. We propose a simple strategy to efficiently collect stress–strain data from the micro model, and we modify the RNN model such that it resembles a nonlinear finite element analysis procedure during training. We then implement the trained RNN model in the FE² scheme and employ automatic differentiation to compute the consistent tangent. The exceptional performance of the proposed model is demonstrated through a number of academic examples using strain-softening Perzyna viscoplasticity as the nonlinear material model at the micro level.