A Recurrent Neural Network-based Surrogate Model for History-Dependent Multi-scale Simulations

Homogenization-based multi-scale analyses are widely used to account for the effect of material heterogeneity at a structural material point. Among the existing different homogenization methods, computational homogenization solves the meso-scale heterogeneous problems using a full field discretization of the micro-structure. When embedded in a multi-scale analyses, computational homogenization results in the so-called FE2 method, which is an accurate methodology but which yields prohibitive computational time. A more efficient approach is to conduct pre-off-line finite element simulations on the meso-scale problem in order to build a surrogate model by means of constructing mapping functions. Once this so-called training step is completed, the surrogate model can be used as the constitutive law of a single-scale simulation, leading to highly efficient simulations.
Artificial neural networks (NNWs) offer the possibility to build such a mapping. However, one difficulty arises for history-dependent material behaviours, such as elasto-plasticity, since state variables are needed to account for the loading history. This difficulty can be solved by considering a Recurrent Neural Network (RNN), which uses sequential information. In [1] a RNN was designed using a Gated Recurrent Unit (GRU). In order to achieve accuracy under multi-dimensional non-proportional loading conditions, the sequential training data were obtained from finite element simulations on an elastoplastic composite RVE subjected to random loading paths. The RNN predictions were found to be in agreement with the finite elements simulations.