Learning constitutive relations of plasticity using neural networks and full-field data

Abstract

Neural networks (NNs) have demonstrated strong capabilities of learning constitutive relations from big data. However, most NN-based constitutive models require experimental data from a considerable number of stress–strain paths that are expensive to collect. Here, we develop a hybrid finite element method - NN (FEM-NN) framework for learning the constitutive relations from full-field data. As a result, the non-uniform displacement field from a deformed sample with geometrical inhomogeneities can be used for training NNs. Such full-field data have the advantage of providing many different stress–strain paths at different locations in the sample by a single test, thereby enabling the highly efficient training of NNs. We apply FEM-NN simulations to learn the constitutive relations of several model materials characterized by rate-independent J2 plasticity. These FEM-NN studies demonstrate that the trained NNs produce the constitutive relations of plasticity with high accuracy and efficiency.