A framework for neural network based constitutive modelling of inelastic materials

Given the significant recent advances in added layer manufacturing and materials engineering, new types of materials or new material micro-structures are becoming available at a fast rate. The finite element analysis of structures or structural components requires a constitutive model that describes the behaviour of the new materials. The formulation of accurate constitutive equations is generally complex and time consuming. Hence, suitable machine learning strategies may be used to render this process obsolete and bridge the gap between experimental data and finite element analysis. In this work, a generic stress update procedure is presented that is suitable for the modelling of rate-independent, elastic or inelastic, isotropic or anisotropic material behaviour. The proposed strategy is based on a recurrent neural network architecture and must be trained on stress and strain data sequences that represent physical or numerical experiments. A training strategy based on gradient-free optimisation is presented. It is shown that piecewise linear behaviour, such as uniaxial elasto-plasticity, can be represented exactly. Further numerical examples include uniaxial damage mechanics and elasto-plasticity under plane strain conditions. An efficient criterion for the verification of thermodynamic consistency is proposed and applied to the trained stress update models. The strategy is compared to GRU or LSTM based architectures and shown to offer advantages.