An Eulerian constitutive model for rate-dependent inelasticity enhanced by neural networks

In the present work, neural networks are used to enhance and generalise an Eulerian formulation of inelasticity. The framework as such has been developed in previous works, and in the present work, neural networks are used to model the rate-dependence and hardening of the material. Functional forms for these material properties are then replaced by neural networks. The neural network-based model is applied to both theoretical reference data as well as actual experimental data in the form of stress–strain data. Simulated annealing is used to optimise/train the neural networks. The model was able to reproduce both the theoretical reference solutions as well as the experimental data very well. An implicit FE formulation was also provided in the form of a subroutine (UMAT) in Abaqus. The implementation was applied to two 3D examples, and the implementation seems to be robust and shows nice convergence properties. Overall, the present neural network-enhanced framework seems to be promising and there is potential for further development, such as inclusion of directional hardening and a more general neural network-based treatment of rate-dependence and material hardening.