  In this work, we present a deep neural network architecture that can
efficiently approximate classical elasto-plastic constitutive relations. The
network is enriched with crucial physics aspects of classical
elasto-plasticity, including additive decomposition of strains into elastic and
plastic parts, and nonlinear incremental elasticity. This leads to a
Physics-Informed Neural Network (PINN) surrogate model named here as
Elasto-Plastic Neural Network (EPNN). Detailed analyses show that embedding
these physics into the architecture of the neural network facilitates a more
efficient training of the network with less training data, while also enhancing
the extrapolation capability for loading regimes outside the training data. The
architecture of EPNN is model and material-independent, i.e. it can be adapted
to a wide range of elasto-plastic material types, including geomaterials and
metals; and experimental data can potentially be directly used in training the
network. To demonstrate the robustness of the proposed architecture, we adapt
its general framework to the elasto-plastic behavior of sands. We use synthetic
data generated from material point simulations based on a relatively advanced
dilatancy-based constitutive model for granular materials to train the neural
network. The superiority of EPNN over regular neural network architectures is
explored through predicting unseen strain-controlled loading paths for sands
with different initial densities.

Machine Learning;Computational Engineering, Finance, and Science