Elasto-plastic multi-scale simulations accelerated by a recurrent neural network-based surrogate model

Computational homogenization embedded in a multi-scale analysis is a versatile tool also called the FE2 method. Although general and accurate, this methodology yields prohibitive computational time. In order to make the methodology affordable, a more
efficient approach is to conduct pre-off-line finite element simulations on the mesoscale
problem in order to build a synthetic data-base. The data-base can in turn be used to train a surrogate model, and once this so-called training step is completed, the surrogate model can be used as a constitutive law on a classical finite element simulation, speeding up the multi-scale process by several orders.
Artificial neural networks (NNWs) offer the possibility to serve as a surrogate model, but a difficulty arises for elasto-plasticity because of its history-dependency. This difficulty can be solved by considering a Recurrent Neural Network (RNN), which uses sequential information [1]. Nevertheless, in order to be accurate under multi-dimensional non-proportional loading conditions, a sufficiently wide data-base is required in order to perform the training. To this end, a sequential training synthetic data-base is obtained
from finite element simulations on an elasto-plastic composite RVE subjected to random loading paths. The RNN predictions are thus found to be in agreement with the FE2 simulations, while reducing the computational cost by 4 orders of magnitude.
[1] L. Wu, V.-D. Nguyen, N.G. Kilingar and L. Noels, Computer Methods in Applied
Mechanics and Engineering, 360:113234, 2020.