  This study presents the applicability of conventional deep recurrent neural
networks (RNN) to predict path-dependent plasticity associated with material
heterogeneity and anisotropy. Although the architecture of RNN possesses
inductive biases toward information over time, it is still challenging to learn
the path-dependent material behavior as a function of the loading path
considering the change from elastic to elastoplastic regimes. Our attempt is to
develop a simple machine-learning-based model that can replicate elastoplastic
behaviors considering material heterogeneity and anisotropy. The basic
Long-Short Term Memory Unit (LSTM) is adopted for the modeling of plasticity in
the two-dimensional space by enhancing the inductive bias toward the past
information through manipulating input variables. Our results find that a
single LSTM based model can capture the J2 plasticity responses under both
monotonic and arbitrary loading paths provided the material heterogeneity. The
proposed neural network architecture is then used to model elastoplastic
responses of a two-dimensional transversely anisotropic material associated
with computational homogenization (FE2). It is also found that a single LSTM
model can be used to accurately and effectively capture the path-dependent
responses of heterogeneous and anisotropic microstructures under arbitrary
mechanical loading conditions.
